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1.2. Thermal history of the Universe and the CMBR

The origins of the CMBR lie in an early hot phase of the expansion of the Universe, where the details of its generation are erased by the close coupling of radiation and matter. Later energy releases, interactions with matter at different temperatures, and other effects can modify the spectrum and brightness distribution of the CMBR. Cosmological data on the gross properties of the Universe are contained in the integrated properties of the CMBR, such as the spectrum and the large-scale brightness structure. Detailed information about the properties and formation of present-day objects, such as clusters of galaxies, is encoded in the small-scale structures in the brightness.

A critical stage in the development of the CMBR occurs when the expansion of the Universe causes the temperature to drop to about 3000 K. At earlier times (higher redshifts), matter and radiation were in good thermal contact because of the abundance of free electrons. But at this stage the number of free electrons drops rapidly as matter becomes neutral, and the radiation and matter become thermally decoupled, so that the temperatures of the photon and matter fluids evolve almost independently. We can distinguish three events that occur at almost the same time: the non-relativistic and relativistic (photon plus neutrino) mass densities are equal at redshift

Equation 3 (3)

most electrons have become bound to ions at the redshift of recombination,

Equation 4 (4)

and the interaction length of photons and electrons exceeds the scale of the Universe at the redshift of decoupling

Equation 5 (5)

(approximate forms taken from Kolb & Turner 1990). In these relations, Omega0 is the present-day mass density of the Universe, and OmegaB is the present-day baryon density, both in units of the critical density, rhocrit (equation 2). The redshifts of recombination and decoupling are similar, and neither phenomenon is sharply-defined, so that there was a moderately broad redshift range from 1500 to 1000 (about 1.6 x 105 (Omega0 h1002)-1/2 years after the Big Bang) when the Universe was becoming neutral, matter-dominated, and transparent to radiation. At some time about then, most of the photons that are now in the cosmic background radiation were scattered by electrons for the last time, and we often refer to a sphere of last scattering or redshift of last scattering at this epoch.

One of the important changes that occurred during this period, because of the change in the interactions of photons and electrons, was that the length scale on which gravitational collapse can occur dropped dramatically, so that fluctuations in the mass density that were stabilized by the radiation field before recombination became unstable after recombination, and were able to collapse (slowly - the expansion of the Universe causes the collapse of gravitationally bound objects to be power-law rather than exponential in time: Landau & Lifshitz 1962; see descriptions in Kolb & Turner 1990). Matter over-densities and under-densities present at recombination, and which later became the large-scale objects that we see in the present-day Universe, such as clusters of galaxies, caused fluctuations in the intensity of the radiation field through their gravitational perturbations (the Sachs-Wolfe effect; Sachs & Wolfe 1967), through thermodynamic fluctuations in the density of radiation coupled to the matter, and through Doppler shifts due to motions of the surface of last scattering. Recent reviews of the introduction of primordial structure in the CMBR by objects near recombination are given by Bond (1995) and White et al. (1994).

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