Age of the CMB: How do we know?

Question

As short as possible: From what I understand the Cosmic Microwave Background was predicted by multiple people as a theoretical consequence of the Big Bang theory, and hence today, is evidence for the Big Bang. So of course there was also a prediction of the age of the CMB, because it was predicted to have occurred at a certain point in time.

Now, is that the only reason cosmology dates the CMB to 13.8 billion years ago, i.e. is the dating inferred by the theory? I assume there must be many types of measurements that somehow connect to this so as to infer the exact age of what we are seeing there.

Answer 1

You have asked a lot of questions here so my apologies if I do not cover them all. Let us start with a misconception which you may (or may not) hold:

The CMB does not originate from the big bang it originates from what is called the surface of last scattering. This occurred about $380,000$ years after the big bang when the universe had a temperature of about $0.23-0.25eV$ ($\sim 3000K$). Consider the reaction: $$p+e^-\leftrightarrow H+\gamma \tag{(1)}$$ above $3000K$ the photons have enough energy to cause this reaction to go into reverse once the universe as cooled (due to the expansion of the universe) the energy of the photons is to small for the reverse reaction to occur. The consequence of this is that all the protons and electrons get taken up to form hydrogen atoms. With no free ions in the universe Thomson scattering becomes less probable ans the universe becomes optically thin. I.e. Before this time photons would travel a very small distance before scattering but after they will travel a very large distance - so large that the photons we see as the CMB are the photons from this time which are yet to scatter.

Now this surface of last scattering will occur at $3000K$ no matter what happened before it (this is determined by something known as the Saha equation). So only the rate of expansion after this time will effect the redshift of the CMB. Now inflation is thought to have happened within approximately $10^{-32}$ seconds after the big bang. Clearly $10^{-32}$ seconds $\lt $ $380,000$ years so inflation will not affect the redshift of the CMB.

Now you actually pose another query in your question - whether the cosmic horizon will change during inflation. The answer to this is yes. And no there is no contradiction here - the cosmic horizon is different from the surface of last scattering. The Cosmic Horizon is the furtherest point we could possible see. I.e. if a photon started traveling at the big bang singularity and has carried on in a straight line (without scattering) to reach us today - the distance it has traveled is the cosmic horizon. This is affected by inflation because the photon is assumed to be traveling through this period.

All that said inflation does have an effect on the CMB. It explains why it looks so homogeneous (something called the horizon problem). Inflation explains this since it means a very large are of the universe now was once all in causal contact since before inflation is was much smaller - allowing photons from one side to the other.

EDIT

Concerning the question of evidence of the age of the CMB. We can only measure the CMB as it appears to us now. This includes things like the wavelength, blackbody spectrum and the angular power spectrum of the anisotropies of the CMB. To work out the age of the CMB however, you need to know the temperature of the CMB when it was created and compare that to its value today (which we can measure). There is no way to measure the temperature when it was created (we simply weren't there) and thus for this we need the theoretical calculation involving the Saha equation.

Answer 2

This is the history of the universe in the Big bang model.

It shows the currently accepted model . The CMB appears at 380.000 years after the origin of the Big Bang. Before that , up to 10^-32seconda from the origin of the Big bang, our theoretical knowledge of particle physics is heavily used. The CMB happens when due to inflation the universe cools enough so that photons can decouple from the rest of the particle soup and thus keep a snapshot of the distribution of matter at the time of decoupling.

The detailed, all-sky picture of the infant universe created from nine years of WMAP data. The image reveals 13.77 billion year old temperature fluctuations (shown as color differences) that correspond to the seeds that grew to become the galaxies. The signal from the our Galaxy was subtracted using the multi-frequency data. This image shows a temperature range of ± 200 microKelvin

In has small non uniformity from the black body radiation curve

the root mean square variations are only 18 µK

on a 2.7K black body radiation curve, and those are the features in the image above.

It carries information on the seeds of galaxies and cluster of galaxies. In this sense it validates the Big Bang model.

So it validates the Big Bang model, together with a number of other observations.

you ask in the title:

Age of the CMB: How do we know?

The CMB is heavily red shifted because of the expanding universe, and one way of finding the age of the universe is in using the standard model of particle physics and thermodynamics to get at the Black body radiation curve at the time of decoupling. There exist a specific model which cosmology uses to define the chronology of the Big Bang, and everything is consistent within the parameters of this model and the time lines quoted depend on it.

The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parametrization of the Big Bang cosmological model in which the universe contains a cosmological constant, denoted by Lambda (Greek Λ), associated with dark energy, and cold dark matter (abbreviated CDM). It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:

the existence and structure of the cosmic microwave background

the large-scale structure in the distribution of galaxies

the abundances of hydrogen (including deuterium), helium, and lithium

the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

So the chronology of the CMB comes out from the "fit" to the observations.