# The Inflaton Effective Potential for General $\epsilon$

## TL;DR

This paper derives an analytic approximation for scalar propagators in cosmological backgrounds, enabling calculation of quantum corrections to the inflaton potential and extending Friedmann equations to more general potentials.

## Contribution

It introduces a new analytic approximation for the scalar propagator and extends the Friedmann equations to include potentials dependent on the Hubble and slow roll parameters.

## Key findings

- Computed one-loop quantum corrections to the inflaton potential.
- Extended Friedmann equations for more general potential dependencies.
- Provided a practical method for quantum field calculations in cosmology.

## Abstract

We develop an analytic approximation for the coincidence limit of a massive scalar propagator in an arbitrary spatially flat, homogeneous and isotropic geometry. We employ this to compute the one loop corrections to the inflaton effective potential from a quadratic coupling to a minimally coupled scalar. We also extend the Friedmann equations to cover potentials that depend locally on the Hubble parameter and the first slow roll parameter.