Numerical simulations of inflationary dynamics: slow roll and beyond
arXiv (Cornell University)(2022)
Abstract
Numerical simulations of the inflationary dynamics are presented here for a
single canonical scalar field minimally coupled to gravity. We spell out the
basic equations governing the inflationary dynamics in terms of cosmic time t
and define a set of dimensionless variables convenient for numerical analysis.
We then provide a link to our simple numerical Python code on GitHub that can
be used to simulate the background dynamics as well as the evolution of linear
perturbations during inflation. The code computes both scalar and tensor power
spectra for a given inflaton potential V(ϕ). We discuss a concrete
algorithm to use the code for various purposes, especially for computing the
enhanced scalar power spectrum in the context of Primordial Black Holes and
scalar-induced Gravitational Waves. We also compare the efficiency of different
variables used in the literature to compute the scalar fluctuations. We intend
to extend the framework to simulate the dynamics of a number of different
quantities, including the computation of scalar-induced second-order tensor
power spectrum in the near future.
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Key words
inflationary dynamics,numerical simulations,slow-roll
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