General Relativity and Quantum Cosmology (gr-qc)

Abstract: We show that a three rank Lanczos type tensor field is an appropriate choice to describe relativistic electromagnetic and gravitational effects. More precisely, we identify the irreducible field-decompositions of this tensor as gravitational and electromagnetic fields. A set of divergence equations are proposed as field equations.

Abstract: We discuss the problem of canonical quantization of a free massive spinor field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the internal region of the black hole, the canonical commutation relations in the resulting theory hold exactly and the Hamiltonian has the standard form. Spin sums are obtained for solutions of the Dirac equation in the Schwarzschild spacetime.

Abstract: General Relativity (GR) and Unimodular Gravity (UG) provide two equivalent descriptions of gravity that differ in the nature of the cosmological constant. While GR is based on the group of diffeomorphisms that permits the cosmological constant in the action, UG is based on the subgroup of volume-preserving diffeomorphisms together with Weyl transformations which forbid the presence of the cosmological constant. However, the cosmological constant reappears in UG as an integration constant so it arises as a global degree of freedom. Since gauge symmetries are simply redundancies in our description of physical systems, a natural question is whether there exists a "parent theory" with the full diffeomorphisms and Weyl transformations as gauge symmetries so that it reduces to GR and UG respectively by performing suitable (partial) gauge fixings. We will explore this question by introducing Stueckelberg fields both in GR and UG to complete the gauge symmetries in each theory to that of the would-be parent theory. Despite the dynamical equivalence of the two theories, we find that precisely the additional global degree of freedom provided by the cosmological constant in UG obstructs the construction of the parent theory.

Abstract: Space-borne gravitational wave detectors can detect sources like the merger of massive black holes. The rapid identification and localization of the source would play a crucial role in multi-messenger observation. The geocentric orbit of the space-borne gravitational wave detector, TianQin, makes it possible to conduct real-time data transmission. In this manuscript, we develop a search and localization pipeline for massive black hole binaries with TianQin, under both regular and real-time data transmission modes. We demonstrate that with real-time data transmission, it is possible to accurately localize the massive black hole binaries on-the-fly. With the approaching of the merger, the localization rapidly shrinks, and the data analysis can be finished at a speed comparable to the data downlink speed.

Abstract: During the last three years the pulsar timing arrays reported a series of repeated evidences of gravitational radiation (with stochastically distributed Fourier amplitudes) at a benchmark frequency of the order of $30$ nHz and characterized by spectral energy densities (in critical units) ranging between $10^{-8}$ and $10^{-9}$. While it is still unclear whether or not these effects are just a consequence of the pristine variation of the space-time curvature, the nature of the underlying physical processes would suggest that the spectral energy density of the relic gravitons in the nHz domain may only depend on the evolution of the comoving horizon at late, intermediate and early times. Along this systematic perspective we first consider the most conventional option, namely a post-inflationary modification of the expansion rate. Given the present constraints on the relic graviton backgrounds, we then show that such a late-time effect is unable to produce the desired hump in the nHz region. We then analyze a modified exit of the relevant wavelengths as it may happen when the gravitons inherit an effective refractive index from the interactions with the geometry. A relatively short inflationary phase leads, in this case, to an excess in the nHz region even if the observational data coming from competing experiments do not pin down exactly the same regions in the parameter space. We finally examine an early stage of increasing curvature and argue that it is not compatible with the observed spectral energy density unless the wavelengths crossing the comoving horizon at early times reenter in a decelerated stage not dominated by radiation.

Abstract: In this article we extend an axion F(R) gravity model, and apply the holographic principle to describe in a unifying manner the early and the late-time universe when the general equation of state (EoS) contains a bulk viscosity. We assume a spatially flat Friedmann-Robertson-Walker (FRW) universe model. We use a description based on the generalized infrared-cutoff holographic dark energy proposed by Nojiri and Odintsov (2006, 2017), and explore the evolution of the universe when the EoS describes the asymptotic behavior between the dust in the early universe and the late universe. We explore various forms of the bulk viscosity, and calculate analytical expressions for the infrared cutoffs in terms of the particle horizon. In this way we obtain a unifying description of the early and the late-time universe in the presence of axion matter, via a viscous holographic fluid model.

Abstract: The number of gravitational wave signals from the merger of compact binary systems detected in the network of advanced LIGO and Virgo detectors is expected to increase considerably in the upcoming science runs. Once a confident detection is made, it is crucial to reconstruct the source's properties rapidly, particularly the sky position and chirp mass, to follow up on these transient sources with telescopes operating at different electromagnetic bands for multi-messenger astronomy. In this context, we present a rapid parameter estimation (PE) method aided by mesh-free approximations to accurately reconstruct properties of compact binary sources from data gathered by a network of gravitational wave detectors. This approach builds upon our previous algorithm (Pathak et al.\cite{pathak2022rapid}) to expedite the evaluation of the likelihood function and extend it to enable coherent network PE in a ten-dimensional parameter space, including sky position and polarization angle. Additionally, we propose an optimized interpolation node placement strategy during the start-up stage to enhance the accuracy of the marginalized posterior distributions. With this updated method, we can estimate the properties of binary neutron star (BNS) sources in approximately 2.4~(2.7) minutes for the \TaylorF~(\texttt{IMRPhenomD}) signal model by utilizing 64 CPU cores on a shared memory architecture. Furthermore, our approach can be integrated into existing parameter estimation pipelines, providing a valuable tool for the broader scientific community.