# On calculation of the cosmological parameters in exact models of inflation

## TL;DR

This paper presents a method to calculate key cosmological parameters in exact inflation models using the scalar factor, providing formulas that relate these parameters to horizon crossing and comparing results with the slow-roll approximation.

## Contribution

It introduces a novel approach to derive cosmological parameters directly from exact solutions of inflation models, extending beyond the slow-roll approximation.

## Key findings

- Derived formulas for power spectrum and spectral indices in exact models
- Expressed cosmological parameters in terms of scalar factor at horizon crossing
- Compared exact model results with slow-roll approximation outcomes

## Abstract

We discuss a method of calculating the key cosmological parameters on the basis of a selected scale factor by using exact solutions of the background equations. We specify the formulas for calculating the power spectrum, the spectral indices and their ratios, and the ratio of squared amplitudes of scalar and tensor perturbations. We obtain, for the first time, expressions for the basic cosmological parameters in terms of the scalar factor value at the instant of crossing the cosmological horizon. In this case, the cosmological parameters are calculated for a wide class of exact models. They are compared with their analogs derived in the slow-rolling approximation.