# What evidence do we have that CMB is the result of the Big bang?

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## Solution 1

The first thing to think about is what exactly we mean by a big bang. A weak version of the big bang hypothesis would simply be the statement that at some time in the past, the universe was extremely hot and dense -- as hot and dense as a nuclear explosion. A stronger statement would be that, at some point in the past, there was a singularity, which is in nontechnical terms a beginning to time itself.

We have a variety of evidence that the universe’s existence does not stretch for an unlimited time into the past. One example is that in the present-day universe, stars use up deuterium nuclei, but there are no known processes that could replenish their supply. We therefore expect that the abundance of deuterium in the universe should decrease over time. If the universe had existed for an infinite time, we would expect that all its deuterium would have been lost, and yet we observe that deuterium does exist in stars and in the interstellar medium.

We also observe that the universe is expanding. There are singularity theorems such as the Hawking singularity theorem and the Borde-Guth-Vilenkin singularity theorem ( http://arxiv.org/abs/gr-qc/0110012 ) that tell us that, given present conditions, there must be a singularity in the past. These theorems depend on general relativity (GR), which at this point is a well tested, fundamental theory of physics with little viable competition. Although there are competing theories, such as scalar-tensor theories, observations constrain them to make very nearly the same predictions as GR under a broad range of conditions.

There is a little bit of wiggle room here because the Hawking singularity theorem requires a type of assumption called an energy condition (specifically, the strong energy condition or the null energy condition), and BGV is more of a model-dependent argument having to do with inflationary spacetimes (which violate an energy condition during the inflationary epoch). An energy condition is basically a description of the behavior of matter, sort of roughly saying that it has positive mass and exerts positive pressure.

Dark energy violates the standard energy conditions. So if dark energy is strong enough, you can evade the existence of a big bang singularity. You can get a "big bounce" instead. However, we have three different methods of measuring dark energy (supernovae, CMB, and BAO), and these constrain it to be too weak, by about a factor of two, to produce a big bounce. The figure below shows the cosmological parameters of our universe, after Perlmutter, 1998, arxiv.org/abs/astro-ph/9812133, and Kowalski, 2008, arxiv.org/abs/0804.4142. The three shaded regions represent the 95% confidence regions for the three types of observations. If you take the intersection of the three shaded regions, I think it's pretty clear that we're just nowhere near the region of parameter space that results in a big bounce.

There are various other observations that verify predictions of the big bang model. For example, abundances of light elements are roughly in agreement with calculations of big-bang nucleosynthesis (although there are some discrepancies that are not understood). The CMB is observed to be very nearly a perfect blackbody spectrum, which is what is predicted by big bang models. This is hard to explain in models that don't include a big bang.

Historically, cosmological expansion was observed, and cosmological models were constructed that fit the expansion. There was competition between the big bang model and steady-state models. The steady-state model began to succumb to contrary evidence when Ryle and coworkers counted radio sources and found that they did not show the statistical behavior predicted by the model. The CMB was the coup the grace, and the big bang model won. When you observe the CMB, you're basically looking up in the sky and directly seeing the big bang.

Note that although in historical cosmological models, perfect symmetry was originally assumed in the form of homogeneity and isotropy, to make models easy to calculate with, these are not necessary assumptions. The singularity theorems do not assume any special symmetry. For the Hawking singularity theorem, you just need to have a positive lower bound on the local value of the Hubble constant, and that bound has to hold everywhere in the universe on some spacelike surface. Of course, we can't observe all of the universe, and you could say that our reason for believing in such a global bound is homogeneity. However, the existence of such a bound would be only a very, very weak kind of homogeneity assumption -- much weaker than the kind of symmetry assumptions made in specific models such as ΛCDM.

## Solution 2

I know this isn't quite what you are asking, but it is important because otherwise the question cannot be answered. I would say this question exhibits a subtle but scientifically important error in the way it is framed. The key way that science works is we devise hypotheses that make specific and often quantitative predictions, and then we go out and test those predictions to the highest accuracy we can. But when the predictions work, we should never say "the predicted phenomenon was the result of our theory", because phenomena do not result from theories, they result from nature. The job of a theory is not to produce a phenomenon, but to explain and predict it. When a theory succeeds, we say it is a good theory. Sometimes we slip a little and say the theory is "correct", but what the scientist means there is simply that it is successful-- that's all we ever get in science, successful theories, not correct ones. We simply fall into the habit of using those terms interchangeably, but it causes fundamental confusion about what science is.

So the scientific way to ask the question here is, "what evidence do we have that the Big Bang model is successful in predicting not only the existence of the CMB, but it's quantitative elements to high accuracy?" We do not have evidence that the CMB comes from the Big Bang, it is not possible for an observed phenomenon to come from a theory, theories are ways of understanding and predicting phenomena, not ways of making them happen. But framed properly, the question is easy to answer-- the evidence that the Big Bang theory is the only theory that is successful at predicting the existence and quantitative aspects of the CMB is simply that the existence of the CMB was predicted, before it was observed, by only one theory, and that's the Big Bang. Also, its quantitative elements have been tested to be consistent with the Big Bang theory, with higher and higher accuracy with several generations of more advanced observations.

However, not only are observations used to test theories, they are also used to modify and improve theories. This is another reason it is important to realize that theories don't produce observations, if you thought that, you could not understand that theories generally require modification and correction once the observations are done. The Big Bang is no exception, as three key elements that were completely lacking from the original Big Bang theory have now been added: dark matter, dark energy, and the era of inflation. That doesn't happen if you imagine that observations "come from" theories!

We make theories to be able to successfully predict observations before we have them, which the Big Bang theory did for the CMB, and to be able to quantitatively understand those observations, which the Big Bang theory does for the CMB. Furthermore, it is the only theory we have that does these things. That's really all that can be said about it. We cannot find evidence that the CMB "comes from" the Big Bang model, that's a category error: the Big Bang model, with whatever modifications it needs to do so, lets us understand the CMB, and no other model does that. Saying the CMB comes from the Big Bang would be like saying the added speed that a bullet has when fired from a moving car "comes from" Galilean relativity. Of course it does not, as there is not Galilean relativity that could make things happen, Galilean relativity is a way of understanding what happens that is never exact and completely breaks down in some limits, and so cannot be the reason that things happen. It is a successful scientific theory if applied appropriately, that is all that may be said without forgetting what separates scientific thinking from almost everything else.

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### Dac0

Updated on December 23, 2020

• Dac0 almost 3 years

I got the main picture repeated over and over again about why if there's a Big bang we indeed should see the CMB with this feature. In this question I'm asking something different: what independent evidences do we have that the CMB is really related with what the Universe was 400k years after the Big bang and not just related with what the Universe is now or just related with something else we don't yet know? What are the effective evidences that is the result of the Big bang as it is usually described?

If the list is too long I would also appreciate one or two references.

what do you mean by what independent evidences , could you elaborate on that, thanks
• AHusain almost 7 years
If you assume homogenous isotropic and GR, you get a small realm of remaining choices (rip,crunch). So we have the other independent tests of GR like Mercury. The isotropy is evidenced by other astronomical measures.
• Qmechanic almost 7 years
@AHusain: What you say is true, but is not the strongest argument available. We know that the universe has only approximate homogeneity and isotropy. As described in my answer, we don't need to assume a high level of symmetry in order to apply singularity theorems. Also, GR is sort of a big tent. Steady-state models did evade a big bang, but one of the prices they paid was that they lost local Lorentz invariance. Usually we consider local Lorentz invariance to be part of the definition of GR, but the Hoyle saw himself as just introducing a new scalar field within the framework of GR.
• Dac0 almost 7 years
@user139561 I mean in a broad sense: evidences that are not directly derived one another
• ProfRob almost 7 years
Indeed, the CMB is simply consistent with the big bang model in its present form. It is open to others to put forward alternative ideas that self-consistently explain the CMB, expansion of the universe, primordial abundances etc. I prefer the word "model" to refer to the big bang and not "theory", since it is a bit of a mish-mash with various things bolted on in an attempt to explain everything that is observed.
This doesn't answer the question, and moreover is not really correct. "Big bang" does not refer only to a certain type of cosmological model but also to an actual thing: a big bang singularity. If you use the phrase in the latter sense, then the CMB does indeed literally "come from" the big bang. A CMB photon arises from a point on the surface of last scattering, and the big bang singularity is in the causal past of that point. The OP asked a legitimate scientific question, requesting specific scientific evidence, and this answer just responds with faux-philosophical linguistic nit-picking.
• Ken G almost 7 years
No, the Big Bang definitely does not refer to a singularity, that has never been tested and would have to be regarded as unscientific. This is exactly why it is important for scientists to understand what science is. To clarify, the presence of a CMB has nothing to do with a singularity, any universe similar to our own at an age of some 300,000 years would produce a CMB. The details of the inhomogeneities in the CMB give us information about much earlier times, including possibly an era of inflation, but even that is not a singularity. The CMB has nothing to say about singularities.
• Ken G almost 7 years
To talk about a singularity, don't you have to assert things about the Planck scale that you cannot possibly know? And isn't the history of science just completely rife with examples of people overinterpreting their own best theories? I would have thought that would have been the clearest of all the lessons of science.
• Tabby almost 7 years
@KenG: I think my answer makes it clear that the singularity being referred to is a singularity that occurs within the context of a specific theory: GR.
No, the Big Bang definitely does not refer to a singularity "Big bang singularity" is a standard usage among experts in the field. For example, when I google on the phrase, the third hit is an article by Stephen Hawking. If you have a gripe with standard terminology and want to start a reform movement, that's your privilege.
• Dac0 almost 7 years
Thank you Ken G for stating the obvious in a very long answer which definetely doesn't asnwer my question. If you prefer just reformulate the question this way "Is there any alternative theory which explains CMB or why it's not possible?" If you want to edit you answer or answer again I will be glad to upvote it
• Dac0 almost 7 years
Thank you for your answer. I didn't know Borde-Guth-Vilenkin singularity theorem and I think it's relevant to my question. Anyway I would ask you, are or were there alternative interpretation for the CMB? How were they discarded? Thank you, I think you're the only one here who knows or has the willing to explain how the situation is.
• Ken G almost 7 years
Making this a scientific discussion is easy-- you simply have to assert a single thing that a Big Bang singularity predicts. Just one. Otherwise, it is not science, it is mathematics.
• Ken G almost 7 years
Yes, I certainly agree that your answer is about a specific theory. That's exactly the reason that the question needs to be reframed in order for an answer about a theory to be the answer to the question. For example, the theory you are using is known to break down before a singularity is reached, it most likely fails at the Planck scale, and has never been tested even close to that scale.
• Ken G almost 7 years
@Daco: if it was obvious, why didn't you simply frame the question that way in the first place? In the modern era, we should all expect science to come under significant attack, both in the areas of evolution and climate science, so why not cosmology as well. Being clear is going to be important, we must defend what a scientific question actually is. But yes, there is no other theory that predicts a CMB, without building it into the model ahead of time in an ad hoc way. But we should all expect the favored model to look different a century from now, so the CMB does not come from a model.
• Tabby almost 7 years
@Dac0: Anyway I would ask you, are or were there alternative interpretation for the CMB? How were they discarded? There's Narlikar's QSS, but it's nonsense: astro.ucla.edu/~wright/stdystat.htm . Historically, the focus turned away from SS models and toward BB models as soon as the CMB was discovered. If you hypothesize surprising properties for matter fields, making them violate energy conditions strongly enough past some temperature T, you can get a bounce rather than a bang. T would have to be high to fit observations. Cyclic cosmologies also tend to have thermodynamic problems.
• Dac0 almost 7 years