Kavli Affiliate: E. P. S. Shellard
| First 5 Authors: Yoann L. Launay, Gerasimos I. Rigopoulos, E. P. S. Shellard, ,
| Summary:
We provide a formulation of Stochastic Inflation in full general relativity
that goes beyond the slow-roll and separate universe approximations. We show
how gauge invariant Langevin source terms can be obtained for the complete set
of Einstein equations in their ADM formulation by providing a recipe for
coarse-graining the spacetime in any small gauge. These stochastic source terms
are defined in terms of the only dynamical scalar degree of freedom in
single-field inflation and all depend simply on the first two time derivatives
of the coarse-graining window function, on the gauge-invariant mode functions
that satisfy the Mukhanov-Sasaki evolution equation, and on the slow-roll
parameters. We validate the efficacy of these Langevin dynamics directly using
an example in uniform field gauge, obtaining the stochastic e-fold number
without the need for a first-passage-time analysis. As well as investigating
the most commonly used gauges in cosmological perturbation theory, we also
derive stochastic source terms for the coarse-grained first-order BSSN
formulation of Einstein’s equations, which enables a well-posed implementation
for 3+1 numerical relativity simulations.
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