118593879
Technically natural dark energy from Lorentz breaking
We construct a model of dark energy with a technically natural small contribution to cosmic acceleration, i.e. this contribution does not receive corrections from other scales in the theory. The proposed acceleration mechanism appears generically in the low-energy limit of gravity theories with violation of Lorentz invariance that contain a derivatively coupled scalar field Theta. The latter may be the Goldstone field of a broken global symmetry. The model, that we call Theta CDM, is a valid effective field theory up to a high cutoff just a few orders of magnitude below the Planck scale. Furthermore, it can be ultraviolet-completed in the context of Horava gravity. We discuss the observational predictions of the model. Even in the absence of a cosmological constant term, the expansion history of the Universe is essentially indistinguishable from that of Lambda CDM. The difference between the two theories appears at the level of cosmological perturbations. We find that in Theta CDM the matter power spectrum is enhanced at subhorizon scales compared to Lambda CDM. This property can be used to discriminate the model from Lambda CDM with current cosmological data.
9484455
Bigravity and Lorentz-violating massive gravity
Bigravity is a natural arena where a nonlinear theory of massive gravity can be formulated. If the interaction between the metrics f and g is nonderivative, 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 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 general relativity are proportional to the square of the graviton mass, and so there is no van Dam-Veltam-Zakharov discontinuity. Surprisingly, the solution of linear theory for a static spherically symmetric source does not agree with the linearization of any of the known exact solutions. The latter coincide with the standard Schwarzschild-(anti)-de Sitter 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.
117351571
Bigravity and Massive Gravity
We discuss some issues concerning the global structure of spherically symmetric solutions of bigravity. We propose maximal extensions of manifolds where two causal structure coexist. Besides we make some comments about the perturbations of these solutions and their relation to massive gravity and the cosmological constant problem.
15368805
On the extra mode and inconsistency of Hořava gravity
We address the consistency of Hořava'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 Stuckelberg 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 Hořava'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 Stuckelberg formalism to Hořava's model due to its non-relativistic nature.
120515188
Some Global and Local Aspects of Bigravity
Abstract
We review some global and local aspects of bigravity theories concerning the causal structure of two interacting metrics. We provide some general settings where global hyperbolicity is lost even if both metrics are independently globally hyperbolic. Finally we say some words about the spectrum of these theories and their relation to the cosmological constant problem.

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.
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.