General Relativity and Quantum Cosmology (gr-qc)

Abstract: In this paper, we investigate the existence of asymptotically flat wormhole geometries within the framework of Rastall-Rainbow modified gravity, a synthesis of two distinct theoretical models: Rastall theory and the Rainbow description. Our study uncovers that, when considering specific combinations of free parameters and equations of state, the emergence of static and spherically symmetric wormholes is not feasible within a zero-tidal-force context. By considering the subset of viable solutions, we conduct a rigorous assessment of their stability through adiabatic sound velocity analysis and scrutinize their compliance with the Weak Energy Condition (WEC). In summary, our inquiry provides insights into how the interplay between Rastall parameters and Rainbow functions may alleviate violations of energy conditions in these modified gravity scenarios.

Abstract: We obtain the closed form expression for the metric perturbation around de Sitter spacetime generated by a matter source below Hubble scale both in generalized harmonic gauge and in Bondi gauge up to quadrupolar order in the multipolar expansion, including both parities (i.e. both mass and current quadrupoles). We demonstrate that such a source causes a displacement memory effect close to future infinity that originates, in the even-parity sector, from a $\Lambda$-BMS transition between the two non-radiative regions of future infinity.

Abstract: In this paper we study quantum field theory in impulsive plane wave spacetimes. We first analyze the geodesics and the formation of conjugate planes in these spacetimes. The behaviors of the world function and the van Vleck determinant near conjugate plane are also considered. For the quantum field, we work out the mode functions, their Bogoliubov transformations, and the construction of the Wightman functions. By examining the Wightman function near and on the conjugate plane, we show how the twofold and fourfold singularity structure of the Wigthman function arise when crossing this plane. Lastly, we come to the stochastic gravity noise kernel which is also the correlation function of the stress energy tensor of the quantum field. Its explicit form is given in terms of the world function and the van Vleck determinant. We investigate its limits for small and large geodesic distances. The leading divergent term of the noise kernel on the conjugate plane are expressed in terms of derivatives of delta functions. Similar to that of the Wightman functions, we also examine how the singularity structure of the noise kernel near the lightcone changes when crossing the conjugate plane.

Abstract: The Hubble constant is one of the most important parameters in cosmology. Discrepancies in values of the Hubble constant estimated from various measurements, the so-called Hubble tension, are a serious problem. In this paper, we study the effects of small-scale inhomogeneities of structure formation on the measurement of the Hubble constant using the luminosity distance-redshift relation. By adopting the adhesion model in Newtonian cosmology as the model of structure formation, we investigate whether or not the effects of inhomogeneities can be sufficiently large to affect the current observations of the Hubble constant. We show that inappropriate treatment of the effects of inhomogeneities can cause a large deviation of the measured value of the Hubble constant from the background value, whose magnitude is comparable with the Hubble tension. Our main message is the importance of adopting an appropriate model of structure formation to investigate the effects of inhomogeneities. We also add discussion on the spatial averaging approach used to estimate the measured Hubble constant in the inhomogeneous universe.

Abstract: Different extended objects can fall in different ways, depending on their internal structures. Some motions are nevertheless impossible, regardless of internal structure. This paper derives universal constraints on extended-body motion, both in Newtonian gravity and in general relativity. In both theories, we identify a weak notion of "local symmetry" which precludes certain force and torque combinations. Local symmetries imply that certain components of a body's quadrupole moment cannot affect its motion. They also imply that some forces arise only in combination with appropriate torques. Many of these symmetries are shown to be determined by the algebraic structure of the tidal tensor. In general relativity, we thus relate qualitative features of extended-body motion to the Petrov type of the spacetime. Doing so shows that local symmetries are in fact ubiquitous. In general relativity, there are at least two in all algebraically-special spacetimes. Some of these are generated by Killing vectors and some by conformal Killing-Yano tensors. However, many local symmetries do not fall into either of these classes.