Emel Altas, Bayram Tekin

Starting from a divergence-free rank-four tensor whose trace is the cosmological Einstein tensor, we give a construction of conserved charges in Einstein's gravity and its higher derivative extensions for asymptotically anti-de Sitter ($AdS$) spacetimes. The current yielding the charge is explicitly gauge-invariant and the charge expression involves the linearized Riemann tensor at the boundary. Hence to compute the mass and angular momenta in these spacetimes, one just needs to compute the linearized Riemann tensor. We give two examples.

Stefano Anselmi, Pier-Stefano Corasaniti, Ariel G. Sanchez, Glenn D. Starkman, Ravi K. Sheth, Idit Zehavi

Leveraging the Baryon Acoustic Oscillations (BAO) feature present in clustering 2-point statistics, we aim to measure cosmological distances independently of the underlying background cosmological model. However this inference is complicated by late-time non-linearities that introduce model and tracer dependencies in the clustering correlation function and power spectrum, which must be properly accounted for. With this in mind, we introduce the "Purely-Geometric-BAO," which provides a rigorous tool to measure cosmological distances without assuming a specific background cosmology. We focus on the 2-point clustering correlation function monopole, and show how to implement such an inference scheme employing two different methodologies: the Linear Point standard ruler (LP) and correlation-function model-fitting (CF-MF). For the first time we demonstrate how, by means of the CF-MF, we can measure very precisely the sound-horizon/isotropic-volume-distance ratio, $r_{d}/D_{V}(\bar{z})$, while correctly propagating all the uncertainties. Using synthetic data, we compare the outcomes of the two methodologies, and find that the LP provides up to $50\%$ more precise measurements than the CF-MF. Finally, we test a procedure widely employed in BAO analyses: fitting the 2-point function while fixing the cosmological and the non-linear-damping parameters at fiducial values. We find that this underestimates the distance errors by nearly a factor of $2$. We thus recommend that this practice be reconsidered, whether for parameter determination or model selection.

Luca Buoninfante, Gaetano Lambiase, Luciano Petruzziello, Antonio Stabile

In this paper, we study the Casimir effect in a curved spacetime described by pure gravitational actions quadratic in the curvature. In particular, we consider the dynamics of a massless scalar field confined between two nearby plates and compute the corresponding mean vacuum energy density and pressure in the framework of quadratic theories of gravity. Since we are interested in the weak-field limit, as far as the gravitational sector is concerned we work in the linear regime. Remarkably, corrections to the flat spacetime result due to extended models of gravity (although very small) may appear at the first-order of our perturbative analysis, whereas general relativity contributions start appearing at the second order. Future experiments on the Casimir effect might represent a useful tool to test and constrain extended theories of gravity.