Microwave Background

Expansion of the Universe

Abundance of the LIght ELements

On the basis of two observations, 1) the Universe is currently in a state of uniform expansion and 2) the Universe is filled with photons that come from background radiation at a temperature of 2.74 K, we can construct our generic cosmological model known as the Hot Big Bang model. This model is but a mere 30 years old so we should not expect it to be a complete description of what we observe and indeed it is not. What the model can explain well is the following:

Microwave Background

• The Origin of the CBR: From its initially extremely hot and dense state, the CBR arises due to photon production from matter-anti-matter annihilation. Once the photon background is produced it simply cools with the expansion of the Universe, in the thermodynamic manner first specified by Gamow. The observed entropy of the Universe, $S$, which is measured by the ratio of baryons to photons is 5 x 10^-10.

  Essentially this means for every 5 billion anti-quarks, there was 5 billion +1 quarks. The residue of this tiny mass assymetry has produced the observed stars and galaxies in the Universe.

  
  Background microwave spectrum as measured by COBE

  The CBR is pretty difficult to ignore. Most radial alternative cosmologies can't really predict it. The discovery of the CBR has an interesting history:

  • Accidentally discovered in 1941 by Mckellar:

    Observations of the excited states of the CN molecule made by McKellar (1941) indicated excitation by a photon background with a characteristic temperature of 2.3 K. But since the CN molecule could only be found where the Galaxy was, the excitation was attributed to the ambient energy density of starlight in the Galaxy as opposed to being energy external to the galaxy (\ie the CMB).

    Accidentally discovered again in 1965 by Penzias and Wilson (who won the Nobel Prize). They were employed at Bell Labs and were testing the feasibility of using Microwaves for communication. The initial measurements (at one frequency only) of Penzias Wilson indicated that the flux density of photons at their millimeter receiver was independent of position in the sky. Failing to see any 24 hour modulation of this signal, the remaining logical conclusion was that the CMB was indeed of cosmological origin and therefore everywhere.

    But shortly after the Universe was discovered to be expanding, theoretical arguments for a background of radiation were presented.:

    In 1934 Tolman made an analogy between the expanding universe and a thermodynamic state. Equating expansion with the thermodynamic concept of entropy led him to conclude that the expansion must cool any background which has a thermal spectrum.

    In 1942, Chandrasekhar and Heinrich suggested that if the Universe in its early history achieved thermal equilibrium at conditions of temperature 10¹⁰ K and density near 10⁷ g/cc, then equilibrium abundances of lighter elements would have frozen out, in ratios that roughly agreed with observations.

    But this argument is only partially correct since the high matter density at the time would have required rapid expansion (to avoid early collapse of the Universe) and hence equilibrium calculations are not appropriate. Gamow (1942, 1946) used this as the basis for his set of arguments that physical processes in the early universe were dynamic in nature as they must have occurred in a rapidly expanding and cooling environment.

    Gamow (1948) later reasoned that at sufficiently high temperatures, (kT in excess of the rest mass energy of a neutron), the energy density in the photon field must have greatly exceeded the energy density of the matter field. In such conditions, the radiation field can photo-dissociate any nuclei, meaning that the early universe had to consist of photons and free elementary particles. Gamow used the estimated abundances of helium to predict that, at the current epoch, the photon field has been redshifted to millimeter wavelengths. In fact he predicted, in 1953, a temperature of 5K for the background.

  Finally, its important to realize that the CMB is measuring the surface of last scattering. Prior to that event, or, more specifically, when the Universe was completely ionized, photons could not free stream through the matter but were scattered (e.g. thomsen scattering) by free electrons. Thus the matter and radiation were coupled. The event we see in the CMB is not the "initial explosion energy of the big bang" but rather, the redshifted photons that emerge from the surface of last scattering. The universe needs to cool to a temperature of about 3000K before ionization ends and the photons can then free stream. That occured at a redshift of 1000 and hence the temperature of the CMB today is 3K.

  Expansion of the Universe

Hubble made redshift measurements of galaxies and assumed that all galaxies had roughly the same physical size. using the angular size as a measure of distance he showed there was a linear correlation between radial velocity away from the observer and the distance to the galaxy. This is called the Hubble law and the slope of the relation is the Hubble constant whose inverse represents the expansion age of the Universe.

Although the data are quite noisy, there is a general trend for more distance objects to exhibit a larger redshift. These data were sufficient to empirically demonstrate that recessional velocity was proportional to distance and hence that the Universe was in a state of uniform expansion. Einstein's General Relativity and the static Universe could now be resolved - the Universe itself was expanding. This determination of uniform, linear expansion of the Universe has a clear prediction. If galaxies are moving apart from one another today, then in the past they must have been closer together. Indeed, there must have been a time when all the galaxies in the Universe were together in the same space. At this time, the Universe was very dense and in a physical state well-removed from how it is observed to be today.

Abundance of the Light Elements

Universe at expansion age of about one second was a hot and dense mixture of electrons, protons, neutrons, neutrinoes and photons. The ratio of protons to neutrons at this time was unity as interactions with neutrinoes mediated the neutron to proton and proton to neutron conversion. However, at expansion age of 2 seconds, the Universe had cooled to the point where it became transparent to neutrinoes and this mediation was gone. Since free neutrons decay with 1/2 life of \app 900 seconds, the proton-to-neutron (P/N) ratio began to increase. As the Universe continued to expand, it cooled to the point where some the nucleons could fuse into light elements such as Deuterium and Helium through the same series of fusion reactions that are presently occuring in our Sun. At the time of this hydrogen to helium fusion P/N = 7

Making Helium:

But, deuterium is a very fragile nucleus and can easily be broken apart by a high energy photon:

pn + photon --> p + n (which will decay in 900 seconds)

Now there is an interesting race condition:

Will deuterium combine with another proton to make a nucleus with 3 nucleons or will it be photodissociated before it can do this?

This race condition depends on the density of protons:

• if the density is high then deuterium will fuse with another proton to make Helium-3
• if the density is low then most of the deuterium will be photo- dissociated before making Helium-3.
• a high density universe means a low density of deuterium
• a low density universe means a low density of Helium (3 and 4).

So things are trying to proceed as follows:

The end result is the conversion of 2 protons and 2 neutrons into 1 Helium-4 nucleus.

Before the Reaction:

• 14 protons and 2 neutrons

After the reaction

• 12 protons and 1 Helium-4 nucleus

The mass of 1 Helium-4 nucleus is about 4 times the mass of a proton

Now we can make a prediction:

The helium abundance reflects three things:

1. The p/n ratio at the time that nucleosynthesis starts
2. The ratio of photons to baryons
3. The actual baryon density

Element Production beyond helium:

• Lithium/Boron Production
• It stops at Boron