General Relativity And Quantum Cosmology

We search for gravitational-wave signals produced by cosmic strings in the Advanced LIGO and Virgo full O3 data set. Search results are presented for gravitational waves produced by cosmic string loop features such as cusps, kinks and, for the first time, kink-kink this http URL template-based search for short-duration transient signals does not yield a detection. We also use the stochastic gravitational-wave background energy density upper limits derived from the O3 data to constrain the cosmic string tension, Gμ , as a function of the number of kinks, or the number of cusps, for two cosmic string loop distribution models.cAdditionally, we develop and test a third model which interpolates between these two models. Our results improve upon the previous LIGO-Virgo constraints on Gμ by one to two orders of magnitude depending on the model which is tested. In particular, for one loop distribution model, we set the most competitive constraints to date, Gμ??? 10 ??5 .

Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the construction of explicit symplectic integrators is frequently difficult in general relativity because all variables are inseparable. Moreover, even if two analytically integrable splitting parts exist in a relativistic Hamiltonian, all analytical solutions are not explicit functions of proper time. Naturally, implicit symplectic integrators, such as the midpoint rule, are applicable to this case. In general, these integrators are numerically more expensive to solve than same-order explicit symplectic algorithms. To address this issue, we split the Hamiltonian of Schwarzschild spacetime geometry into four integrable parts with analytical solutions as explicit functions of proper time. In this manner, second- and fourth-order explicit symplectic integrators can be easily made available. The new algorithms are also useful for modeling the chaotic motion of charged particles around a black hole with an external magnetic field. They demonstrate excellent long-term performance in maintaining bounded Hamiltonian errors and saving computational cost when appropriate proper time steps are adopted.

The procedure of the holonomy-flux algebra construction along a piecewise linear path, which consists of a countably infinite number of pieces, is described in this article. The related construction approximates the continuous distribution of the holonomy-flux algebra location along a smooth link arbitrarily well. The presented method requires the densitized dreibein flux and the corresponding operator redefinition. The derived result allows to formulate the gravitational Hamiltonian constraint regularization by applying the Thiemann technique adjusted to a piecewise linear lattice. By using the improved Ashtekar connection holonomy representation, which is more accurate than the one used in canonical loop quantum gravity, the corrections related to the redefined densitized dreibein flux vanish. In this latter case, the Poisson brackets of the continuously distributed holonomy-flux algebra along a link between a pair of nodes are equal to the brackets for these smeared variables located at the nodes.

We present a new regularisation of Euclidean Einstein gravity in terms of (sequences of) graphs. In particular, we define a discrete Einstein-Hilbert action that converges to its manifold counterpart on sufficiently dense random geometric graphs (more generally on any sequence of graphs that converges to the manifold in the sense of Gromov-Hausdorff). Our construction relies crucially on the Ollivier curvature of optimal transport theory. Our methods also allow us to define an analogous discrete action for Klein-Gordon fields. These results may be taken as the basis for a combinatorial approach to quantum gravity where we seek to generate graphs that approximate manifolds as metric-measure structures.

We present an analytical model for the evolution of brown dwarfs in quadratic Palatini f(R) gravity. We improve previous studies by adopting a more realistic description of the partially-degenerate state that characterizes brown dwarfs. Furthermore, we take into account the hydrogen metallic-molecular phase transition between the interior of the brown dwarf and its photosphere. For such improved model, we revise the cooling process of sub-stellar objects.

Whenever an alternative theory of gravity is formulated in a background Minkowski space, the conditions characterizing admissible coordinate systems, in which the alternative theory of gravity may be applied, play an important role. We here propose Lorentz covariant coordinate conditions for the composite theory of pure gravity developed from the Yang-Mills theory based on the Lorentz group, thereby completing this previously proposed higher derivative theory of gravity. The physically relevant static isotropic solutions are determined by various methods, the high-precision predictions of general relativity are reproduced, and an exact black-hole solution with mildly singular behavior is found.

Using computer simulations we study the geometry of a typical quantum universe, i.e. the geometry one might expect before a possible period of inflation. We display it using coordinates defined by means of four classical scalar fields satisfying the Laplace equation with non-trivial boundary conditions. The field configurations reveal cosmic web structures surprisingly similar to the ones observed in the present-day Universe. Inflation might make these structures relevant for our Universe.

We calculate the cosmological complexity under the framework of scalar curvature perturbations for a K-essence model with constant potential. In particular, the squeezed quantum states are defined by acting a two-mode squeezed operator which is characterized by squeezing parameters r k and ? k on vacuum state. The evolution of these squeezing parameters are governed by the Schr o ¨ dinger equation, in which the Hamiltonian operator is derived from the cosmological perturbative action. With aid of the solutions of r k and ? k , one can calculate the quantum circuit complexity between unsqueezed vacuum state and squeezed quantum states via the wave-function approach. One advantage of K-essence is that it allows us to explore the effects of varied sound speeds on evolution of cosmological complexity. Besides, this model also provides a way for us to distinguish the different cosmological phases by extracting some basic informations, like the scrambling time and Lyapunov exponent etc, from the evolution of cosmological complexity.

We construct a cosmological model from the inception of the Friedmann-Lemâitre-Robertson-Walker metric into the field equations of the f(R, L m ) gravity theory, with R being the Ricci scalar and L m being the matter lagrangian density. The formalism is developed for a particular f(R, L m ) function, namely R/16?+(1+?R) L m , with ? being a constant that carries the geometry-matter coupling. Our solutions are remarkably capable of evading the Big-Bang singularity as well as predict the cosmic acceleration with no need for the cosmological constant, but simply as a consequence of the geometry-matter coupling terms in the Friedmann-like equations.

Dimensional analysis shows that the speed of light and Newton's constant of gravitation can be combined to define a quantity F ??= c 4 G N with the dimensions of force (equivalently, tension). Then in any physical situation we must have F physical =f F ??, where the quantity f is some dimensionless function of dimensionless parameters. In many physical situations explicit calculation yields f=O(1) , and quite often f??1 4 . This has lead multiple authors to suggest a (weak or strong) maximum force/maximum tension conjecture. Working within the framework of standard general relativity, we will instead focus on counter-examples to this conjecture, paying particular attention to the extent to which the counter-examples are physically reasonable. The various counter-examples we shall explore strongly suggest that one should not put too much credence into any universal maximum force/maximum tension conjecture. Specifically, fluid spheres on the verge of gravitational collapse will generically violate the weak (and strong) maximum force conjectures. If one wishes to retain any general notion of "maximum force" then one will have to very carefully specify precisely which forces are to be allowed within the domain of discourse.