# Inflation from $(R+\gamma R^n-2\Lambda)$ Gravity in Higher Dimensions

## TL;DR

This paper derives an inflaton potential from higher-dimensional modified gravity theories, linking extra-dimensional parameters to observable inflationary predictions, including the tensor-to-scalar ratio in the CMB.

## Contribution

It introduces a method to obtain the inflaton potential from $(R+ ext{gamma} R^n - 2 ext{Lambda})$ gravity in higher dimensions, establishing conditions on parameters and connecting them to inflation observables.

## Key findings

- Consistency requires n=D/2 and D to be a multiple of four.
- Derived inflaton potentials for D=8 and D=12.
- Predicts observable tensor-to-scalar ratio r in CMB.

## Abstract

We propose a derivation of the inflaton scalar potential from the higher $(D)$ dimensional $(R+\gamma R^n-2\Lambda)$ gravity, with the new coupling constant $\gamma$ and the cosmological constant $\Lambda$. We assume that a compactification of extra dimensions happened before inflation, so that the inflaton scalar potential in four spacetime dimensions appears to be dependent upon the parameters $(\gamma,\Lambda ,D,n)$. We find that consistency requires $n=D/2$, while the dimension $D$ has to be a multiple of four. We calculate the potential for any $D$, and determine the values of $\gamma$ and $\Lambda$ from observations. The cases of $D=8$ and $D=12$ are considered in more detail. Our approach results in the viable models of chaotic large-field inflation, and leads to the sharp predictions of an observable value of the tensor-to-scalar ratio $r$ of the Cosmic Microwave Background radiation.