Inflationary epoch

Measurements of the CMB anisotropy made in the last 5 years have moved cosmology into a new era of precise parameter determination and the ability to probe the conditions during the inflationary epoch. These results depend on the study of perturbations that are still in the linear, small amplitude regime, and thus are not confounded by non-linearities and the difficulties associated with hydrodynamics. 

Since during its evolution beyond the horizon, any dynamical change in the fluctuation spectra was causally forbidden, the fluctuating gravitational field experienced by the recombining hydrogen atoms was directly related to the fluctuation spectra of the inflationary epoch, determined by the quantum fluctuations of the field(s) of that era. This observation leads promptly to the conclusion that the spectra should be very close to the ZeTdovich-Harrison spectra. Detailed features of the power spectra seem to effectively rule out some of the concurrent inflationary models. 

Concluding, it becomes a more and more established fact that the chemical elements formed from baryonic matter contribute less than 5% to the total energy density of the present Universe. In view of the complete symmetry of laws governing matter and antimatter in our present-day Universe it is actually a rather nontrivial fact that baryonic matter did not completely annihilate into radiation in the hot Universe directly after the inflationary epoch and also that the original energy density was transformed into a high-temperature gas of ordinary elementary particles. 

Before continuing the study of the dynamics of the inflationary phase, let us focus on one specific example of inflationary scenario chaotic inflation. Historically, this was not the first model that was proposed but we think it was the first to provide a satisfactory scenario. The main difficulty with inflation is to have the slow roll conditions to be satisfied at some epoch. Indeed, as we saw, one need to put the field away from the minimum of its potential for the inflaton to behave like a cosmological constant. The first inflationary model ( Guth 1981) supposed a potential like that of Eq. (7.28) where the field slowly moved away from its minimum because of a phase transition. However, this led to a number of difficulties, see for example Ref. (Liddle Lyth). Fortunately, it was soon realized that it was not necessary to have a time dependent potential for inflation to proceed. Linde (Linde 1985) noticed that inflation could start as soon as the Universe would exit the Planck era. The idea was that it is reasonable to suppose that at the end of the Planck era (when p > ), no large-scale correlation could be expected in the scalar field, so that one could expect very irregular (hence, chaotic) initial condition with... 

Figure 16.8. Relic density of gravitationally-produced WIMPZILLAs as a function of their mass Mx Hi is the Hubble parameter at the end of inflation, 1 i, is the reheating temperature, and Mpi 3 x 1019 GeV is the Planck mass. The dashed and solid lines correspond to inflationary models that smoothly end into a radiation or matter dominated epoch, respectively. The dotted line is a thermal distribution at the temperature indicated. Outside the thermalization region WIMPZILLAs cannot reach thermal equilibrium. (Figure from Chung, Kolb Riotto (1998).)...

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