Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity

Understand

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.