cosmic-microwave-background - 2.7 degrees but does the Big Bang care?

Question

The Big Bang is a proposed answer to the beginning of the universe, and the Cosmic Microwave Background or CMB is a central part of the evidence for it.

Now suppose the measurement returned a different value than 2.7K.

What if it were 0.27K or 27K? Would the Big Bang theory still work with a few minor adjustments or is the specific temperature of 2.7K critical evidence that the theory works?

Edit: I have removed a paragraph which was not mine asking about small changes in temperature. It is a fundamentally different question. I am more interested in how firm the evidence for the BB theory is, not its details. At least for this question. However if uhoh who seems to have done the editing thinks it a fair question, I would certainly welcome it - in another post.

Answer 1

Yes, I think it is a constraint, but don't think I can tell you how different it could be from 2.73 K to cause a problem.

The CMB tells us that the universe was once much hotter ($>3000$ K), so that hydrogen nuclei and electrons had sufficient kinetic energies to remain uncombined. In the big-bang model, the universe expands and cools, then at temperatures just below this the protons and electrons combine to form atoms that are almost transparent to the blackbody radiation that filled the universe before that. This radiation is then redshifts by the cosmological expansion and we still see it today as microwaves.

In the big-bang model, the temperature of the universe scales as $(1+z)^{-1}$, where $z$ is the redshift corresponding to a particular look back time. That we see the CMB at 2.73 K now, means it occurred at $z=1100$. Your question amounts to - would it matter if this were $z=110$ or $z=11000$?

It's less complicated to deal with the lower of these possibilities. At $z<3400$, the energy density of the universe is matter dominated, and the scale factor $a \simeq (t/t_0)^{2/3}$, where $t_0$ is the age of the universe and $a(t_0)=1$. Since $1+z = a^{-1}$, this means the connection between age and redshift is $$ t(z) \simeq t_0 (1+z)^{-3/2}$$

If the CMB was formed at $z=1100$ this would be 370,000 years after the big bang (using the usual accepted cosmological parameters and an age of the universe of 13.7 billion years$^1$). If instead we use $z=110$, the CMB formed about 14 million years after the big bang.

That in itself is not a problem. We are just changing the expansion rate of the universe to match the redshift of the CMB and demanding this occurs just below 3000 K.

But this alters the temperature versus time relationship at all later and earlier times. How might this affect some other cosmological observations?

I think one area where the change in timescales would be hugely important is in primordial nucleosynthesis. By slowing down (or speeding up) the expansion rate, one allows an order of magnitude more (or less) time for nuclear reactions to take place.

An example: The neutron to proton ratio in the early universe freezes out at 1/6, but neutron decay with a half-life of 15 minutes, reduces the final ratio to 1/7 during the window of time available to nuclear reactions. If this window is made much bigger, the ratio will decrease further, if it is made much smaller the ratio will remain at 1/6.

Almost all of those neutrons end up in helium nuclei, so the primordial He abundance would vary between 10 H atoms per He atom through to something considerably bigger. The primordial He abundance is known to better than 1%, and it is around 12 H atoms per He atom. i.e. There was just enough time when primordial nuclear reactions were taking place for some of the free neutrons to decay, but not all. This would certainly seem to rule out order of magnitude changes in the CMB temperature.

I may add to this as other things occur to me. There is likely another constraint based on the observed formation redshift of the first stars and the epoch of reionization.

Answer 2

The expansion of the universe is described by a scale factor that we normally call $a(t)$. We take the scale factor to be equal to one right now, so if $a(t)$ is less than one that means the universe has contracted while if $a(t)$ is greater than one the universe has expanded.

General relativity allows us to calculate how the scale factor depends on time. If you're interested I do this in the question How does the Hubble parameter change with the age of the universe? on the Physics SE. This is what the results look like:

The point of this is that the CMB temperature is directly related to the scale factor so if we can calculate how the scale factor has changed with time then we can calculate the current CMB temperature.

But the way the scale factor changes with time depends on the density of matter and energy in the universe. Specifically it depends on how much light, matter (normal and dark) and dark energy is present. The matter/energy density could in principle have any values, that is there is no fundamental principle in physics that specifies what the densities of the of the various types of matter and energy have to be.

Our current best measurements of the matter/energy density come from the Planck experiment, and they suggest the total density has a value close to the critical density. This density gives us the form of the scale factor that I drew above, and it gives us the CMB temperature of 2.7K. If the density were lower than critical we would get a lower CMB temperature and if the density were higher than critical we get a higher CMB temperature. So the answer to your question is that the CMB temperature is not uniquely determined and it could be higher or lower. Ultimately the CMB temperature is an experimental parameter that we have to determine by making experimental measurements.

But we should note that there are excellent reasons why we would expect the matter/energy density to be equal to the critical density, so we would expect the CMB temperature to be what we observe. If the CMB temperature were different by a factor of ten that would be hard to explain theoretically.

Finally we should note that there are other independent constraints of the form of the scale factor function. Rob Jeffries describes some of these in his answer so I won't go through them again here, but for example the ratio of hydrogen to helium depends on how quickly $a(t)$ increased after the Big Bang. If the scale factor had increased significantly faster or more slowly it would have changed the hydrogen to helium ratio and we'd be able to measure this change.

Answer 3

I'd say it doesn't care all that much, but that 27 degrees Kelvin is a step too far.

See the 1965 NASA csomic times article big hiss missed by others. You can read how Andrei Doroshkevic and Igor Novikov published a Big Bang study in 1964 saying the remaining heat would now be between 1 and 10 degrees Kelvin. They proposed the use of the Holmdel horn measurements made in 1961 by Edward Ohm, who “had already identified in his data what seemed to be a 3.3 degrees Kelvin background radiation”. The article also says “Ten years ago Émile Le Roux reported a microwave background radiation of 3 degrees Kelvin, plus or minus 2 degrees at the Nançay Radio Observatory”. And this: “In 1957 it was Tigran Shmaonov who nearly made the discovery. He reported measuring background temperature of 4 degrees Kelvin, give or take 3 degrees”.

Of course, everybody knows about the famous back-to-back papers to the Astrophysical Journal in July 1965. They were A Measurement of Excess Antenna Temperature at 4080 Mc/s by Penzias and Wilson, and Cosmic Black-Body Radiation by Dicke, Peebles, Roll, and Wilkinson. What people don't generally know is that Dicke et al were talking about "a closed universe, oscillating all the time". So according to them, the evidence for the Big Bounce had been found!

Personally I don't see any way by which the universe can ever contract. So I think the Big Bounce is a non-starter. However even though I'm 110% sure that the universe is expanding, I'm not happy with inflation or creation ex nihilo. So I think you're right to question the Big Bang. The $64,0000 question is this: what banged?