Braneworld cosmology in $f(\mathbb{Q})$ gravity

TL;DR

This paper explores thick brane cosmology within $f( ext{ extbf{Q}})$ gravity, showing that cosmic acceleration can arise from bulk geometry without a fundamental cosmological constant, and analyzing various cosmological scenarios.

Contribution

It introduces a novel $f( ext{ extbf{Q}})$ gravity framework for brane cosmology, demonstrating natural emergence of effective cosmological constants and diverse cosmic behaviors from bulk geometry.

Findings

Accelerated expansion solutions without a fundamental cosmological constant

Effective cosmological constant arises from bulk geometry

Different cosmological scenarios achieved by varying parameters

Abstract

This work investigates the cosmology of a thick brane within the context of $f(\mathbb{Q})$ gravity, an extension of symmetric teleparallelism. Using a five-dimensional Friedmann-Lema\^itre-Robertson-Walker metric, we solve the field equations to obtain dynamic solutions for the scale factor. We demonstrate that the effective cosmological constant on the brane naturally emerges as a function of the extra dimension $\Lambda(y)$, being both generated and confined by the curved geometry of the bulk. We analyze two distinct regimes: Randall-Sundrum-type thin brane and thick brane through the Sine-Gordon model. Our model reproduces accelerated expansion solutions without requiring the introduction of a fundamental cosmological constant on the brane, showing that the cosmic acceleration emerges as a consequence of the brane's embedding and the gravitational dynamics in the bulk . The variation of the $c_i$ parameters in symmetric teleparallelism enables different cosmological scenarios, including de Sitter-type expansion, contraction, and oscillatory solutions. The results indicate that the brane's position in the bulk determines its cosmology, providing a geometric explanation for the smallness of the observed cosmological constant.