On power-counting renormalizability of Ho\v{r}ava gravity with detailed balance

We consider the version of Ho\v{r}ava gravity where "detailed balance" is consistently implemented, so as to limit the huge proliferation of couplings in the full theory and obtain healthy dynamics at low energy. Since a superpotential which is third-order in spatial derivatives is not sufficient to guarantee the power-counting renormalizability of the spin-0 graviton, one needs to go an order beyond in derivatives, building a superpotential up to fourth-order spatial derivatives. Here we perturb the action to quadratic order around flat space and show that the power-counting renormalizability of the spin-0 graviton is achieved only by setting to zero a specific coupling of the theory, while the spin-2 graviton is always power-counting renormalizable for any choice of the couplings. This result raises serious doubts about the use of detailed balance.Comment: v1: 4 pages; v2: references added, published versio

On the Anisotropic Interior Solutions in Ho\v{r}ava Gravity and Einstein-{\ae}ther Theory

We find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Ho\v{r}ava gravity and Einstein-\ae ther theory in presence of anisotropic fluids. We focus for simplicity on the case of a static \ae ther finding a large class of possible viable interior star solutions which present a very rich phenomenology. We study one illustrative example in more detail.Comment: v1: 5 pages, 1 figure; v2: 6 pages, 1 figure. Matches published version in EP

Horava-Lifshitz gravity with detailed balance

Horava-Lifshitz gravity with "detailed balance" but without the projectability assumption is discussed. It is shown that detailed balance is quite efficient in limiting the proliferation of couplings in Horava-Lifshitz gravity, and that its implementation without the projectability assumption leads to a theory with sensible dynamics. However, the (bare) cosmological constant is restricted to be large and negative.Comment: Contribution to the proceedings of NEB 15 conference, Chania, 20-23 June 2012 (talk given by D.V.

Equivalence between Palatini and metric formalisms of f(R)-gravity by divergence free current

The equivalence between metric and Palatini formalisms in f(R)-gravity can be achieved in the general context of theories with divergence free current. This equivalence is a necessary result of a symmetry which is included in a particular conservation equation of the current. In fact the conservation equation, by an appropriate redefinition of the introduced auxiliary field, may be encoded in a massless scalar field equation.Comment: 6 page

Gravity beyond General Relativity: New Proposals and their Phenomenology

This Thesis is devoted to the study of phenomenologically viable gravitational theories, in order to address the most pressing open issues both at very small and very large energy scales. Lovelock\u2019s theorem singles out General Relativity as the only theory with secondorder field equations for the metric tensor. So, two possible ways to circumvent it and modify the gravitational sector are taken into account. The first route consists in giving up diffeomorphism invariance, which generically leads to extra propagating degrees of freedom. In this framework Horava gravity is discussed, presenting two restrictions, called respectively "projectability" and "detailed balance", which are imposed in order to reduce the number of terms in the full theory. We introduce a new version of the theory assuming detailed balance but not projectability, and we show that such theory is dynamically consistent as both the spin-0 and spin-2 gravitons have a well behaved dynamics at low-energy. Moreover three-dimensional rotating black hole solutions are found and fully studied in the context of Horava gravity, shedding light on its causal structure. A new concept of black hole horizon, dubbed "universal horizon", arises besides the usual event horizon one, since in Lorentz-violating gravity theories there can be modes propagating even at infinite speed. The second route which is considered, consists in adding extra fields to the gravitational action while diffeomorphism invariance is preserved. In this respect we consider the less explored option that such fields are auxiliary fields, so they do not satisfy dynamical equations but can be instead algebraically eliminated. A very general parametrization for these theories is constructed, rendering also possible to put on them very tight, theory-independent constraints. Some insight about the cosmological implications of such theories is also given. Finally in the conclusions we discuss about the future challenges that the aforementioned gravity theories have to face

Relativistic polytropic equations of state in Ho\v{r}ava gravity and Einstein-\ae ther theory

The equations of state for a characteristic spacetime are studied in the context of the spherically symmetric interior exact and analytical solutions in Horava gravity and Einstein-aether theory in which anisotropic fluids are considered. In particular, for a given anisotropic interior solution, the equations of state relating the density to the radial and tangential pressure are derived, by means of a polynomial best-fit. Moreover, the well-known relativistic polytropic equations of state are used in order to obtain the profile of the thermodynamical quantities inside the stellar object as provided by the specific exact solution considered. It is then shown that these equations of state need to be modified in order to account for the profiles of density and pressures.Comment: 9 pages, 6 figures. Matches published version in PR

Rotating black holes in three-dimensional Ho\v{r}ava gravity

We study black holes in the infrared sector of three-dimensional Ho\v{r}ava gravity. It is shown that black hole solutions with anti-de Sitter asymptotics are admissible only in the sector of the theory in which the scalar degree of freedom propagates infinitely fast. We derive the most general class of stationary, circularly symmetric, asymptotically anti-de Sitter black hole solutions. We also show that the theory admits black hole solutions with de Sitter and flat asymptotics, unlike three-dimensional general relativity. For all these cases, universal horizons may or may not exist depending on the choice of parameters. Solutions with de Sitter asymptotics can have universal horizons that lie beyond the de Sitter horizon.Comment: 16 pages, 9 figures, final published versio

Gravity with Auxiliary Fields

Modifications of General Relativity usually include extra dynamical degrees of freedom, which to date remain undetected. Here we explore the possibility of modifying Einstein's theory by adding solely nondynamical fields. With the minimal requirement that the theory satisfies the weak equivalence principle and admits a covariant Lagrangian formulation, we show that the field equations generically have to include higher-order derivatives of the matter fields. This has profound consequences for the viability of these theories. We develop a parametrization based on a derivative expansion and show that - to next to leading order - all theories are described by just two parameters. Our approach can be used to put stringent, theory-independent constraints on such theories, as we demonstrates using the Newtonian limit as an example.Comment: 5 pages, no figures; v2: clarifications and minor improvements, matches published versio

Covariant action for bouncing cosmologies in modified Gauss-Bonnet gravity

Cyclic universes with bouncing solutions are candidates for solving the big bang initial singularity problem. Here we seek bouncing solutions in a modified Gauss-Bonnet gravity theory, of the type $R+f(G)$, where $R$ is the Ricci scalar, $G$ is the Gauss-Bonnet term, and $f$ some function of it. In finding such a bouncing solution we resort to a technique that reduces the order of the differential equations of the $R+f(G)$ theory to second order equations. As general relativity is a theory whose equations are of second order, this order reduction technique enables one to find solutions which are perturbatively close to general relativity. We also build the covariant action of the order reduced theory.Comment: 8 page

String duality transformations in f(R)f(R) gravity from Noether symmetry approach

We select $f(R)$ gravity models that undergo scale factor duality transformations. As a starting point, we consider the tree-level effective gravitational action of bosonic String Theory coupled with the dilaton field. This theory inherits the Busher's duality of its parent String Theory. Using conformal transformations of the metric tensor, it is possible to map the tree-level dilaton-graviton string effective action into $f(R)$ gravity, relating the dilaton field to the Ricci scalar curvature. Furthermore, the duality can be framed under the standard of Noether symmetries and exact cosmological solutions are derived. Using suitable changes of variables, the string-based $f(R)$ Lagrangians are shown in cases where the duality transformation becomes a parity inversion.Comment: v1: 13 pages; v2: minor rephrasings, published versio