Mathematics – Probability
Scientific paper
Jan 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..43..362i&link_type=abstract
Physical Review D, Vol. 43, No. 2, p. 362 - 368
Mathematics
Probability
12
Scientific paper
The authors solve the stochastic evolution equations for the inflation field during the slow-roll period of chaotic inflation. They find exact analytic solutions for the V(Φ) = λΦ4/4 potential. The authors provide an explicit demonstration of the dependence of the solutions on the interpretation of the random noise. The resulting probability distributions are sharply peaked around the classical deterministic trajectory and are almost Gaussian. The exact probability distributions show that the skewness is very sensitively dependent on λ and also weakly dependent on initial and final conditions. The number of effective standard deviations, N, required for significant non-Gaussian effects is given by N > cλ-1/6 where the constant c (>10-2) is determined by initial and final conditions. The current constraint on λ (<≡5×10-14) for adiabatic fluctuations makes non-Gaussian effects very small. Improved constraints on λ can completely rule out any significant non-Gaussian effects in inflation-generated adiabatic fluctuations.
Insu Yi
Mineshige Shin
Vishniac Ethan T.
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