No, energy is not always conserved

Energy conservation: what is at stake

The law of conservation of energy comes up from time to time in the science and faith debate. In various ways. Let me just bring up 2.

  • Some will invoke it to argue that the universe must be eternal, since if there is energy in it, and if this energy is conserved, then it has always been there. Indeed, if I have 1 Joule (unit of energy) in my pocket and if this Joule is indestructible, then it must have been there always. Logical, isn’t?
  • Others want a universe with a supernatural beginning, which would be a proof of the existence of God. They will therefore claim that if the Big Bang was the beginning [1], then it could not have been natural. Otherwise, the energy the universe contains today would have suddenly pop up at the Big Bang, violating the conservation of energy. Therefore, the beginning must have been supernatural. Logical, isn’t?

The problem is that the law of conservation of energy, sometimes called “the first law of thermodynamics”, does not always hold.

Picture a photon undergoing redshift as it travels through space. Its wavelength goes down, together with its energy. Question: where does this energy goes? Answer: nowhere. It is lost. Let’s see what happens.

Energy conservation: when it fails

What I am about to tell is not revolutionary at all. It’s about 200 years old. If it’s surprising, it’s simply because it takes a few years of college to hear about it. If doubt persists, you can always watch Leonard Susskind, Stanford big shot, telling the exact same thing to his students.

All known laws of physics have their limits. That is, circumstances where they will stop making predictions that fit reality. Fluid mechanics doesn’t like it when it’s too small. Newton’s laws don’t like it when it’s too fast or too small. Etc.

And the law of conservation of energy, what is its limit? Well, energy conservation doesn’t like change. What does it mean? Simply put, it means that if an experiment done yesterday gives the same result as if done today, then energy is conserved [2]. It’s called “time invariance”.

So yes, energy conservation relies on an assumption, too.

Obviously, the time invariance assumption is almost always met. Your cellphone, 24/7 experiment, works the same today than a month ago. Yet there is an “almost”. To understand it, we just have to imagine a situation, or a time, where doing an experiment yesterday cannot give the same result than today.

An example? The moments that followed the Big Bang, precisely. At this time, the universe is expanding rapidly. Try to reproduce today an experiment made yesterday, when all the dimensions of your lab are doubling every day! If space itself does not hold in place, goodbye time invariance… and goodbye energy conservation. If energy is conserved in the experiments conducted nowadays, it is because on their scale, the expansion of the universe, which indeed keeps on going, is completely undetectable [3].

The law of energy conservation is capricious. I’m afraid it slips away when some need it most.


[1] I won’t even discuss the fact that the Big Bang may not have been the beginning.

[2] Less simply put, it means that if the Lagrangian of your system does not explicitly depend on time, then energy is conserved. On this topic, and many others, I strongly recommend the discovery of the marvelous Noether’s theorem.

[3] And in fact, inexistent, as proved by Einstein and Strauss in 1945.

A collapse is possible

Translated from “Un colapso es posible”, published in the Spanish journal Acontecimiento n. 138, 2021, pp. 10-12.

I don’t know what André Malraux meant by “The 21st century will be spiritual, or it won’t be”. What I do think is that the 21st century could be the one of the collapse of our civilization, which of course does not prevent it from being spiritual.

I am used to explaining this in a four-months college course. Summarizing it in some 1000+ words without looking like a lunatic announcer of the apocalypse, is an interesting challenge. I will be as synthetic as possible, perhaps to the detriment of style.

What is the problem?

80% of the world’s energy comes from fossil fuels (oil, gas, coal). A stable percentage for decades. When we burn them, these fuels emit greenhouse gases like carbon dioxide (CO2). In the atmosphere, they act like a blanket: they heat up. As a result, the global temperature has increased by about 1 degree (Celsius) in the last 100 years. Under a business-as-usual scenario, it could increase 2 or 3 degrees more during the 21st century. Minus 4, it’s an ice age. So plus 2 or 3 would mean a planet where billions of people would just have a hard time to live. The challenge of the 21st century is to bring this 80% of fossil fuels down to 0% in the next 50 years.

Why is it very difficult to solve?

Clothes, food, computer, car, chair, desk… everything I use requires energy for its production, its transport, its operation. The heart of our civilization beats with oil, gas, coal… and their emissions. According to the International Energy Agency, they fell 5.8% in 2020, due to COVID-19. And we all saw what it cost. Well, achieving zero emissions in 50 years means such a reduction every year, for the next 5 decades. Here are a few reasons why achieving this is a considerable challenge.

  • Replacing fossil fuels with “green” sources is not easy, even materially. To supply the world’s energy consumption, it would be necessary to cover two Spains with solar panels. Or fill up twenty Spains with wind turbines. This is why we started with fossil fuels. They are more practical. The other sources are much less so, be it for the room they require. We did what children do when they eat: starting with the cool dishes. Broccoli always come last.
  • If there is too much CO2 in the atmosphere, why not extract it? There is a technology that achieves just that from solar energy. It is called a tree. How many do we need? A forest as large as Spain contains around 1 year of global CO2 emissions. So, to suck up a year of global emissions, you need to plant 1 Spain of trees, and of course wait for it to grow. Since it’ll take a few decades to do so, it will take just as long to absorb your single year of emissions.
  • The energy transition has only just begun. Worldwide, sources such as solar, wind or geothermal, generate less than 2% of production.
  • Clean energy production is growing. But production from fossil sources has grown 4 times more since 2000. The world is like a patient on diet who eats 100 more grams of vegetables… and 400 more grams of Nutella.
  • Speaking of diet, I wish there were few fossil fuels left. Thus, we would be obliged to reduce their exploitation. But no. There is a lot of coal left, for example. Regarding its need to cut fossil fuels, the world is like a patient who must go on a diet in a delicatessen.
  • When looking at how global energy consumption is shared, a bad surprise comes up. There is no dominant activity. Hopefully, for example, transport used 80% of our energy. We would then know that we can cut emissions by 80% by decarbonizing transportation. But no. Transportation represents only 14%. In other words: if all the planes, cars, trucks, motorcycles in the world turned green tomorrow, we would only gain 14% of emissions. The whole industry set green? Minus 21%. All green electricity production? Minus 25%. All buildings energetically carbon neutral? Minus 7%. There is no public enemy number 1. There are several.
  • An energy transition takes about 50 years, even when stimulated by the market.
  • It is not the western countries that are raising emissions. These ones have not increased in the last 30 years. It is the developing countries that push emissions up. An Indian, for example, uses 4 times less energy than a Spaniard. But he/she wants to reach the Spaniard’ standard of living. And achieving it is a matter of energy, that is, for now, a matter of emissions.
  • Some climate science to finish. So far, we were in the “easy” part. Even Exxon got it right… in 1982. More CO2, more temperature, and that’s it. We are now entering a climate zone where anything can happen. For example, the permafrost, the permanently frozen layer of soil in northern Russia or Canada, is thawing. Doing so, it releases methane, another greenhouse gas. These emissions then generate more warming, which in turn generates more thawing, generating more emissions, etc. Passed a certain threshold of heating, the vicious circle can be activated. If that happens, permafrost emissions will skyrocket, regardless of what we’re doing, until it has released all the methane it contains. Now, eight more vicious circles have been identified. They are interconnected, so that triggering one can trigger others. Their activation thresholds are difficult to pin down, but several scientists believe that we are getting closer.

So, “Foutu pour foutu?” [1]

This doesn’t look good. In fact, one just has to read authors like Joseph Tainter or Jared Diamond to see that the collapse of a civilization has nothing exceptional historically.

Some say that if Spain were to bring its emissions down to 0 tomorrow, the world’s emissions would drop by only 0.6%. They are right. The possibility then arises to conclude, “Why should I do anything at all if everything depends on the Chinese or the Indians? “Foutu pour Foutu”, give me my SUV!”.

Although I understand such an attitude, I think it is deeply flawed. It loses sight of the fact that global warming is only a symptom. A symptom of a deeply unethical attitude towards nature.

Nobody, when looking at a forest, thinks, “I would cut this all and put a huge parking there”, or when discovering a seabed, “I wish there were plastic bags here” [2]. However, this is what humanity has been doing for millennia in its understandable desire to live better and better; that’s why the problem is complicated.

Global warming is only a symptom of a deeper evil: the use and abuse of the earth as if it were a tissue. When we were 100 million, it was not so perceptible. With almost 80 times more people, the consequences are catching up with us.

“Foutu pour Foutu”, give me my SUV! “, comes to say that I can be a jerk on the Titanic. Quite the opposite. It is about deciding to be an angel, even on the Titanic, regardless of the consequences, in the same way that no one says “I love you” to a loved one to put an end to the Israeli-Palestinian conflict.

What’s that you say? Hopeless? -Why, very well!-
But a man does not fight merely to win!
No-no-better to know one fights in vain!

Edmond Rostand, Cyrano de Bergerac, Act 5, Scene 6


[1] “Foutu pour foutu” is a colloquial French expression. It means something like “ruined for ruined.” It is also the title of a remarkable documentary made by 2 young French people that can be viewed for free here (in French).

[2] There are plastic debris in the deepest trench in the world, the Mariana trench. Human footprint in the abyss: 30 year records of deep-sea plastic debris, Marine Policy, 96, 204, 2018.

Science always questions itself? Well, no.

  • Do you think the sun might not rise tomorrow?
  • Do you think your GPS might not work tomorrow because of a change in the laws of nature (and not because of a breakdown) ?
  • Do you shun surgery for fear that the laws of physics that govern the electronic devices in the operating room, might change during it?
  • Do you avoid airplanes only for fear that the laws of fluid mechanics may change during the flight?

If you answered “no” four times, then you trust the laws of nature enough to entrust your life to them. So do I. And so do all the people I know.

Indeed, the sun will rise tomorrow “because” of Newton’s laws (conservation of angular momentum). The same Newton’s laws dictate the equations of fluid mechanics ruling the flight of your airplane, and in the absence of damage here or there in a satellite, your GPS will keep guiding guide you tomorrow if electromagnetism, quantum mechanics and general relativity are still the same.

What do we mean then when we say “science always questions itself”?

It seems to me that we are eventually only talking about scientific issues that are not yet solved. We are certainly far from the last word on the mysteries of dark matter, dark energy, the origin of the universe, high temperature superconductivity, quantum gravity, etc. So many areas where, for sure, “science can completely question itself”. For example, it is quite possible that in 100 years we will no longer talk about dark matter. Here is, for example a list of more than 2,000 articles that mention an alternative.

As for electromagnetism, quantum mechanics or general relativity, it is precisely because science no longer questions them within their respective range of validity (the nuance is paramount), that industry seized them to make technological toys… that we would not buy if their operating principles could be “questioned”!

Can you imagine buying a device with a sticker on the box that would say “Warning, for unknown reasons, this device may not work tomorrow”? Me neither… Seems we both admit “settled science ” definitely exists.

So, “science always questions itself”? No, not necessarily. For the contrary, read Barjavel.

Scientist and believer (3): does science contradict the book of Genesis?

In two recent articles I identified 3 reasons why some are surprised that a scientist can be a believer:

  1. Scientists are people who only believe what they can see and touch. So they are people who can’t have faith.
  2. Science explains a lot of things. We don’t need God to explain them.
  3. Science contradicts the book of Genesis.

After addressing the first reason, then the second, I finally come to the third: Does science contradict the Genesis account? If indeed we consider that the account of Genesis is historical, that it describes events that really unfolded in the literal sequence and on the timescale it tells, the clash with, to name a few, cosmology, geology, biology, paleontology, glaciology, so many fields which are not the monopoly of abominable atheists, is inevitable.

Let’s see this.

Is Genesis history?

I became a Christian in 1993 while studying for my PhD in physics. The compatibility between science and Genesis has never been a problem for me. Why? Simply because from the start it seemed obvious to me that Genesis was not a book of history or science. I never felt compelled to consider historical, real, days and plants before the creation of the Sun, a tree of life and another one of the knowledge of good and evil, a man who gives names to all the livestock, the birds in the sky and all the wild animals in a single 24 hours day (Gen 2.20), a God walking in his garden in the cool of the day (Gen 3.8) and who would have made trees that were pleasing to the eye (Gen 2.9)… for blind beings, since the eyes of Adam and Eve would not be opened until later (Gen 3.7), if the text is to be taken literally.

For me, making this story stick to the findings of science was like wondering about the Zip code of the Good Samaritan. The important is not there.

The Church I was a member of did not teach this reading and it was not until some 15 years later that I learned to my surprise that some Christians considered the first chapters of Genesis as historical.

What about the original sin?

Shortly after learning that some Christians had adopted a historical reading of Genesis, I learned that many of them had done so because, among other things, of the doctrine of the original sin. The idea being, for example, that, quoted from here, “We would actually agree with the atheist that evolution, if true, would disprove the need for a savior”, or alternatively, as the title of this article sums it up very directly, “No Adam, No Original Sin, No Christ”. The subject is vast, and I invite the curious reader to consult this document which lists the position of 86 theologians on the historicity of Adam and Eve. The question of the original sin comes up often.

As I said before, the idea of ​​an historical reading of Genesis surprised me. Well, this original sin story surprised me as well. Indeed, the Church I was a member of did not teach this doctrine either and I thought it was the prerogative of Catholicism. Although I often disagreed with the Church of my Christian childhood (I left it in 2003), I do not deny its silence on the original sin. I still find that the expression “original sin” does not appear anywhere in the Bible (neither does turbocharge, I know), that this doctrine did not really take hold, I believe, until Augustine, that the Pauline passages which support it are far from being the clearest in the Bible, that verses like Ezekiel 18.19-20 clearly teach kids do not inherit the sins of their parents, and above all, that Jesus never spoke of any “original sin”. On the other hand, he clearly spoke of dying for our sins. And these were, and unfortunately still are, perfectly tangible.

Under influence?

Some could argue that a non-historical reading of Genesis is ultimately dictated by the “spirit of the age”. That if a twenty or twenty-first century reader does not take Genesis literally, it is precisely because he was told from kindergarten that the world is billion years old. In other words, the modern reader would succumb, consciously or not, to the pressure of modern science.

I don’t think the argument is valid, for the simple reason that the “non-literal” reading is nothing new.

Many ancient writers did not think, for example, that all the “days” of Genesis were literally 24 hours long. These include Justin Martyr (100-165), Irenaeus (130-202), Cyprian (200-258) or Victorinus of Pettau (250-304) [1].

Did they think the world was billion years old? Probably not. In the same way, they probably did not think the earth turns around the sun [2]. Did other early writers think the days of Genesis were literal 24 hours days? Yes of course. But as we can see, the “literal” reading of Genesis was not universally shared, even from the very first centuries of our era.


I really don’t think that science and Genesis are opposed for the simple reason that I don’t think Genesis is a book of history or science. In addition, the insistence on an historical Genesis raises another problem: if the universe is about 6,000 years old, as one can deduct from a “literal” reading, how is it that it absolutely does not look so [3]? That its apparent age goes in billions of years instead of thousands? Is God deceiving us?

I have already quoted some ancient authors. It is to yet another one that I leave the last word: Origen of Alexandria, early “Church Father” astride the second and third centuries, already wrote some 1,800 years ago,

“For who that has understanding will suppose that the first, and second, and third day, and the evening and the morning, existed without a Sun, and Moon, and stars? And that the first day was, as it were, also without a sky?
And who is so foolish as to suppose that God, after the manner of a husbandman, planted a paradise in Eden, towards the east, and placed in it a tree of life, visible and palpable, so that one tasting of the fruit by the bodily teeth obtained life?
And again, that one was a partaker of good and evil by masticating what was taken from the tree? And if God is said to walk in the paradise in the evening, and Adam to hide himself under a tree, I do not suppose that anyone doubts that these things figuratively indicate certain mysteries, the history having taken place in appearance, and not literally.”

Origen, De Principiis 4:16, 3rd century AD


[1] More, with references, here, or in David Bercot, A Dictionary of Early Christian Beliefs, Hendrickson 1998, p. 189.

[2] Geocentrism was unanimous until Copernicus. I got this from my friend Pablo de Felipe who is finishing a PhD thesis on a related topic.

[3] Recall that in view of the observations, there’s no debate on this since, at the very, very least, 100 years.

Scientist and believer (2): if it’s explained, it’s not God?

In a recent article I listed 3 reasons why some people seem surprised that a scientist can be a believer. Here they are,

  1. Scientists are people who only believe what they can see and touch. So they are people who can’t have faith.
  2. Science explains a lot of things. We don’t need God to explain them.
  3. Science contradicts the book of Genesis.

The first article discussed the first reason. I will here address the second one, well summarized by Physics Nobel Prize Steven Weinberg [1],

As science explains more and more, there is less and less need for religious explanations.

Let’s see this.

It’s not from the Bible …

When I started to read the Bible seriously in 1993, during my PhD in physics, I quickly realized that Steven Weinberg’s idea of ​​God was not from the Bible. Of course, the Bible talks about miracles without naturalistic explanation, like the resurrection of Jesus. But it also talks about perfectly explainable facts, which it attributes at the same time… to God. Some examples:

  • In Genesis 45.5, Joseph tells his brothers, “it was to save lives that God sent me ahead of you” (NIV). Did an angel parachute him into Egypt? Not at all. On the contrary, the text goes on great lengths to describe, from chapter 37, the chain of events that led him to utter these words.
  • Exodus 1.1-13 recounts in detail the events that led the Egyptians to enslave the Israelites. Sounds like sociology. Oddly enough, Psalm 105.25 provides another perspective, “he [God] turned the Egyptians against the Israelites, and they plotted against the Lord’s servants” (NLT). Here again the Bible explicitly attributes an event to God, while at the same time explaining in detail how it came about.
  • In Psalm 71.6, the psalmist declares “you [God] brought me forth from my mother’s womb” (NIV). Did he miraculously gush out, like suddenly materializing out of his mother’s womb? Of course not. His birth probably required the help of a midwife, whose existence no one would deny on the pretext that the Bible says that it was God who brought the psalmist out of the womb.
  • Let us finish this far from exhaustive inventory with Acts 14.17, “he [God] did good, and gave us rain from heaven, and fruitful seasons” (KJV). Here again, neither the rain nor the seasons are miraculous phenomena (I can hear some: “not miraculous for us, but for them?”. I’ll come back to it).

… nor from Jesus

So it seems to me that the Bible does not teach that “if it is explained, it is not God”. Jesus does not teach it either, as these passages from the Sermon on the Mount show, among others,

  • Matthew 5.45 “[God] causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous” (NIV). Yet, neither the sunrise nor the sunset nor the rain are supernatural phenomena.
  • Matthew 6.26 “Look at the birds of the air; they do not sow or reap or store away in barns, and yet your heavenly Father feeds them” (NIV). So it is God who feeds the birds of the air, while Jesus knew very well how they fed. Who would deny the existence of earthworms that birds eat under the pretext that the Bible says that it is God who feeds them?
  • Matthew 6.30 “God clothes the grass of the field” (NIV). However complex may the growth of a plant be, it is not miraculous.

One might object that the authors of the Bible did not know the mechanism of the seasons, for example. Granted. But they were certainly familiar with the course of childbirth or the feeding of a bird. Likewise, the enslavement of Israel narrated in Exodus 1 does appeal to motives that the author fully understood. These people did not only attribute to God phenomena that they did not understand. They also attributed to God phenomena that they understood very well.

So, this idea that God only fits where we don’t know what’s going on, the famous “God of the gaps”, does not come from the Bible. If denying God’s existence was just a matter of explaining something the Bible attributes to God, a bird’s breakfast would suffice.

I’ll leave the last words to wiser than me,

Weizsäcker’s book The World-View of Physics is still keeping me very busy. It has again brought home to me quite clearly how wrong it is to use God as a stop-gap for the incompleteness of our knowledge. If in fact the frontiers of knowledge are being pushed further and further back (and that is bound to be the case), then God is being pushed back with them, and is therefore continually in retreat. We are to find God in what we know, not in what we don’t know; God wants us to realize his presence, not in unsolved problems but in those that are solved. Dietrich Bonhoeffer [2].


Either God is in the whole of Nature, with no gaps, or He’s not there at all. Charles Coulson [3].


For in him we live and move and have our being. Acts 17.28



[1] Steven Weinberg, Newsweek, 23 mars 2008.

[2] Dietrich Bonhoeffer, Letters and Papers from Prison, letter to Eberhard Bethge, may 29, 1944.

[3] Charles Alfred Coulson, Science and Christian Belief, Oxford University Press, 1955, p. 22.

Scientist and believer (1) : Only believe what I see ?

More than a year ago, it was before the COVID, I found myself on a panel answering questions of the teens in my church. As the scientist on duty, I answered: “How can one be a scientist and a believer?”

When the evening was over, I asked her feedback to my youngest daughter who had attended. She answered straightforwardly, “Daddy, I didn’t understand anything to your answer”. That’s how I came to realize that there are a lot of reasons why people are surprised that a scientist can be a believer. I had answered the “wrong reason”. Having conducted my little investigation, I found at least three [1],

  1. Scientists are people who only believe what they can see and touch. So they are people who can’t have faith.
  2. Science explains a lot of things. We don’t need God to explain them.
  3. Science contradicts the book of Genesis.

I will shortly comment on the last 2 reasons. For now, I will rather dwell on the first one. I will do so through two anecdotes that, in my opinion, show that scientists are much more flexible than people think.

I will talk about marriage and Laurent Schwartz.


What is marriage doing here? It’s pretty simple: when I married Isabel almost 25 years ago, my intention was to be united with her for life. When I saw her walking down the aisle, I didn’t think “well, let’s give it a try one or two years, and see what happens. After all, nothing is certain”. All the contrary, the idea was to finish my life with her.

Now, in this day of November 1996, what proved me with 100% certainty that we would stay together for ever and ever? Nothing. Of course, a bundle of clues gave me enough confidence to decide to marry her. But no time traveler had come from 2050 to certify “no problem, the future is clean: you end up together for better or for worse. Go ahead!”. In short, I had “faith” that it would work [2].

I’m not the only married scientist, and I hope the others didn’t get married wondering whether the warranty was 1 or 2 years. I then take it that a large number of scientists made at least once in their life a very important decision based on some kind of faith.

Laurent Schwartz

What is Laurent Schwartz doing in here? Laurent Schwartz was one of the top mathematicians of the last century, recipient of the Fields Medal in 1950. In his memoirs, he shared a remarkable anecdote. Rather than paraphrase him, I prefer to leave him the floor [3],

The great mathematician Boussinesq lost his wife. The day of the funeral started out quite beautiful,  but ended under a rainstorm. Everyone was soaked. Boussinesq married again, but again became a widower. The same meteorological phenomenon occurred during the second burial. When his third wife also died, the funeral took place under a beautiful blue sky, but everyone there brought an umbrella.

Let’s take a break. What were these people doing with an umbrella under a beautiful blue sky? What does the weather have to do with the burial of the third wife of poor Boussinesq ? Nothing. However, Schwartz is very clear: everyone [4] there brought an umbrella. As the rest of the quote shows, some, like us, were surprised,

Emile Borel, the grand guru of probability theory at the Sorbonne, turned to Polya, a foreign mathematician who happened to be visiting France just then, and said “Look, Polya, isn’t this ridiculous? We’re all university professors, I’m a probabilist, I know perfectly well that there is no relation at all between the weather and the funeral of Madame Boussinesq. Yet, I brought my umbrella.” “Well,” replied Polya, “we’re scientists, we work on observed facts. And it’s a scientifically observed fact that it often rains at the funeral of Madame Boussinesq.” [5]

Make no mistake. We are here in the presence of world class mathematicians. A Google search will quickly show the influence Emile Borel and Georges Polya had on the mathematics of their time. Yet, Borel, honest man as well as rigorous mathematician, laments to see that everyone at the funeral gave way to a kind of “superstition”, that the final joke of Polya highlights even more. 

So, do scientists only believe what they can see and touch? Seems not. It is perhaps one reason why those who excel in science, excel. But that’s another story.



[1] If you know of others that are fundamentally different, I’m interested.

[2] The fact that it works for now, doesn’t change anything. The idea is that this very important decision could not, in 1996, be taken 100% by sight.

[3] Laurent Schwartz, A Mathematician Grappling with His Century, Birkhäuser, 2001, p. 144.

[4] Noteworthily, the original, French version, doesn’t say “everyone”. It rather says, “all academics”.

[5] In the French version, Schwartz added after the quoted passages: “This story circulated some time and then fell into oblivion, because most of his protagonists were gone. Polya, whom I met in the United States in 1960, was probably the last witness to this case. I was curious if my memories were faithful and I begged him to confirm it, which he did. I am now the last custodian of this story that I am delivering to the public.”

Is my science champion really a champion?

Suppose I tell you my neighbor’s son is one of the best soccer player in the world. How would you check? You would immediately Google him to see in which team, in which league, the prodigy plays. If you couldn’t find anything, you would be wondering. Who is this world-class player Google doesn’t know (just try with Messi or Cristiano Ronaldo)? In the same vein, if you found him playing for the Miguelturra team in Spain, you would equally wonder. Who is this alleged best player in the world who plays in Spain, granted, but not in Madrid or Barça, but in the CD Migueltureño, a third division team ?

 The universe Science and Faith is full of names supposed to represent “great” scientists. Obviously, the more the scientist says what I think, the “greater” he is. How can you check? How can you know if such and such, presented as great scientists, really are?      

Just see if they play in first league, in the NBA. For physics, astrophysics, climate science (see the blue section below for climate science), here’s how.

The “astrophysics data system” database

Scientists write articles to explain their work. In these articles, they cite the articles upon which they rely. When I was a PhD student at Orsay University (France) in the early 90s, I would go to the library every week to read the journals publishing articles related to my research. Nature, Science, Physical Review, Physics of Fluids, etc. It was very common for one article to cite another, which cited another, which cited another, which made me navigate from journals to journals. Quickly, I would realize that a given author was often cited for having written one or more influential articles.

I now make this weekly pilgrimage from my computer. In the 90s, when the internet took off [1], databases were organized to index all this information. One of them is the astrophysics data system (“ADS”). Run by NASA and the Harvard–Smithsonian Center for Astrophysics, it indexes nearly 15 million articles in math, physics and astrophysics, some of which date back to the 16th century [2]. There are other databases, but this one has the advantage of being free and powerful. Let me emphasize that it only indexes journals dealing with physics, math or astro. So if you query it about one of the last Nobel Prize winners in medicine, it will only give you what he published in multidisciplinary journals like Nature or Science. Not his complete works.

For each scientific article, ADS indexes the authors, their academic affiliation, the list of all other articles that cite it, etc. Thanks to ADS, a bibliographic search which took 1 week during my PhD thesis is now done in a few minutes. Starting from the name of a scientist, you can easily check,

  1. If your scientist is currently active, that is to say if his last article dates from 2020 or goes back to 1980.
  2. If his work has an impact, that is, if it is often cited because it sparked further research.

All the “big ones” satisfy the second criterion. By definition, all the “big ones” currently active satisfy the first as well.    

How does it work?

When you get to the main page, you find this,



Let’s just ask for the articles of a so-called “Einstein, A”. By clicking on the white magnifying glass on the blue background on the right, or by typing “Enter” on my keyboard, I get this,

As you can see, you have to filter a little more because there is at this very moment at least one other “Einstein, A” in activity, which is obviously not our Albert. I will therefore filter the results to retain only the articles published between 1901 and 1955, the date of his death. I therefore replace 2019 with 1955 in the red enclosed area at the bottom right and press “Apply”. I get this,


The search box now contains the weird formula I could have typed directly to get there. The area I mark in red indicates his co-authors. Insiders will recognize Rosen and Infeld, but we also discover Laub and de Haas. The green area tells that the database contains 155 articles in peer-reviewed journals (“refereed”), and 49 elsewhere. As we can see, with 204 works in 53 years (1901-1954), Einstein was remarkably productive.   

But this is not the most important. One can very well publish 204 articles without any impact. This is not the case with Einstein. To see this, let’s click on the menu circled in orange where we see “Date”, and choose “Citation Count” instead. We get that,

Where there was “Date” before, there is now “Citation Count” (marked in orange). Here ADS tells us that Einstein has been cited almost 20,000 times (in red). In case you are wondering, yes, that’s a lot. Articles are now ordered by number of citations received, not by date. The first one has been cited 7,231 times (in green) so far, which is huge. I cannot resist the pleasure of pointing out that this article is false. It is that of the famous EPR paradox. But so it is with brilliant people: they are interesting even when they are wrong [3].

I urge you to play around with the database a bit. I have only commented on a few of its options. But you can filter by journal, co-authors, academic affiliation, etc. It is quite intuitive.

A few comments

A few remarks now. Each time I quote a scientist, it suffices to click on his/her name to see the record in the ADS database.

  • Anglo-Saxons often have a middle name allowing to further refine the search. For example, searching for the works of Freeman Dyson (this is his Wikipedia page. See below for his works on ADS) yields more precise results by typing “Dyson, Freeman J”. The “J” sets him apart from others Freeman Dyson’s. If that is not enough, which is the case for the Dyson I’m interested in, we can filter on the left by “AFFILIATIONS”. Cornell and Princeton for Dyson.      
  • It can be very difficult to isolate the works of a scientist whose name is too common. Knowing what an Anglo-Saxon named “John Smith” or a Korean named “Jeon Park” did can be a real puzzle. Unless additional filters save you the day, you’ll have to hope they posted their publication list on their own website, or that they have an ORCID number.
  • ADS does not tell you if people have a PhD. In fact, frankly, nobody cares. The database tells you what someone accomplished scientifically, PhD or not, and that’s what matters. Freeman Dyson did not have a PhD, but his work had a huge influence.
  • A corollary is that being a PhD does not say anything about your scientific contributions. A “prominent”, “world-class”, “renowned” scientist is someone whose articles matter, PhD or not.      
  • Public fame is not synonymous with scientific stature. Perhaps Einstein and Stephen Hawking are the only ones whose public fame matches scientific contributions. Roger Blandford is one of the most influential astrophysicists of the past 50 years, and he is virtually unknown to the public. Same for Lev Landau, John Wheeler, Iakov Zeldovitch, Carlo Rovelli or Peter Goldreich (the list is far longer).
  • Watch out for the numbers. Blandford has more articles and citations than Einstein, which doesn’t mean he outshines him. He would be the first to recognize it (I know him personally). Beyond a few tens of thousands of quotes, we are dealing with a “big one”, with a very uncertain hierarchy. Now a physicist cited 20,000 times has clearly brought more than another cited 100 or even 1,000 times [4].

So, is my science champion really a champion?

The Science and Faith debate is teeming with scientists presented as “eminent”, “world class”, and alike. Are they really so? Sometimes, alas, well, not really. Just a few examples (let’s make friends):  

  • A Christian apologist once called David Berlinski a “world leading physicist”. As you can see, the ADS version is nearly “who is Berlinski?”.  
  • Hugh Ross, sometimes referred to as “a respected astronomer” [5], has not published anything since 1977 and his 10 articles have had little impact (53 citations to date). He’s “respected” by many, but not by the scientific community.
  • Young Earth Creation (YEC) Astrophysicist Jason Lisle published the last of his 6 papers in 2008, and received just 193 citations in all. His colleague Russell Humphreys, who now tortures General Relativity, only received 204 citations for his 9 articles. The case of Danny Faulkner is similar, with 209 citations for 27 articles [6].

Note that being a champion in one discipline does not mean you are a champion in another field. Rafael Nadal sucks at curling and Stephen Hawking was a far better physicist than philosopher.

Let’s finish with some scientists who are both Christians and genuine champions : Ian Hutchinson (MIT), Anthony Bell (Oxford), Katherine and Stephen Blundell (Oxford), Lorenzo Sironi (Columbia), John Barrow (Cambridge), Karin Oberg (Harvard), Don Page (Alberta), Juan Maldacena (Princeton), Gerald Gabrielse (Harvard), George Ellis (Cape Town), Eric Priest (St Andrew),… 

So all those declared “champions” are not necessarily so. Fortunately, some are, definitely. You now know how to spot them.

What about climate science?

Climate science is also indexed in ADS. Here’s what you get when you plug some good climate scientists in the database: Stefan Rahmstorf, Katharine Hayhoe, Hervé Le Treut, Michael Mann, Richard Alley, Edouard Bard, James Hansen, Raymond Pierrehumbert.


[1] I received my first email in 1994. I didn’t even know I had an email address.

[2] To launch a query that returns the full content of the database, just ask for the articles written between 1500 and 2020. As of September 16, 2020, the query returns 14,843,813 articles. The oldest, in Latin, is from 1502! Noteworthily, 90% of these 15 million were written in the last 50 years.

[3] This reminds me of Niels Bohr when he said “the opposite of a profound truth may very well be another profound truth”.

[4] Todate I’ve been cited more than 2,000 times, and I know very well that my contributions are not those of Blandford.

[5] The Google query “Hugh Ross” ” respected astronomer” returns about 100 pages.

[6] It seems there are several Danny Faulkners. So I filtered by affiliations (Indiana where he did his thesis, then South Carolina, where he is a professor). The 27 items found fit well the “two dozen” mentioned on his page.








It was Julius Caesar who killed Napoleon

And if you disagree, it’s because official history has brainwashed you…

Irritating, isn’t?

Let’s see why this is irritating.

For a start, that wouldn’t irritate everyone. This sentence would leave a 5-year-old child unmoved, for example. Save extreme precocity, he has no idea of ​​the history of the world and can easily buy that Julius Caesar killed Napoleon. Ditto for the Yanomami Indian of South America who is probably clueless on the history of Europe. On the other hand, the same Indian would laugh when watching me confusing two birds or two plants species, which are like night and day to him.

Another example. Imagine Google Maps does not exist, and I claim that in Madrid, General Moscardo Street is now called Aviator Zorita Street. You would take my word for it. Yet anyone who knows my neighborhood would know I’m dead wrong. General Moscardo Street did change its name, but it is not called Aviator Zorita Street now. Not at all. But since 99.99% of my readers probably don’t know anything about my neighborhood in Madrid, my mistake would surely go unnoticed. The remaining 0.01%, however, would wonder, “What’s the matter with Antoine? “.

Where am I going with this? Some claims are clearly right or wrong, but it takes some initiation to see it. A little knowledge of history is enough to know that Caesar did not kill Napoleon (everyone knows it was President Roosevelt). A little knowledge of Madrid is enough to know, without a doubt, that General Moscardo Street is not now Aviator Zorita Street.

And in the Science & Faith debate, do we have similar patterns? Yes. For example, as explained here, some knowledge of General Relativity is enough to know that the Minkowski metric is not the FLRW, which is not that of Schwarzschild, and that time and light do not stop when the coefficient of dt2 in a metric changes sign, as Russell Humphreys claims in his “cosmology”.

Yet, if most adults know enough history to shrug their shoulders, or call a doctor, on hearing someone claim that Julius Caesar killed Napoleon, few know enough my Madrid neighborhood to detect my mistake in the names of the streets, and few know enough of General Relativity to detect the enormities uttered by Humphreys.

What can we learn from this? Let us be careful when using science for apologetics. Stimulated by apologetic zeal, it is very easy to find yourself saying that Julius Caesar killed Napoleon. The result will be stumbling block apologetic. Learn before you preach. 1600 years ago, Augustine warned against this very mistake,

“Usually, even a non-Christian knows something about the earth, the heavens, and the other elements of the world, about the motion and orbit of the stars and even their size and relative positions, about the predictable eclipses of the sun and moon, the cycles of the years and the seasons, about the kinds of animals, shrubs, stones, and so forth, and this knowledge he holds to as being certain from reason and experience.

It is a disgraceful and dangerous thing for an infidel to hear a Christian, presumably giving the meaning of Holy Scripture, talking nonsense on these topics; and we should take all means to prevent such an embarrassing situation, in which people show up vast ignorance in a Christian and laugh it to scorn… If they find a Christian mistaken in a field which they themselves know well and hear him maintaining his foolish opinions about our books, how are they going to believe those books in matters concerning the resurrection of the dead, the hope of eternal life, and the kingdom of heaven, when they think their pages are full of falsehoods on facts which they themselves have learnt from experience and the light of reason?

Reckless and incompetent expounders of Holy Scripture bring untold trouble and sorrow on their wiser brethren when they are caught in one of their mischievous false opinions and are taken to task by those who are not bound by the authority of our sacred books.”

Augustine, The literal meaning of Genesis, Book 1, 19.39 (circa AD 415).

Why Russell Humphreys’ cosmology is (really) wrong

The starlight “problem”

Young Earth Creationist (YEC) claim the universe is 6,000 (or 10,000) years old. If it’s really that young, how can we see stars 30,000 (and more, much more) light years away?

Some, like Russell Humphreys, think General Relativity (GR) can help.

How General Relativity works: The Interstellar movie

In the movie Interstellar, Matthew McConaughey misses the teen years of his daughter Murphy for having spent too much time on a planet too close to the “Gargantua” Black Hole. One single hour on “Miller’s planet” is 7 years on Earth! Gargantua weights about 100 million times more than the sun[1], and yes, according to General Relativity (GR), a planet orbiting it like “Miller’s planet”, would enjoy such a crazy time contraction.

According to his own wristwatch, Matthew McConaughey spends a little more than 3 hours on this planet. When he comes back to his mother ship, he finds he’s been away for 23 years. His daughter Murphy was about 10 when he left. She’s now 30 something.

How does it work?

The gravity of the Black Hole (BH) increases as you get closer to it. As long as gravity is not too strong, one may define a so-called gravitational potential, which goes down and down as you approach Gargantua, like in the figure below (absolutely not to scale).

interstellar 3

What GR tells you is that time goes slower in the potential well [2]. The deeper you’re in the well, the slower time passes with respect to Earth. Until you get to the “Event Horizon”.

What happens past then? If you were to fly to the Event Horizon, an observer from Earth would see you approaching it closer and closer, without never crossing it. As for you in your spaceship, you would definitely cross the Event Horizon. Passed this point, it would be impossible to turn back. You would inevitably crash at the center in a time that can be calculated [3].

Note that talking about a “gravitational potential” only makes sense while General Relativistic effects are small. It makes no sense at all below the Event Horizon.

In Interstellar, all this happens over a few billion kilometers. The Earth is far away from this all, completely out of the potential well of the black hole. And yes, according to Einstein’s General Relativity, you would get such a crazy time contraction of Miller’s planet.

In Interstellar, 1 hour on the planet becomes 7 years out there. And 6,000 years? What would they give out there? 0.36 billion years!

Could GR hold the key to thousands of years on earth being like billions in the rest of the universe?

Russell Humphreys’ cosmology

I refer to the cosmology described here.

Humphreys imagine the Earth is at the center of a huge expanding spherical shell with “waters above”. Using GR, he “derives” (why between quotes? See below) the gravitational potential inside the sphere. As you can see on the figure below, the sphere is huge [4]. The Earth is somewhere inside.

humphrey 2

The gravitational potential goes down as one approaches the sphere. It is constant inside. So a clock in the inside, where the Earth is, will tick slower than a clock outside. Like in Interstellar, clocks tick slower as you go down the gravitational potential.

From there Humphreys argues that if “during the fourth day, God creates star masses” so as to lower even more the flat potential inside the sphere, around the Earth, time there would have stopped. It’s even better than Miller’s planet…

Let’s now see the problems.

It just turns out that 1) observations do not back up the existence of Humphreys’ spherical shell and 2) Humphreys’ claims about what would happen if the inside gravitational potential were lowered beyond a “critical potential” (see his figure 7), is wrong according to GR.

What observations tell about the spherical shell

To start with, Humphreys’ solution of GR equations (his equation 2) is not “new”, as he claims. This is just the solution Karl Schwarzschild found in 1916. And it cannot be otherwise. Why? Because there is only one solution to GR equations with spherical symmetry [5] and it is Schwarzschild’s solution (if  there’s but one solution and you find one, then this must be the one). So Humphreys’ solution cannot be “new”.


  • The waters above the spherical shell cannot be liquid. Why? Because nothing sits on top. So it is under 0 pressure. And under 0 pressure, water cannot be liquid. It is either solid ice, or vapor.
  • What about the shell itself? The universe is expanding, and it seems Humphreys admits this (even though his universe is not expanding. See last point.). So let’s play backward the movie of the universe. The spherical shell and the universe contract. They get hotter and hotter. Regardless of what it is made of (what is it made of?), the hotter and hotter spherical shell vaporizes. Its molecules are broken, as are those of the universe inside. Then the atoms that made this all are also broken into electrons, protons, and neutrons. Then protons and neutrons are broken into quarks [6].
    Let’s now play the movie forward from this quark epoch (we don’t really know what came before because we don’t know the laws that applied then). The universe cools down and these quarks assemble to make protons and neutrons. These protons and neutrons assemble to make atoms [7]. The universe keeps expanding, hence cooling down, and these atoms can combine to make molecules. Question: at one point does the spherical shell forms? At the beginning of our movie, it wasn’t there. So when and how did it form? No natural phenomenon is going to make a spherical shell of “something” with “waters above”. And if it was supernaturally there from the start, why going to such great length to come up with a pseudo-natural scenario “explaining” the starlight problem?
  • According to GR, the interior of the spherical shell is “flat”. It’s good old space time. The problem is that such a space time does not expand [8]. That’s what GR dictates. Even if the spherical shell does, the interior does not, and Humphreys equations 2 & 3 are OK with that. Two inside points 1 million light years from each other will still be so 1 billion years later
    This is a problem because we observe the expansion. Stars recede from us. The farther, the faster. In Humphreys’ “cosmology”, there’s no redshift. In Humphreys’ “cosmology”, the temperature of the Cosmos Microwave Background doesn’t change with time. Yet, such a temperature change has been observed.

Humphreys’ GR below the “critical potential” is wrong

Looking at the math of how time passes slower inside the shell than outside, one notices that if the ratio R/M is large enough (R = radius of the shell, M = its mass), something strange happens to the math [9]. If that happens, Humpreys writes that “physical clocks would stop completely. Time would no longer exist” and “light cannot propagate”!

Obviously, stopped clocks allow to squeeze anything you want in just no time.

The problem is that if R/M turned to be large enough, and contrary to what Humphreys claims, GR states that clocks inside the shell would not stop. And light would keep propagating.

These are very well-known results since the situation produced for R/M large enough is precisely the one produced inside the event horizon of a black hole. Admittedly, what happens there is quite weird and it took physicists decades to grasp it. Yet, however involved it may be, some things are sure: clocks keep ticking inside an event horizon, and light keeps propagating. A classical calculation of General Relativity even consists in computing the time it would take for an astronaut to reach the center of a Black Hole [10]. Part of this time is definitely the one is takes to go from the event horizon to the center. According to GR, clocks do tick “inside”. Besides, light does propagate.


Let’s wrap it up. Humphreys’ cosmology fails at various stages. It assumes a huge spherical shell around us, that cannot have formed unless it got there miraculously. Then General Relativity inside this sphere gives a space time which is not expanding whereas observations do show it does. Finally, Humphreys has GR tell that in some special circumstances, time no longer stops inside the shell, and light cannot propagate, whereas GR doesn’t tell this at all [11].

This is clearly some conclusion-driven, bad, “science”. Humphreys comes up with an arbitrary scenario only designed to explain away the YEC starlight problem. Then it becomes bad science: the spherical shell invoked cannot have formed naturally, and its consequences do not match observations. And then it becomes bad GR: after having invoked GR to the rescue, Humphreys has GR predicts phenomena it doesn’t.

This is a good example of why “mainstream science” rejects “creacion science”. The reason why “mainstream science” rejects “creation science” has nothing to do with religion. Einstein talked about God, Abdus Salam was a devout Muslim, Ramanujan attributed his findings to a Hindu goddess. Many of my friends astrophysicists talk about God in the lab. I talk about God.

No, the real reason why creation science is rejected, is because it tramples logic, observations and experiments. It perfectly fits CS Lewis’ words [12],

Science twisted in the interests of apologetics would be sin and folly


[1] See The Science of Interstellar by Nobel Prize Kip Thorne. The reader will also find more technical data on the same topic here.

[2] Such gravitational time shift has been checked experimentally many times and is now in use in your GPS.

[3] The falling time is computed in Gravitation, by Misner, Thorne, and Wheeler, page 820. It is finite for the astronaut, and infinite for the observer.

[4] Its size is a little less than the one of the observable universe, about 46 billion light years, see

[5] That’s the Birkhoff’s theorem.

[6] All these states of matter have been studied in the lab. There’s no conjecture here. Matter does that when you heat it more and more.

[7] Using the known laws of physics, you can derive from this scenario the relative abundances of light elements and compare to observations. It was done from 1948 and works well. Others expected and observed consequences of the movie are the Cosmic Microwave Background or the Baryonic Acoustic Oscillations.

[8] The “Minkowski metric” describes the good old flat space time. If you want expansion you need something like the “Friedmann–Lemaître–Robertson–Walker metric”. See for example equation (28.9) page 1371 of Modern Classical Physics by Thorne and Blandford. Or simply Google “FLRW metric”.
By the way, George Lemaître was a priest.

[9] Technically, the coefficient of dt2 in Eq. (2) becomes negative.

[10] See note [3].

[11] Just check for example Figure 26.4 page 1269 of Modern Classical Physics by Thorne and Blandford. It shows how light does propagate within the Even Horizon.

[12] CS Lewis, God in the Dock: Essays on Theology and Ethics, Eerdmans Publishing Co, 1972, p. 93.

Consensus. What’s that?

We often hear about scientific “consensus”. The thing seems quite misunderstood, sometimes seemingly considered as a gentleman agreement between researchers tired of getting headaches over a topic, or wanting to impose a conclusion. “Let’s say it’s like this, and that’s it!”.

No, it doesn’t work like that.

As an illustration, let’s see how a consensus was reached… on the sources of the Nile river. We will then make the comparison with the consensus reached on the Big Bang.

The sources of the Nile

The Nile delta has been known for millennia. Not the same for its source [1] which location remained a mystery for almost the same time. Let’s make this long story short [2]:

  • When Alexander the Great saw the Indus river around 325 BC, he thought he had found the source of the Nile. Still in the 6th century, the Byzantine historian Procopius of Caesarea wrote “the Nile flows from India to Egypt…”.
  • Egyptians contemporary of Herodotus saw the source at Aswan.
  • Juba II king of Mauretania (50 BC – 23 AD) thought he had discovered the sources of the Nile in the Atlas Mountains, northwest of Africa.
  • Ptolemy (2nd century) was perhaps the first to near reality by placing the source of the Blue Nile at Lake Tana, and that of the White Nile further south, in some legendary “Mountains of the Moon”.
  • The British explorer John Speke discovered Lake Victoria in 1858 and thought it would make an excellent source. Of course, his colleagues were not satisfied with his testimony only.
  • It was Henry Stanley who confirmed the discovery in 1875 during the expedition where he was to meet Livingstone and ask the famous and so British “Dr. Livingstone, I presume?”.

So was solved the enigma of the source of the Nile, after literally thousands of years of research. Long before satellite pictures, and, interestingly, long before someone navigated it from start to finish, which only happened in 2004 [3]!

The Big Bang

Well for the Big Bang, pretty much the same happened. On the Nile side, we had:

  • Competing hypotheses: India? Aswan? Mountains of the Moon? Atlas Mountains?
  • A discovery, that of Speke, is not enough.
  • Verification.

It would be difficult to imagine explorers of the 6th century complaining,

We’re fed up with this Nile business. Enough of it. Let’s choose a location for the source, and settle the case!

It is obvious that they were going to seek until they’d find it, that competing hypotheses were going to arise, and that the end of the story would come by checking them all.

What about the Big Bang? Ditto, almost,

  • Competing hypotheses: Static universe or not? From Aristotle to Einstein in his 1917 article, the first option had strong supporters. The second, that of a dynamic universe, was mainly introduced by Hubble’s observations in 1929, but precisely…
  • Hubble’s observations didn’t settle the matter [4]. Einstein changed his mind in 1931 [5], but the controversy did not end there.
  • People wanted to check, which is perfectly normal. One check came from the solution of Einstein’s equations found by Friedmann, Lemaître, Robertson and Walker. The cosmic microwave background (CMB), predicted in 1948 and discovered in 1964, impressed many. The relative abundance of light elements did the same.
  • It was towards the end of the 1960s that the consensus arose, mainly the fruit of the discovery of the CMB [6].

Today, nearly all cosmologists think that some 14 billion years ago, the universe went through a very dense and hot phase and that it has been expanding since then. Other checks [7] have come to strengthen the picture which, ultimately, mainly owes its raison d’être to the expansion of the universe. Just rewind the movie.

Whether it be quantum mechanics, general relativity, plate tectonics, anthropogenic global warming or shockwaves in interstellar vacuum, consensus were established the same way. They don’t arise because people are fed up with not knowing, or fear any conclusion. They arise because years of study and checking have left no choice.

One only needs to make sure he/she doesn’t see consensus were there’s not (like on how the universe began – if it ever did).

But that is another story.


[1] Or rather its sources, since we have to distinguish the White Nile from the Blue, but let’s simplify.

[2] For the long version, see for example Terje Oestigaard & Gedef Abawa Firew, The Source of the Blue Nile: Water Rituals and Traditions in the Lake Tana Region, Cambridge Scholars Publishing, 2014.

[3] “National Geographic” produced in 2005 a documentary on this expedition entitled The Longest River.

[4] The main alternative to redshift as indicating receding velocities was Fritz Zwicky’s “tired light”. It has been discarded for many reasons (distant objects would be blurred, shift would depend on the frequency, etc. More here or here).

[5] Harry Nussbaumer, Einstein’s conversion from his static to an expanding universe, European Physics Journal – History, 39, 37-62 (2014).

[6] See for example Helge Kragh, Cosmology and Controversy, Princeton University Press, 1999.

[7] Temperature of the CMB at several epochs, structures of the universe and their distribution, baryonic acoustic oscillations, etc.