On Brane Inflation Potentials and Black Hole Attractors

TL;DR

This paper introduces a novel arctangent-based potential for brane inflation, demonstrating its ability to reproduce known models and connect black hole attractor mechanisms with inflationary dynamics in a unified framework.

Contribution

It proposes a new inflation potential that unifies small and large field behaviors and links black hole attractors to brane inflation.

Findings

Reproduces chaotic and MSSM potentials in small field limit

Enables black hole attractor interpretation of Friedmann equations

Provides explicit inflationary quantity computations

Abstract

We propose a new potential in brane inflation theory, which is given by the arctangent of the square of the scalar field. Then we perform an explicit computation for inflationary quantities. This potential has many nice features. In the small field approximation, it reproduces the chaotic and MSSM potentials. It allows one, in the large field approximation, to implement the attractor mechanism for bulk black holes where the geometry on the brane is de Sitter. In particular, we show, up to some assumptions, that the Friedman equation can be reinterpreted as a Schwarzschild black hole attractor equation for its mass parameter.