Numerical simulations of inflationary dynamics: Slow roll and beyond

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>t</mml:mi> </mml:math> 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(\phi) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> . 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.