Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity

TL;DR

This paper presents an analytic hyperscaling violating solution in a coupled dilaton and squared curvature gravity model, analyzing parameter constraints and perturbations to address IR singularities.

Contribution

It introduces a new hyperscaling violating solution with a specific dilaton-curvature coupling, extending previous models to non-zero hyperscaling parameters.

Findings

Derived an analytic hyperscaling violating solution with non-zero θ.

Identified parameter regions satisfying energy and stability conditions.

Studied perturbations around AdS geometries to resolve IR singularities.

Abstract

Considering a model with Coupled Dilaton-Squared Curvature terms and a dilatonic potential which replace the cosmological constant, we present an analytic hyperscaling violating solution which is the generalization of arXiv:1305.3279 for non zero $\theta$. We show that a specific coupling between dilaton and the squared curvature terms produces a simple logarithmic behavior for the dilaton. By imposing the null energy condition and stability constraints, we investigate the allowed regions for the parameters of this model. We then study the perturbations around $\mathrm{AdS_4} $ in the UV and $\mathrm{\mathrm{AdS}_2\times \mathbb{R}^2} $ in the IR of the Einstein-Weyl gravity which can support an intermediate hyperscaling violating solution in order to resolve the $\mathrm{IR} $ singularity of the metric in 4d.