General Brane Geometries from Scalar Potentials: Gauged Supergravities and Accelerating Universes

TL;DR

This paper develops a unified method to generate broad classes of brane and cosmological solutions in gauged supergravities and higher-dimensional theories using scalar potentials, revealing new geometries and accelerating universe models.

Contribution

It introduces a solution-generating technique based on a single nonlinear ODE for scalar potentials, extending known brane solutions and exploring their cosmological implications.

Findings

Found new brane geometries with multiple horizons.

Constructed accelerating universe solutions with positive cosmological constant.

Connected solutions to 10D supergravity and gauged supergravities.

Abstract

We find broad classes of solutions to the field equations for d-dimensional gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field with non-vanishing potential. Our construction generates these configurations from the solution of a single nonlinear ordinary differential equation, whose form depends on the scalar potential. For an exponential potential we find solutions corresponding to brane geometries, generalizing the black p-branes and S-branes known for the case of vanishing potential. These geometries are singular at the origin with up to two (regular) horizons. Their asymptotic behaviour depends on the parameters of the model. When the singularity has negative tension or the cosmological constant is positive we find time-dependent configurations describing accelerating universes. Special cases give explicit brane geometries for (compact and non-compact) gauged supergravities in various dimensions, as well as for massive 10D supergravity, and we discuss their interrelation. Some examples lift to give new solutions to 10D supergravity. Limiting cases with a domain wall structure preserve part of the supersymmetries of the vacuum. We also consider more general potentials, including sums of exponentials. Exact solutions are found for these with up to three horizons, having potentially interesting cosmological interpretation. We give several additional examples which illustrate the power of our techniques.