A crucial hypothesis for Inflation

TL;DR

This paper proposes that during cosmic inflation, the Ricci scalar remains a positive constant, leading to a unique scalar potential that aligns with observational data and relates to Liouville gravity in two dimensions.

Contribution

It introduces a hypothesis that the Ricci scalar is constant during inflation, deriving a unique scalar potential consistent with observations and connecting to Liouville gravity.

Findings

The scalar potential derived matches the known inflationary potential.

The spectral index prediction agrees with experimental data.

In two dimensions, the model is equivalent to Liouville gravity.

Abstract

As is well known there are many different inflationary models that can explain the accelerated expansion occurred in the early Universe. It is possible that there exists a fundamental property of this period that could provide the corresponding field theory. Our hypothesis is that the Ricci scalar should assume a positive constant value during Inflation. Considering a single scalar field that drives the inflationary phase, we obtain uniquely the scalar potential and the coupling term between the scalar field and spacetime geometry. For this potential, that is well known in the inflationary scenario, the theoretical prediction of the spectral index $n_{s}$ is in perfect agreement with the experimental data. Interestingly in two dimensions, our model is equivalent to Liouville gravity.