Inflationary models with a quadratic relationship between the parameters of cosmological perturbations

TL;DR

This paper introduces a new inflationary model with a quadratic relationship between perturbation parameters, derived from a specific scalar field evolution, and validated against observational data using machine learning techniques.

Contribution

It proposes a novel approach to construct inflation models based on scalar field evolution dependence on e-folds, including a new exponential potential model consistent with observations.

Findings

Model obeys quadratic law between perturbation parameters

New inflation model with exponential potential aligns with observational constraints

Comparison with machine learning solutions supports model validity

Abstract

An approach to construct cosmological inflation models on the basis of a certain dependence of the scalar field evolution on the e-folds number is considered. The reconstruction of the model background parameters according to the kind of specific connection between the parameters of cosmological perturbations is proposed. By the slow-roll approximation, as functions of the e-fold number, the scalar field potential and the Hubble parameter are determined. The logarithmic dependence between the scalar field evolution and the number of e-folds is investigated as the example. The derived model was found to obey a quadratic law between the parameters of cosmological perturbations. On the basis of suggested approach, a new cosmological inflation model with an exponential potential is proposed. This complies with existing observational constraints for both background and perturbation spectrum parameters. A comparison of obtained results with the solutions obtained by the symbol regression is made. The restrictions for arbitrary parameters in the model with logarithmic potential are also considered. The proposed form of the scalar field potential is consistent with one of the optimal potentials obtained when using machine learning methods to analyze the correspondence of inflationary models to observational data and gravitational waves contribution to the anisotropy and polarization of the CMB.