General Relativity And Quantum Cosmology

Singularity theorems constitute a major milestone of relativity. They generated a panoply of fertile lines of research with dazzling physical consequences. (Los teoremas de singularidades constituyen uno de los mayores hitos de la relatividad. Generaron una panoplia de fértiles líneas de investigación con consecuencias físicas deslumbrantes).

The Hubble tension is shown to be solvable, without any free parameter, conceptually and quantitatively, within the approach of modified weak-field General Relativity involving the cosmological constant ? . That approach enables one to describe in a unified picture both the dynamics of dark matter containing galaxies and the accelerated expansion of the Universe, thus defining a {\it local} Hubble constant of a local flow and the {\it global} one. The data on the dark matter content of peculiar galaxy samples are shown to be compatible to that unified picture. Future more refined surveys of galaxy distribution, hierarchical dynamics and flows within the vicinity of the Local group and the Virgo supercluster can be decisive in revealing the possible common nature of the dark sector.

Hydrodynamic self-similar solutions, as obtained by Chi [J. Math. Phys. 24, 2532 (1983)] have been generalized by introducing new variables in place of the old space and time variables. A systematic procedure of obtaining a complete set of solutions has been suggested. The Newtonian analogs of all homogeneous isotropic Friedmann dust universes with spatial curvature k=0,±1 have been given.

We carry on a comprehensive study on static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible application of this kind of fluids requires extreme physical conditions where quantum effects are expected to play an important role. Also, it is found that the fluid distribution cannot fill the region close to the center of symmetry. Such a region may be represented by a vacuum cavity around the center. A suitable definition of mass function, as well as the Tolman mass are explicitly calculated. While the former is positive defined, the latter is negative in most cases, revealing the repulsive nature of gravitational interaction. A general approach to obtain exact solutions is presented and some exact analytical solutions are exhibited.

In Einstein-Gauss-Bonnet gravity, for a group of warped product spacetimes, we get a generalized master equation for the perturbation of tensor type. We show that the "effective metric" or "acoustic metric" for the tensor perturbation equation can be defined even without a static condition. Since this master equation does not depend on the mode expansion, the hyperbolicity and causality of the tensor perturbation equation can be investigated for every mode of the perturbation. Based on the master equation, we study the hyperbolicity and causality for all relavent vacuum solutions of this theory. For each solution, we give the exact hyperbolic condition of the tensor perturbation equations. Our approach can also applied to dynamical spacetimes, and Vaidya spacetime have been investigated as an example.

Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which Cauchy initial data is specified on a three-dimensional spatial hypersurface, and then evolved forwards in time. The Wolfram model offers an inherently discrete formulation of the Einstein field equations as an a priori Cauchy problem, in which Cauchy initial data is specified on a single spatial hypergraph, and then evolved by means of hypergraph substitution rules, with the resulting causal network corresponding to the conformal structure of spacetime. This article introduces a new numerical general relativity code based upon the conformal and covariant Z4 (CCZ4) formulation with constraint-violation damping, with the option to reduce to the standard BSSN formalism if desired, with Cauchy data defined over hypergraphs; the code incorporates an unstructured generalization of the adaptive mesh refinement technique proposed by Berger and Colella, in which the topology of the hypergraph is refined or coarsened based upon local conformal curvature terms. We validate this code numerically against a variety of standard spacetimes, including Schwarzschild black holes, Kerr black holes, maximally extended Schwarzschild black holes, and binary black hole mergers (both rotating and non-rotating), and explicitly illustrate the relationship between the discrete hypergraph topology and the continuous Riemannian geometry that is being approximated. Finally, we compare the results produced by this code to the results obtained by means of pure Wolfram model evolution (without the underlying PDE system), using a hypergraph substitution rule that provably satisfies the Einstein field equations in the continuum limit.

The novel idea is that the undergoing accelerated expansion of the universe happens due to infrared quantum gravity modifications at intermediate astrophysical scales of galaxies or galaxy clusters, within the framework of Asymptotically Safe gravity. The reason is that structures of matter are associated with a scale-dependent positive cosmological constant of quantum origin. In this context, no extra unproven energy scales or fine-tuning are used. Furthermore, this model was confronted with the most recent observational data from a variety of probes, and with the aid of Bayesian analysis, the most probable values of the free parameters were extracted. Finally, the model proved to be statistically equivalent with ? CDM, and thus being able to resolve naturally the concept of dark energy and its associated cosmic coincidence problem.

Strong gravitational lensing is a gravitational wave (GW) propagation effect that influences the inferred GW source parameters and the cosmological environment. Identifying strongly-lensed GW images is challenging as waveform amplitude magnification is degenerate with a shift in the source intrinsic mass and redshift. However, even in the geometric-optics limit, type II strongly-lensed images cannot be fully matched by type I (or unlensed) waveform templates, especially with large binary mass ratios and orbital inclination angles. We propose to use this mismatch to distinguish individual type II images. Using planned noise spectra of Cosmic Explorer, Einstein Telescope and LIGO Voyager, we show that a significant fraction of type II images can be distinguished from unlensed sources, given sufficient SNR ( ??0 ). Incorporating models on GW source population and lens population, we predict that the yearly detection rate of lensed GW sources with detectable type II images is 172.2, 118.2 and 27.4 for CE, ET and LIGO Voyager, respectively. Among these detectable events, 33.1%, 7.3% and 0.22% will be distinguishable via their type II images with a log Bayes factor larger than 10. We conclude that such distinguishable events are likely to appear in the third-generation detector catalog; our strategy will significantly supplement existing strong lensing search strategies.

Cosmological phase transitions are thought to have taken place at the early Universe imprinting their properties on the observable Universe. There is strong evidence that, through the dynamics of a scalar field that lead a second order phase transition, inflation shaped the Universe accounting for the most conspicuous features of the observed Universe. It is shown that inflation has also striking implications for the vacuum energy. Considerations for subsequent second order phase transitions are also discussed.

We accurately approximate the contribution that photons make to the effective potential of a charged inflaton for inflationary geometries with an arbitrary first slow roll parameter ϵ . We find a small, nonlocal contribution and a numerically larger, local part. The local part involves first and second derivatives of ϵ , coming exclusively from the constrained part of the electromagnetic field which carries the long range interaction. This causes the effective potential induced by electromagnetism to respond more strongly to geometrical evolution than for either scalars, which have no derivatives, or spin one half particles, which have only one derivative. For ϵ=0 our final result agrees with that of Allen on de Sitter background, while the flat space limit agrees with the classic result of Coleman and Weinberg.