# Cosmological Correlations in Power Law Inflation models

## TL;DR

This paper investigates scalar fields with non-minimal coupling in power law inflation, analyzing their infrared behavior, perturbation spectra, and implications for cosmological correlations.

## Contribution

It provides a detailed analysis of infrared limits and perturbation spectra in power law inflation models with non-minimal scalar coupling, highlighting growing modes for negative coupling.

## Key findings

- Infrared two-point functions exhibit growing modes for negative coupling.
- Perturbation spectra show characteristic features influenced by non-minimal coupling.
- Simplified density perturbation calculations elucidate the impact of mode functions.

## Abstract

Scalar field with non-minimal coupling to curvature scalar is studied in Robertson-Walker background. The infrared limit of two point function, and, in turn, of the energy-momentum tensor of scalar field have been considered in the power law inflation model. In this limit, within the perfect fluid model, consistent evolution of scale factor following power law inflation gives rise to growing mode solution for negative value of coupling constant. A simplified calculation for density perturbation in power law inflationary models is presented with these mode functions. Salient features of the perturbation spectra has been commented upon.