Brane Cosmology from AdS/BCFT

TL;DR

This paper explores the dynamics of end-of-the-world branes in AdS space, linking holography and cosmology, and introduces new solutions describing universe creation and brane symmetries.

Contribution

It provides a novel analysis of brane dynamics in AdS/BCFT, including a Friedman-like equation, classification of solutions, and connections to Liouville gravity and boost symmetric branes.

Findings

Derived a Friedman-like equation for brane cosmology.

Classified all solutions with constant potential.

Connected brane dynamics to universe creation and Liouville gravity.

Abstract

In this paper, we study the time-dependent dynamics of an end-of-the-world (EOW) brane in AdS with a scalar field localized on the brane. We mainly studied several aspects of holography and cosmology. Standard requirements in the AdS$_{d+1}$/CFT$_d$ lead to a constraint on the conformal dimension in the dS$_d$/CFT$_{d-1}$. We also prove a time-like analog of g-theorem using the null energy condition in the context of AdS$_3$/BCFT$_2$. In the cosmological interpretation, we rewrite the equation of motion of the brane as a Friedman-like equation, which enables us to consider its dynamics in analogy with the ordinal cosmology. And then we classify all possible solutions of the brane when the potential takes a constant value. We find that our brane cosmology model can describe a process of creating a universe via a big-bang. Additionally, we show that when the brane is close to a hyperplane, its effective action is given by a Liouville gravity with a scalar field matter. Finally, we also obtain brane solutions with boost symmetry, which are obtained by analytical continuation of Euclidean branes with a torus topology.