Mathematics – Probability
Scientific paper
Jun 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvd..39.3568h&link_type=abstract
Physical Review D (Particles and Fields), Volume 39, Issue 12, 15 June 1989, pp.3568-3570
Mathematics
Probability
24
Particle-Theory And Field-Theory Models Of The Early Universe
Scientific paper
We directly solve the Langevin equation of motion for a scalar field in the slow-roll limit for a λφ4/4 potential. The probability distribution for the inflaton and several moments of the distribution are also calculated. An upper bound to the percentage deviation of the mean of the distribution from the classical value is also derived. For the case of an initially uniform field, non-Gaussian features only appear when the inflaton deviates from the classical value by more than ~λ-1/2 standard deviations. We also show that in the non-Gaussian regime the slow-roll Langevin equation of motion is no longer adequate.
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