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

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-Lemaître-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 $Λ(y)$, 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.

Figures (9)

• Figure 1: $\Lambda(y)$ for RS solution ( \ref{['lambdaRS']}) for different values of the parameters $c_i$.
• Figure 2: Scale factor for RS solution (\ref{['b(t)RS1']}), for $b_0=1$, $\frac{A}{A+B}=5/13$ and $C=0.$
• Figure 3: Scale factor for RS solution (\ref{['b(t)RS2']}), for $b_0=1$, $c_1=3/4$, $c_3=5/4$, $c_5=1/2$ and $C=0.$
• Figure 4: Scale factor for RS solution (\ref{['b(t)RS3']}), for $b_0=1$, $c_1=-5/4$, $c_3=1/4$, $c_5=-3/2$ and $C=0.$
• Figure 5: $\Lambda(y)$ of (\ref{['lambdayGordon']}) for different values of the coefficients $c_i$, with $\Lambda^{(5)}=0$.