42928922
Unitary evolution and uniqueness of the Fock quantization in flat cosmologies with compact spatial sections
We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in flat Friedmann-Robertson-Walker spacetimes, generally including a suitable scaling of them by a background function. We prove that the requirements of vacuum invariance under the spatial isometries and of a unitary quantum dynamics select (a) a unique canonical pair of field variables among all those related by time dependent canonical transformations which scale the field configurations, and (b) a unique Fock representation for the canonical commutation relations of this pair of variables. Though the proof is generalizable to other compact spatial topologies in three or less dimensions, we focus on the case of the three-torus owing to its relevance in cosmology, paying a especial attention to the role played by the spatial isometries in the determination of the representation.
119111361
Quantization of the massless scalar field in de Sitter spacetime with unitary dynamics
We present a Fock quantization with unitary dynamics for the massless scalar field in de Sitter spacetime.
73642712
Inhomogenous loop quantum cosmology with matter
The linearly polarized Gowdy T3 model with a massless scalar field with the same symmetries as the metric is quantized by applying a hybrid approach. The homogeneous geometry degrees of freedom are loop quantized, fact which leads to the resolution of the cosmological singularity, while a Fock quantization is employed for both matter and gravitational inhomogeneities. Owing to the inclusion of the massless scalar field this system allows us to modelize flat Friedmann-Robertson-Walker cosmologies filled with inhomogeneities propagating in one direction. It provides a perfect scenario to study the quantum back-reaction between the inhomogeneities and the polymeric homogeneous and isotropic background.
56182798
Massless scalar field in de Sitter spacetime: unitary quantum time evolution
We prove that, under the standard conformal scaling, a free scalar field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. Since this applies in particular to the massless case, this result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch–Davies vacuum.
30884654
Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model
We apply a hybrid approach which combines loop and Fock quantizations to fully quantize the linearly polarized Gowdy T{sup 3} model in the presence of a massless scalar field with the same symmetries as the metric. Like in the absence of matter content, the application of loop techniques leads to a quantum resolution of the classical cosmological singularity. Most importantly, thanks to the inclusion of matter, the homogeneous sector of the model contains flat Friedmann-Robertson-Walker solutions, which are not allowed in vacuo. Therefore, this model provides a simple setting to study at the quantum level interesting physical phenomena such as the effect of the anisotropies and inhomogeneities on flat Friedmann-Robertson-Walker cosmologies.
119329279
Gauge symmetry and consistent spin-2 theories
We study Lagrangians with the minimal amount of gauge symmetry required to propagate spin-2 particles without ghosts or tachyons. In general, these Lagrangians also have a scalar mode in their spectrum. We find that, in two cases, the symmetry can be enhanced to a larger group: the whole group of diffeomorphisms or an enhancement involving a Weyl symmetry. We consider the nonlinear completions of these theories. The intuitive completions yield the usual scalar–tensor theories except for the pure spin-2 cases, which correspond to two inequivalent Lagrangians giving rise to Einstein's equations. A more constructive self-consistent approach yields a background-dependent Lagrangian.
118471121
Aspects of Infrared Modifications of Gravity
In the first part of the thesis, and after an introduction to certain models of modified gravity, we study consistent Lagrangians for Lorentz invariant (massive and massless) spin-2 and spin-3/2 particles in flat space. The second part of the dissertation is devoted to non-linear extensions for the spin-2 case, focusing on unimodular gravity and bigravity. Both theories lead to modifications of General Relativity at large distances and we will study exact solutions, causal structure of those solutions, and perturbation theory (specially for the Lorentz breaking case). Some comments on quantization of these theories can be found in an appendix.
119155605
Models of non-relativistic quantum gravity: the good, the bad and the healthy
Hořava’s proposal for non-relativistic quantum gravity introduces a preferred time foliation of space-time which violates the local Lorentz invariance. The foliation is encoded in a dynamical scalar field which we call ‘khronon’. The dynamics of the khronon field is sensitive to the symmetries and other details of the particular implementations of the proposal. In this paper we examine several consistency issues present in three non-relativistic gravity theories: Hořava’s projectable theory, the healthy non-projectable extension, and a new extension related to ghost condensation. We find that the only model which is free from instabilities and strong coupling is the non-projectable one. We elaborate on the phenomenology of the latter model including a discussion of the couplings of the khronon to matter. In particular, we obtain the parameters of the post-Newtonian expansion in this model and show that they are compatible with current observations.
59466440
Horava gravity versus thermodynamics: The black hole case
Under broad assumptions, breaking of Lorentz invariance in gravitational theories leads to tension with unitarity because it allows for processes that apparently violate the second law of thermodynamics. The crucial ingredient of this argument is the existence of black hole solutions with the interior shielded from infinity by a causal horizon. We study how the paradox can be resolved in the healthy extension of Horava gravity. To this aim we analyze classical solutions describing large black holes in this theory with the emphasis on their causal structure. The notion of causality is subtle in this theory due to the presence of instantaneous interactions. Despite this fact, we find that within exact spherical symmetry a black hole solution contains a space-time region causally disconnected from infinity by a surface of finite area-the "universal horizon.'' We then consider small perturbations of arbitrary angular dependence in the black hole background. We argue that aspherical perturbations destabilize the universal horizon and, at the nonlinear level, turn it into a finite-area singularity. The causal structure of the region outside the singularity is trivial. If the higher-derivative terms in the equations of motion smear the singularity while preserving the trivial causal structure of the solutions, the thermodynamics paradox would be obviated. As a by-product of our analysis we prove that the black holes do not have any nonstandard long-range hair. We also comment on the relation with Einstein-aether theory, where the solutions with a universal horizon appear to be stable.
118722197
Testing Lorentz invariance of dark matter
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.