arXiv subjects
Publications and source records attributed to D. Blas.
We show that, contrary to the claim made in arXiv:0911.1299, the extended Horava gravity model proposed in arXiv:0909.3525 does not suffer from a strong coupling problem. By studying the observational constraints on the model we determine the bounds on the scale of the ultraviolet modification for which the proposal yields a phenomenologically viable, renormalizable and weakly coupled model of quantum gravity.
We address the consistency of Horava's proposal for a theory of quantum gravity from the low-energy perspective. We uncover the additional scalar degree of freedom arising from the explicit breaking of the general covariance and study its properties. The analysis is performed both in the original formulation of the theory and in the Stueckelberg picture. A peculiarity of the new mode is that it satisfies an equation of motion that is of first order in time derivatives. At linear level the mode is manifest only around spatially inhomogeneous and time-dependent backgrounds. We find two serious problems associated with this mode. First, the mode develops very fast exponential instabilities at short distances. Second, it becomes strongly coupled at an extremely low cutoff scale. We also discuss the "projectable" version of Horava's proposal and argue that this version can be understood as a certain limit of the ghost condensate model. The theory is still problematic since the additional field generically forms caustics and, again, has a very low strong coupling scale. We clarify some subtleties that arise in the application of the Stueckelberg formalism to Horava's model due to its non-relativistic nature.
We propose a natural extension of Horava's model for quantum gravity, which is free from the notorious pathologies of the original proposal. The new model endows the scalar graviton mode with a regular quadratic action and remains power-counting renormalizable. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity theory. The deviations with respect to general relativity can be made weak by an appropriate choice of parameters.
A systematic study of the different phases of Lorentz-breaking massive gravity in a curved background is performed. For tensor and vector modes, the analysis is very close to that of Minkowski space. The most interesting results are in the scalar sector where, generically, there are two propagating degrees of freedom (DOF). While in maximally symmetric spaces ghost-like instabilities are inevitable, they can be avoided in a FRW background. The phases with less than two DOF in the scalar sector are also studied. Curvature allows an interesting interplay with the mass parameters; in particular, we have extended the Higuchi bound of dS to FRW and Lorentz breaking masses. As in dS, when the bound is saturated there is no propagating DOF in the scalar sector. In a number of phases the smallness of the kinetic terms gives rise to strongly coupled scalar modes at low energies. Finally, we have computed the gravitational potentials for point-like sources. In the general case we recover the GR predictions at small distances, whereas the modifications appear at distances of the order of the characteristic mass scale. In contrast with Minkowski space, these corrections may not spoil the linear approximation at large distances.
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.
We study the possible covariant Lagrangians that describe the propagation of pure spin-3/2 particles. We show that, apart from the well-known Rarita-Schwinger Lagrangian, there is another possibility where the field is described by a gamma-traceless combination and that both Lagrangians yield the same physical predictions for the interaction of conserved sources. We also prove that for the case when the spin-2 field is described by a traceless field, there is no possible spin-3/2 action that makes the system supersymmetric. Nevertheless, the interaction between this field andthe spin-3/2 field may be possible.
Bigravity is a natural arena where a non-linear theory of massive gravity can be formulated. If the interaction between the metrics $f$ and $g$ is non-derivative, spherically symmetric exact solutions can be found. At large distances from the origin, these are generically Lorentz-breaking bi-flat solutions (provided that the corresponding vacuum energies are adjusted appropriately). The spectrum of linearized perturbations around such backgrounds contains a massless as well as a massive graviton, with {\em two} physical polarizations each. There are no propagating vectors or scalars, and the theory is ghost free (as happens with certain massive gravities with explicit breaking of Lorentz invariance). At the linearized level, corrections to GR are proportional to the square of the graviton mass, and so there is no vDVZ discontinuity. Surprisingly, the solution of linear theory for a static spherically symmetric source does {\em not} agree with the linearization of any of the known exact solutions. The latter coincide with the standard Schwarzschild-(A)dS solutions of General Relativity, with no corrections at all. Another interesting class of solutions is obtained where $f$ and $g$ are proportional to each other. The case of bi-de Sitter solutions is analyzed in some detail.
We study Lagrangians with the minimal amount of gauge symmetry required to propagate spin-two 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 a enhancement involving a Weyl symmetry. We consider the non-linear completions of these theories. The intuitive completions yield the usual scalar-tensor theories except for the pure spin-two cases, which correspond to two inequivalent Lagrangians giving rise to Einstein's equations. A more constructive self-consistent approach yields a background dependent Lagrangian.
We consider some flat space theories for spin 2 gravitons, with less invariance than full diffeomorphisms. For the massless case, classical stability and absence of ghosts require invariance under transverse diffeomorphisms (TDiff). Generic TDiff invariant theories contain a propagating scalar, which disappears if the symmetry is enhanced in one of two ways. One possibility is to consider full diffeomorphisms (Diff). The other (which we denote WTDiff) adds a Weyl symmetry, by which the Lagrangian becomes independent of the trace. The first possibility corresponds to General Relativity, whereas the second corresponds to "unimodular" gravity (in a certain gauge). Phenomenologically, both options are equally acceptable. For massive gravitons, the situation is more restrictive. Up to field redefinitions, classical stability and absence of ghosts lead directly to the standard Fierz-Pauli Lagrangian. In this sense, the WTDiff theory is more rigid against deformations than linearized GR, since a mass term cannot be added without provoking the appearance of ghosts.