Generalized multi-Proca fields

We extend previous results on healthy derivative self-interactions for a Proca field to the case of a set of massive vector fields. We obtain non-gauge invariant derivative self-interactions for the vector fields that maintain the appropriate number of propagating degrees of freedom. In view of the potential cosmological applications, we restrict to interactions with an internal rotational symmetry. We provide a systematical construction order by order in derivatives of the fields and making use of the antisymmetric Levi-Civita tensor. We then compare with the one single vector field case and show that the interactions can be broadly divided into two groups, namely the ones obtained from a direct extension of the generalized Proca terms and genuine multi-Proca interactions with no correspondence in the single Proca case. We also discuss the curved spacetime version of the interactions to include the necessary non-minimal couplings to gravity. Finally, we explore the cosmological applications and show that there are three different vector fields configurations giving rise to isotropic solutions. Two of them have already been considered in the literature and the third one, representing a combination of the first two, is new and offers unexplored cosmological scenarios.Comment: 13 page

Ghosts in metric-affine higher order curvature gravity

We disprove the widespread belief that higher order curvature theories of gravity in the metric-affine formalism are generally ghost-free. This is clarified by considering a sub-class of theories constructed only with the Ricci tensor and showing that the non-projectively invariant sector propagates ghost-like degrees of freedom. We also explain how these pathologies can be avoided either by imposing a projective symmetry or additional constraints in the gravity sector. Our results put forward that higher order curvature gravity theories generally remain pathological in the metric-affine (and hybrid) formalisms and highlight the key importance of the projective symmetry and/or additional constraints for their physical viability and, by extension, of general metric-affine theories.Comment: 7 page

Spacetimes with vector distortion: Inflation from generalised Weyl geometry

Spacetime with general linear vector distortion is introduced. Thus, the torsion and the nonmetricity of the affine connection are assumed to be proportional to a vector field (and not its derivatives). The resulting two-parameter family of non-Riemannian geometries generalises the conformal Weyl geometry and some other interesting special cases. Taking into account the leading order quadratic curvature correction to the Einstein-Hilbert action results uniquely in the one-parameter extension of the Starobinsky inflation known as the alpha-attractor. The most general quadratic curvature action introduces, in addition to the canonical vector kinetic term, novel ghost-free vector-tensor interactions.Comment: 5 pages, 1 table, 0 figures. V2: Added the general quadratic theor

Limits on the anomalous speed of gravitational waves from binary pulsars

A large class of modified theories of gravity used as models for dark energy predict a propagation speed for gravitational waves which can differ from the speed of light. This difference of propagations speeds for photons and gravitons has an impact in the emission of gravitational waves by binary systems. Thus, we revisit the usual quadrupolar emission of binary system for an arbitrary propagation speed of gravitational waves and obtain the corresponding period decay formula. We then use timing data from the Hulse-Taylor binary pulsar and obtain that the speed of gravitational waves can only differ from the speed of light at the percentage level. This bound places tight constraints on dark energy models featuring an anomalous propagations speed for the gravitational waves.Comment: 6 pages, 1 figure, Prepared for the IWARA2016 proceeding

Dark Energy in vector-tensor theories of gravity

We consider a general class of vector-tensor theories of gravity and show that solutions with accelerated expansion and a future type III singularity are a common feature in these models. We also show that there are only six vector-tensor theories with the same small scales behavior as General Relativity and, in addition, only two of them can be made completely free from instabilities. Finally, two particular models as candidates for dark energy are proposed: on one hand, a cosmic vector that allows to alleviate the usual naturalness and coincidence problems and, on the other hand, the electromagnetic field is shown to give rise to an effective cosmological constant on large scales whose value can be explained in terms of inflation at the electroweak scale.Comment: 4 pages, 1 table. Contribution to the proceedings of Spanish Relativity Meeting 2009, Bilbao, Spain, 7-11 September 200

A cosmic vector for dark energy

In this work we show that the presence of a vector field on cosmological scales could explain the present phase of accelerated expansion of the universe. The proposed theory contains no dimensional parameters nor potential terms and does not require unnatural initial conditions in the early universe, thus avoiding the so called cosmic coincidence problem. In addition, it fits the data from high-redshift supernovae with excellent precision, making definite predictions for cosmological parameters. Upcoming observations will be able to clearly discriminate this model from standard cosmology with cosmological constant.Comment: 5 pages, 3 figures, 1 table. New comments and references included. Final version to appear in Phys. Rev.

Infrared lessons for ultraviolet gravity: the case of massive gravity and Born-Infeld

We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a {\it minimal} version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. In vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.Comment: 31 pages, 3 figures (Journal version, references added

Cosmology with a Continuous Tower of Scalar Fields

We study the cosmological evolution for a universe in the presence of a continuous tower of massive scalar fields which can drive the current phase of accelerated expansion of the universe and, in addition, can contribute as a dark matter component. The tower consists of a continuous set of massive scalar fields with a gaussian mass distribution. We show that, in a certain region of the parameter space, the {\it heavy} modes of the tower (those with masses much larger than the Hubble expansion rate) dominate at early times and make the tower behave like the usual single scalar field whose coherent oscillations around the minimum of the potential give a matter-like contribution. On the other hand, at late times, the {\it light} modes (those with masses much smaller than the Hubble expansion rate) overcome the energy density of the tower and they behave like a perfect fluid with equation of state ranging from 0 to -1, depending on the spectral index of the initial spectrum. This is a distinctive feature of the tower with respect to the case of quintessence fields, since a massive scalar field can only give acceleration with equation of state close to -1. Such unique property is the result of a synergy effect between the different mass modes. Interestingly, we find that, for some choices of the spectral index, the tower tracks the matter component at high redshifts (or it can even play the role of the dark matter) and eventually becomes the dominant component of the universe and give rise to an accelerated expansion.Comment: 13 pages, 8 figures. V2: minor changes to match published versio

The canonical frame of purified gravity

In the recently introduced gauge theory of translations, dubbed Coincident General Relativity, gravity is described with neither torsion nor curvature in the spacetime affine geometry. The action of the theory enjoys an enhanced symmetry and avoids the second derivatives that appear in the conventional Einstein-Hilbert action. While it implies the equivalent classical dynamics, the improved action principle can make a difference in considerations of energetics, thermodynamics, and quantum theory. This essay reports on possible progress in those three aspects of gravity theory. In the so-called purified gravity, 1) energy-momentum is described locally by a conserved, symmetric tensor, 2) the Euclidean path integral is convergent without the addition of boundary or regulating terms and 3) it is possible to identify a canonical frame for quantisation.Comment: 7 pages, no figure