Table of contents

The dynamics of an inhomogeneous universe is studied with the methods of loop quantum cosmology, via a so-called hybrid quantization, as an example of the quantization of vacuum cosmological spacetimes containing gravitational waves (Gowdy spacetimes). The analysis of this model with an infinite number of degrees of freedom, performed at the effective level, shows that (i) the initial Big Bang singularity is replaced (as in the case of homogeneous cosmological models) by a Big Bounce, joining deterministically two large universes, (ii) the universe size at the bounce is at least of the same order of magnitude as that of the background homogeneous universe and (iii) for each gravitational wave mode, the difference in amplitude at very early and very late times has a vanishing statistical average when the bounce dynamics is strongly dominated by the inhomogeneities, whereas this average is positive when the dynamics is in a near-vacuum regime, so that statistically the inhomogeneities are amplified.

Recently, a mechanism for relaxing a large cosmological constant (CC) has been proposed by Bauer et al (2009 Phys. Lett. B 678 427), which permits solutions with low Hubble rates at late times without fine-tuning. The setup is implemented in the ΛXCDM framework, and we found a reasonable cosmological background evolution similar to the ΛCDM model with a fine-tuned CC. In this work, we analyse analytically the perturbations in this relaxation model, and we show that their evolution is also similar to the ΛCDM model, especially in the matter era. Some tracking properties of the vacuum energy are discussed, too.

We found the exact solution of the Poisson equation for the multidimensional space with topology . This solution describes the smooth transition from the newtonian behavior 1/r₃ for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior 1/r^{1 + d}_{3 + d} in the opposite limit. In the case of one extra dimension d = 1, the gravitational potential is expressed via compact and elegant formulae. These exact solutions are applied to some practical problems to get the gravitational potentials for considered configurations. Found potentials are used to calculate the acceleration for point masses and gravitational self-energy. Models with test masses smeared over some (or all) extra dimensions are proposed. In ten-dimensional spacetime with three smeared extra dimensions, it is shown that the size of three rest extra dimensions can be enlarged up to a submillimeter for the case of 1 TeV fundamental Planck scale M_Pl(10). In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the newtonian one regardless of the size of the extra dimensions. Nevertheless, the hierarchy problem can be solved in these models.

We establish a new self-consistent system of equations accounting for a non-minimal interaction of gravitational, electromagnetic and axion fields. The procedure is based on a non-minimal extension of the standard Einstein–Maxwell–axion action. The general properties of a ten-parameter family of non-minimal linear models are discussed. We apply this theory to the models with pp-wave symmetry and consider propagation of electromagnetic waves non-minimally coupled to the gravitational and axion fields. We focus on exact solutions of electrodynamic equations, which describe quasi-minimal and non-minimal optical activity induced by the axion field. We also discuss empirical constraints on coupling parameters from astrophysical birefringence and polarization rotation observations.

Making use of a minimal action principle, in this work we derive the dynamics of a test rigid body moving in a curved spacetime by means of a parametric invariant Lagrangian formalism. In doing so we complete a line of research due to Bailey–Israel and Anandan–Dadhich–Singh. This is accomplished through the following new contributions: by fixing the Lagrangian of the system, the elaboration of a complete variational procedure, the formulation of a rigidity constraint and the derivation of conserved quantities, already found, but in a very different form, in other approaches to the problem. The dynamics and the equations obtained are also generalized to all orders in the metric expansion by means of new mathematical tools. Besides, by the selection of an appropriate spatial section of the body world-tube, we obtain the simple Papapetru expression of the canonical momentum which, remaining unchanged to all orders, contributes to some reductions of complexity of the dynamics. Finally, in the quadrupolar approximation, applications of our results are presented in the form of useful observables in the context of ideal tests in general relativity.

Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e.g. by cosmic microwave anisotropy probes. A key issue in that theory is to extract the gauge-invariant degrees of freedom which allow unambiguous comparison between theory and experiment. When one goes beyond first (linear) order, the task of writing the Einstein equations expanded to nth order in terms of quantities that are gauge-invariant up to terms of higher orders becomes highly non-trivial and cumbersome. This fact has prevented progress for instance on the issue of the stability of linear perturbation theory and is a subject of current debate in the literature. In this series of papers we circumvent these difficulties by passing to a manifestly gauge-invariant framework. In other words, we only perturb gauge-invariant, i.e. measurable quantities, rather than gauge variant ones. Thus, gauge invariance is preserved non-perturbatively while we construct the perturbation theory for the equations of motion for the gauge-invariant observables to all orders. In this first paper we develop the general framework which is based on a seminal paper due to Brown and Kuchař as well as the relational formalism due to Rovelli. In the second, companion, paper we apply our general theory to FRW cosmologies and derive the deviations from the standard treatment in linear order. As it turns out, these deviations are negligible in the late universe, thus our theory is in agreement with the standard treatment. However, the real strength of our formalism is that it admits a straightforward and unambiguous, gauge-invariant generalization to higher orders. This will also allow us to settle the stability issue in a future publication.

In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless dust which plays the role of a dynamically coupled observer. The evolution of those observables is governed by a physical Hamiltonian and we derived the corresponding equations of motion. Linear perturbation theory of those equations of motion around a general exact solution in terms of manifestly gauge-invariant perturbations was then developed. In this paper we specialize our previous results to an FRW background which is also a solution of our modified equations of motion. We then compare the resulting equations with those derived in standard cosmological perturbation theory (SCPT). We exhibit the precise relation between our manifestly gauge-invariant perturbations and the linearly gauge-invariant variables in SCPT. We find that our equations of motion can be cast into SCPT form plus corrections. These corrections are the trace that the dust leaves on the system in terms of a conserved energy–momentum current density. It turns out that these corrections decay; in fact, in the late universe they are negligible whatever the value of the conserved current. We conclude that the addition of dust which serves as a test observer medium, while implying modifications of Einstein's equations without dust, leads to acceptable agreement with known results, while having the advantage that one now talks about manifestly gauge-invariant, that is measurable, quantities, which can be used even in perturbation theory at higher orders.

By an argument similar to that of Gibbons and Stewart (1984 Absence of asymptotically flat solutions of Einstein's equations which are periodic and empty near infinity Classical General Relativity (London, 1983) ed W Bonnor, J N Islam and M A H Callum (Cambridge: Cambridge University Press) pp 77–94), but in a different coordinate system and less restrictive gauge, we show that any weakly asymptotically simple, analytic vacuum or electrovacuum solutions of the Einstein equations which are periodic in time are necessarily stationary.

Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat isotropic and homogeneous cosmologies with a nonminimally coupled scalar field. It is shown that both singular and nonsingular models are possible. Exact general solutions of an analogous problem in the torsion-less case are derived. The role of torsion in the evolution of models is elucidated.

Although all popular approaches to quantum gravity are able to recover the Bekenstein–Hawking entropy-area law in the thermodynamic limit, there are significant differences in their descriptions of the microstates and in the application of statistics. Therefore, they can have significantly different phenomenological implications. For example, requiring indistinguishability of the elementary degrees of freedom should lead to changes in the black hole's radiative properties away from the thermodynamic limit and at low temperatures. We demonstrate this for the Bañados–Teitelboim–Zanelli (BTZ) black hole. The energy eigenstates and statistical entropy in the thermodynamic limit of the BTZ black hole were obtained earlier by us via symmetry reduced canonical quantum gravity. In that model the BTZ black hole behaves as a system of Bosonic mass shells moving in a one-dimensional harmonic trap. Bose condensation does not occur in the thermodynamic limit but this system possesses a finite critical temperature, T_c, and exhibits a large condensate fraction below T_c when the number of shells is finite.

We describe an -statistic search for continuous gravitational waves from galactic white-dwarf binaries in simulated LISA data. Our search method employs a hierarchical template-grid-based exploration of the parameter space. In the first stage, candidate sources are identified in searches using different simulated laser signal combinations (known as TDI variables). Since each source generates a primary maximum near its true 'Doppler parameters' (intrinsic frequency and sky position) as well as numerous secondary maxima of the -statistic in Doppler parameter space, a search for multiple sources needs to distinguish between true signals and secondary maxima associated with other 'louder' signals. Our method does this by applying a coincidence test to reject candidates which are not found at nearby parameter space positions in searches using each of the three TDI variables. For signals surviving the coincidence test, we perform a fully coherent search over a refined parameter grid to provide an accurate parameter estimation for the final candidates. Suitably tuned, the pipeline is able to extract 1989 true signals with only 5 false alarms. The use of the rigid adiabatic approximation allows recovery of signal parameters with errors comparable to statistical expectations, although there is still some systematic excess with respect to statistical errors expected from Gaussian noise. An experimental iterative pipeline with seven rounds of signal subtraction and reanalysis of the residuals allows us to increase the number of signals recovered to a total of 3419 with 29 false alarms.

We analyze in detail the quantum instability which characterizes charged scalar field on three special de Sitter charged black hole backgrounds. In particular, we compute exactly the imaginary part of the effective action for scalar charged fields on the ultracold I, ultracold II and Nariai charged black hole backgrounds. Both the transmission coefficient approach and the zeta-function approach are exploited. Thermal effects on this quantum instability are also taken into account in the presence of a non-zero black hole temperature (ultracold I and Nariai).