General Relativity And Quantum Cosmology

In this paper, we study the impact of non-trivial sound on the evolution of cosmological complexity in inflationary period. The vacuum state of curvature perturbation could be treated as squeezed states with two modes, characterized by the two most essential parameters: angle parameter ? k and squeezing parameter r k . Through Schr o ¨ dinger equation, one can obtain the corresponding evolution equation of ? k and r k . Subsequently, the quantum circuit complexity between a squeezed vacuum state and squeezed states are evaluated in scalar curvature perturbation with a type of non-trivial sound speed. Our results reveal that the evolution of complexity at early times shows the rapid solution comparing with c S =1 , in which we implement the resonant sound speed with various values of ξ . In these cases, it shows that the scrambling time will be lagged with non-vanishing ξ . Further, our methodology sheds a new way of distinguishing various inflationary models.

The present work investigates the dissipation of configurational entropy in some of the most widely studied Chaplygin gas models, such as the generalized Chaplygin gas and the modified Chaplygin gas, and communicate the existence of a wide range of parameter space which gives rise to a viable dissipation of configurational entropy, and therefore certifying its time derivative to hit a minimum at a scale factor which complies with the current observational constraints on the redshift of transition from a dust to an accelerated Universe.

In these lectures my aim is to review enough of conformal differential geometry in four dimensions to give an account of Penrose's conformal cyclic geometry.

We construct a conformal scattering theory for Dirac fields in the interior of a Reissner-Nordström-like black hole, between the black hole event horizon and the Cauchy horizon. The main result is a resolution of the characteristic Cauchy problem for the Dirac equation on the horizons by solving a system of wave equations and re-interpreting its solution as the components of the required Dirac solution.

We consider two consecutive conformally flat eons in Penrose's Conformal Cyclic Cosmology and study how the perfect fluid matter content of the past eon determines the matter content of the present eon by means of Penrose's reciprocity hypothesis.

We investigate a form of f(R)= R 1+δ / R δ c and study the viability of the model for inflation in the Jordan and the Einstein frames. This model is further analysed by using the power spectrum indices of the inflation and the reheating temperature. During the inflationary evolution, the model predicts a value of δ parameter very close to one ( δ=0.98 ), while the reheating temperature T re ∼ 10 17 GeV at δ=0.98 is consistent with the standard approach to inflation and observations. We calculate the slow roll parameters for the minimally coupled scalar field within the framework of our model. It is found that the values of the scalar spectral index and tensor-to-scalar ratio are very close to the recent observational data, including those released by Planck 2018. We also show that the Jordan and the Einstein frames are equivalent when δ∼1 by using the scalar spectral index, tensor-to-scalar ratio and reheating temperature.

The recent observation of the shadow of the supermassive compact object M87 ??by the Event Horizon Telescope (EHT) collaboration has opened up a new window to probe the strong gravity regime. In this paper, we study shadows cast by two viable alternatives to the Kerr black hole, and compare them with the shadow of M87 ??. The first alternative is a horizonless compact object (HCO) having radius r 0 and exterior Kerr geometry. The second one is a rotating generalisation of the recently obtained one parameter ( r 0 ) static metric by Simpson and Visser. This latter metric, constructed by using the Newman-Janis algorithm, is a special case of a parametrised rotating non-Kerr geometry obtained by Johannsen. Here, we constrain the parameter r 0 of these alternatives using the results from M87 ??observation. We find that, for the mass, inclination angle and the angular diameter of the shadow of M87 ??reported by the EHT collaboration, the maximum value of the parameter r 0 must be in the range 2.54 r + ??r 0,max ??.51 r + for the dimensionless spin range 0.5??a ????.94 , with r + being the outer horizon radius of the Kerr black hole at the corresponding spin value. We conclude that these black hole alternatives having r 0 below this maximum range (i.e. r 0 ??r 0,max ) is consistent with the size and deviation from circularity of the observed shadow of M87 ??.

We perform a new test of general relativity (GR) with signals from GWTC-2, the LIGO and Virgo catalog of gravitational wave detections. We search for the presence of amplitude birefringence, in which left versus right circularly polarized modes of gravitational waves are exponentially enhanced and suppressed during propagation. Such an effect is present in various beyond-GR theories but is absent in GR. We constrain the amount of amplitude birefringence consistent with the data through an opacity parameter κ , which we bound to be κ??.74 Gpc ?? . We then use these theory-agnostic results to constrain Chern-Simons gravity, a beyond-GR theory with motivations in quantum gravity. We bound the canonical Chern-Simons lengthscale to be ??0 ??.0? 10 3 km, improving on previous long-distance measurement results by a factor of two.

We study the imprint that certain quantization ambiguities may leave in effective regimes of the hybrid loop quantum description of cosmological perturbations. More specifically, in the case of scalar perturbations we investigate how to reconstruct the Mukhanov-Sasaki field in the effective regime of Loop Quantum Cosmology, taking as starting point for the quantization a canonical formulation in terms of other perturbative gauge invariants that possess different dynamics. In this reconstruction, we impose that the effective Mukhanov-Sasaki equations adopt a similar form and display the same Hamiltonian structure as the classical ones. The restrictions that result from this condition are used to constrain ambiguities that arise in the quantization process. Such ambiguities affect the quantum representation of certain Poisson brackets that appear in the Hamiltonian constraint of the system, and their effects on the Mukhanov-Sasaki equations reflect the different Hamiltonian evolution of the homogeneous cosmological background that is found in the effective regime of Loop Quantum Cosmology compared to the classical trajectories. Our analysis constitutes an important step to trascend the effective description and put forward quantization prescriptions with satisfactory physical results.

This article is dedicated to the use the MICROSCOPE mission's data to test chameleon theory of gravity. We take advantage of the technical sessions aimed to characterize the electrostatic stiffness of MICROSCOPE's instrument intrinsic to its capacitive measurement system. Any discrepancy between the expected and measured stiffness may result from unaccounted-for contributors, i.e. extra-forces. This work considers the case of chameleon gravity as a possible contributor. It was previously shown that in situations similar to these measurement sessions, a chameleon fifth force appears and acts as a stiffness for small displacements. The magnitude of this new component of the stiffness is computed over the chameleon's parameter space. It allows us to derive constraints by excluding any force inconsistent with the MICROSCOPE data. As expected --since MICROSCOPE was not designed for the purpose of such an analysis--, these new bounds are not competitive with state-of-the-art constraints, but they could be improved by a better estimation of all effects at play in these sessions. Hence our work illustrates this novel technique as a new way of constraining fifth forces.