General Relativity And Quantum Cosmology

We study the frequency shift of photons generated by rotating gravitational sources in the framework of curvature based Extended Theories of Gravity. The discussion is developed considering the weak-field approximation. Following a perturbative approach, we analyze the process of exchanging photons between Earth and a given satellite, and we find a general relation to constrain the free parameters of gravitational theories. Finally, we suggest the Moon as a possible laboratory to test theories of gravity by future experiments which can be, in principle, based also on other Solar System bodies.

We select 37 most common and realistic dense matter equation of states to integrate the general relativistic stellar structure equations for static spherically symmetric matter configurations. For all these models, we check the compliance of the acceptability conditions that every stellar model should satisfy. It was found that some of the non-relativistic equation of states violate the causality and/or the dominant energy condition and that adiabatic instabilities appear in the inner crust for all equation of state considered.

We show that the Plebanski-Demianski spacetime persists as a solution of General Relativity when the theory is supplemented with both, a conformally coupled scalar theory and with quadratic curvature corrections. The quadratic terms are of two types and are given by quadratic combinations of the Riemann tensor as well as a higher curvature interaction constructed with a scalar field which is conformally coupled to quadratic terms in the curvature. The later is built in terms of a four-rank tensor S λ? μν that depends on the Riemann tensor and the scalar field, and that transforms covariantly under local Weyl rescallings. Due to the generality of the Plebanski-Demianski family, several new hairy black hole solutions are obtained in this higher curvature model. We pay particular attention to the C-metric spacetime and the stationary Taub-NUT metric, which in the hyperbolic case can be analytically extended leading to healthy, asymptotically AdS, wormhole configurations. Finally, we present a new general model for higher derivative, conformally coupled scalars, depending on an arbitrary function and that we have dubbed Conformal K-essence. We also construct spherically symmetric hairy black holes for these general models.

We calculate the possible interaction between a superconductor and the static Earth's gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg-Landau theory. We try to estimate which are the most favourable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behaviour of high- T c and classical low- T c superconductors with respect to the gravity/superfluid interplay.

A couple of dozen Earth-like planets orbiting M dwarfs have been discovered so far. Some of them have attracted interest because of their potential long-term habitability; such a possibility is currently vigorously debated in the literature. I show that post-Keplerian (pK) orbit precessions may impact the habitability of a fictitious telluric planet orbiting an oblate late-type M dwarf of spectral class M9V with M ??=0.08 M ??at a=0.02au , corresponding to an orbital period P b ??d , inducing long-term variations of the planetary obliquity ε which, under certain circumstances, may not be deemed as negligible from the point of view of life's sustainability. I resume the analytical orbit-averaged equations of the pK precessions, both classical and general relativistic, of the unit vectors S ^ , h ^ of both the planet's spin and orbital angular momenta S,L entering ε , and numerically integrate them by producing time series of the pK changes ?ε(t) of the obliquity. For rapidly rotating M dwarfs with rotational periods of the order of P ????.1??d , the planet's obliquity ε can undergo classical pK large variations ?ε(t) up to tens of degrees over timescales ?t??0??00kyr , depending on the mutual orientations of the star's spin J ??, of S , and of L . Instead, ?ε(t) are ????1.5 ??for the planet b of the Teegarden's Star. In certain circumstances, the M dwarf's oblateness J ??2 should be considered as one of the key dynamical features to be taken into account in compiling budgets of the long-term habitability of rocky planets around fast spinning late M dwarfs. (Abridged)

There are many astrophysical scenarios where extreme mass ratio inspiral (EMRI) binaries can be surrounded by matter distribution. The distribution of mass can affect the dynamical properties (e.g. orbital frequency, average energy radiation rate, etc.) of the EMRI. In this matter distribution, instead of Kepler-Newton potential, one may consider a more general form of potential i.e. power law potential. Moreover, due to the power law potential, the velocity profile of test particles does not fall as much as that predicted by Kepler-Newton potential and this feature of the velocity profile may be observationally important. In this study, we have obtained the first post-Newtonian (1PN) expressions for dynamical quantities and the average energy radiation rate from the circular orbit EMRI which is surrounded by a matter distribution. We show that the energy radiation rate and orbital frequency of EMRI can be significantly different in the presence of power law potential as compared to that in the Kepler-Newton potential, signatures of which may be observed in gravitational waves from EMRI.

Einstein's general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a SO(4) - Yang-Mills theory. In addition to the gauge fields we include a vector field in the vector representation of the gauge group. The gauge - and diffeomorphism - invariant kinetic terms for these fields permit a well-defined euclidean functional integral, in contrast to metric gravity with the Einstein-Hilbert action. The propagators of all fields are well behaved at short distances, without tachyonic or ghost modes. The long distance behavior is governed by the composite metric and corresponds to general relativity. In particular, the graviton propagator is free of ghost or tachyonic poles despite the presence of higher order terms in a momentum expansion of the inverse propagator. This pregeometry seems to be a valid candidate for euclidean quantum gravity, without obstructions for analytic continuation to a Minkowski signature of the metric.

In pregeometry a metric arises as a composite object at large distances. For short distances we investigate a Yang-Mills theory with fermions and vector fields. The particular representation of the vector fields permits to formulate diffeomorphism invariant kinetic terms. Geometry and general relativity emerge at large distances by spontaneous symmetry breaking inducing masses for the gauge bosons. We propose here a model of pregeometry for which the difference between time and space, as reflected by the signature of the metric, arises from spontaneous symmetry breaking of the local SO(4,\, C )-gauge symmetry. For a euclidean metric all fields have a standard propagator at high momenta. Analytic continuation to a Minkowski-metric is achieved by a change of field values. We conjecture that a quantum effective action of this type is consistent with unitarity and well behaved in the short distance limit.

In this paper, we prove precise late-time asymptotics for solutions to the wave equation supported on angular frequencies greater or equal to ??on the domain of outer communications of subextremal Reissner-Nordström spacetimes up to and including the event horizon. Our asymptotics yield, in particular, sharp upper and lower decay rates which are consistent with Price's law on such backgrounds. We present a theory for inverting the time operator and derive an explicit representation of the leading-order asymptotic coefficient in terms of the Newman-Penrose charges at null infinity associated with the time integrals. Our method is based on purely physical space techniques. For each angular frequency ??we establish a sharp hierarchy of r -weighted radially commuted estimates with length 2??5 . We complement this hierarchy with a novel hierarchy of weighted elliptic estimates of length ??1 .

Chaotic inflation is inconsistent with the observational constraint at 68\% CL. Here, we show that the enhancement mechanism with a peak function in the noncanonical kinetic term not only helps the chaotic model V(?)= V 0 ? 1/3 satisfy the observational constraint at large scales but also enhances the primordial scalar power spectrum by seven orders of magnitude at small scales. The enhanced curvature perturbations can produce primordial black holes of different masses and secondary gravitational waves with different peak frequencies. We also show that the non-Gaussianities of curvature perturbations have little effect on the abundance of primordial black holes and energy density of the scalar-induced secondary gravitational waves.