Stochastic Inflation and Inflationary Density Fluctuations

Details Stochastic Inflation and Inflationary Density Fluctuations Stochastic Inflation and Inflationary Density Fluctuations

Jan 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt........18y&link_type=abstract

Thesis (PH.D.)--THE UNIVERSITY OF TEXAS AT AUSTIN, 1992.Source: Dissertation Abstracts International, Volume: 53-08, Section: B,

Mathematics

Logic

Cosmology

Scientific paper

We examine the stochastic dynamics of chaotic inflation. The nonlinear stochastic behavior of inflation is studied with an emphasis on possible non-Gaussian statistics in initial conditions for cosmological large scale structure formation. Large scale non-random phase correlations and interesting dynamical features are analyzed using stochastic dynamics. We solve the stochastic evolution equations for the inflation field during the slow-roll period of chaotic inflation. We find exact analytic solutions for the quartic potential. Although the resulting statistics of the scalar field fluctuations are non-Gaussian, the current cosmic microwave constraint on the strength of the self-coupling for adiabatic fluctuations makes non -Gaussian effects negligibly small. Coarse-grained (long wavelength) scalar fields in stochastic dynamics become nonlinear stochastic variables whose stochastic random evolution is derived from generation and addition of short wave-length quantum noises. The interplay between the classical roll-down and quantum fluctuations makes the evolution of the scalar fields nonclassical. Only during the very late stage of inflation do the fields acquire their classical interpretation. The statistics of initial conditions for cosmological density fluctuations depend on the details of scalar field dynamics during inflation. We point out that initial conditions for large scale structure in inflationary scenarios with the simplest models are Gaussian to a high precision. However, as we consider more finely tuned models of inflation designed to yield special power spectra, Gaussian initial conditions should not be taken for granted, even on astrophysically interesting scales. We use stochastic dynamics to examine the probability of successful inflation from various initial conditions at the Planck epoch. The slow-roll stochastic framework is extended to non-slow-roll evolution. The well-known classical slow-roll attractors exist even when large quantum fluctuations are included. However, a significant fraction of the initial condition phase space which leads to a successful inflationary stage in the classical analysis fails to inflate.

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