Low energy bounds on Poincare violation in causal set theory

In the causal set approach to quantum gravity, Poincar\'{e} symmetry is modified by swerving in spacetime, induced by the random lattice discretization of the space-time structure. The broken translational symmetry at short distances is argued to lead to a residual diffusion in momentum space, whereby a particle can acquire energy and momentum by drift along its mass shell and a system in equilibrium can spontaneously heat up. We consider bounds on the rate of momentum space diffusion coming from astrophysical molecular clouds, nuclear stability and cosmological neutrino background. We find that the strongest limits come from relic neutrinos, which we estimate to constrain the momentum space diffusion constant by $k < 10^{-61} {\rm GeV}^3$ for neutrinos with masses $m_\nu > 0.01 {\rm eV}$, improving the previously quoted bounds by roughly 17 orders of magnitude.Comment: Additional discussion about behavior of alpha particles in nuclei added. Version matches that accepted in PR

Relativistic kinematics beyond Special Relativity

In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity that preserves the relativity principle at leading order in 1/M.Comment: Version with minor corrections, to appear in Phys. Rev.

The Theory of a Quantum Noncanonical Field in Curved Spacetimes

Much attention has been recently devoted to the possibility that quantum gravity effects could lead to departures from Special Relativity in the form of a deformed Poincar\`e algebra. These proposals go generically under the name of Doubly or Deformed Special Relativity (DSR). In this article we further explore a recently proposed class of quantum field theories, involving noncanonically commuting complex scalar fields, which have been shown to entail a DSR-like symmetry. An open issue for such theories is whether the DSR-like symmetry has to be taken as a physically relevant symmetry, or if in fact the "true" symmetries of the theory are just rotations and translations while boost invariance has to be considered broken. We analyze here this issue by extending the known results to curved spacetime under both of the previous assumptions. We show that if the symmetry of the free theory is taken to be a DSR-like realization of the Poincar\'e symmetry, then it is not possible to render such a symmetry a gauge symmetry of the curved physical spacetime. However, it is possible to introduce an auxiliary spacetime which allows to describe the theory as a standard quantum field theory in curved spacetime. Alternatively, taking the point of view that the noncanonical commutation of the fields actually implies a breakdown of boost invariance, the physical spacetime manifold has to be foliated in surfaces of simultaneity and the field theory can be coupled to gravity by making use of the ADM prescription.Comment: 9 pages, no figure

Mechanics of universal horizons

Modified gravity models such as Ho\v{r}ava-Lifshitz gravity or Einstein-{\ae}ther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-{\ae}ther theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-{\ae}ther Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very different causal structure as long as the universal horizon remains the unique causal boundary when matter fields are added.Comment: Minor clarifications. References update

K-essence Explains a Lorentz Violation Experiment

Recently, a state of the art experiment shows evidence for Lorentz violation in the gravitational sector. To explain this experiment, we investigate a spontaneous Lorentz violation scenario with a generalized scalar field. We find that when the scalar field is nonminimally coupled to gravity, the Lorentz violation induces a deformation in the Newtonian potential along the direction of Lorentz violation.Comment: 8 pages, the final version, discussion and references adde

Remarks on the consistency of minimal deviations from General Relativity

We study the consequences of the modification of the phase space structure of General Relativity imposed by breaking the full diffeomorphism invariance but retaining the time foliation preserving diffeomorphisms. We examine the different sectors in phase space that satisfy the new structure of constraints. For some sectors we find an infinite tower of constraints. In spite of that, we also show that these sectors allow for solutions, among them some well known families of black hole and cosmologies which fulfill all the constraints. We raise some physical concerns on the consequences of an absolute Galilean time, on the thermodynamical pathologies of such models and on their unusual vacuum structure.Comment: latex 28 pages, 1 figure. Added comments and a reference. Text improved

Strong field effects on binary systems in Einstein-aether theory

"Einstein-aether" theory is a generally covariant theory of gravity containing a dynamical preferred frame. This article continues an examination of effects on the motion of binary pulsar systems in this theory, by incorporating effects due to strong fields in the vicinity of neutron star pulsars. These effects are included through an effective approach, by treating the compact bodies as point particles with nonstandard, velocity dependent interactions parametrized by dimensionless "sensitivities". Effective post-Newtonian equations of motion for the bodies and the radiation damping rate are determined. More work is needed to calculate values of the sensitivities for a given fluid source, so precise constraints on the theory's coupling constants cannot yet be stated. It is shown, however, that strong field effects will be negligible given current observational uncertainties if the dimensionless couplings are less than roughly 0.01 and two conditions that match the PPN parameters to those of pure general relativity are imposed. In this case, weak field results suffice and imply one further condition on the couplings. Thus, there exists a one-parameter family of Einstein-aether theories with "small-enough" couplings that passes all current observational tests. No conclusion can yet be reached for large couplings.Comment: 23 pages, 1 figure; v2: fixed error in Eqn. (70) and resulting bounds on c'

Planck-scale modifications to Electrodynamics characterized by a space-like symmetry-breaking vector

In the study of Planck-scale ("quantum-gravity induced") violations of Lorentz symmetry, an important role was played by the deformed-electrodynamics model introduced by Myers and Pospelov. Its reliance on conventional effective quantum field theory, and its description of symmetry-violation effects simply in terms of a four-vector with nonzero component only in the time-direction, rendered it an ideal target for experimentalists and a natural concept-testing ground for many theorists. At this point however the experimental limits on the single Myers-Pospelov parameter, after improving steadily over these past few years, are "super-Planckian", {\it i.e.} they take the model out of actual interest from a conventional quantum-gravity perspective. In light of this we here argue that it may be appropriate to move on to the next level of complexity, still with vectorial symmetry violation but adopting a generic four-vector. We also offer a preliminary characterization of the phenomenology of this more general framework, sufficient to expose a rather significant increase in complexity with respect to the original Myers-Pospelov setup. Most of these novel features are linked to the presence of spatial anisotropy, which is particularly pronounced when the symmetry-breaking vector is space-like, and they are such that they reduce the bound-setting power of certain types of observations in astrophysics

Time-delay and Doppler tests of the Lorentz symmetry of gravity

Modifications to the classic time-delay effect and Doppler shift in General Relativity (GR) are studied in the context of the Lorentz-violating Standard-Model Extension (SME). We derive the leading Lorentz-violating corrections to the time-delay and Doppler shift signals, for a light ray passing near a massive body. It is demonstrated that anisotropic coefficients for Lorentz violation control a time-dependent behavior of these signals that is qualitatively different from the conventional case in GR. Estimates of sensitivities to gravity-sector coefficients in the SME are given for current and future experiments, including the recent Cassini solar conjunction experiment.Comment: 13 pages, 4 figures, references added, matches PRD versio

Lorentz Violating Inflation

We explore the impact of Lorentz violation on the inflationary scenario. More precisely, we study the inflationary scenario in the scalar-vector-tensor theory where the vector is constrained to be unit and time like. It turns out that the Lorentz violating vector affects the dynamics of the chaotic inflationary model and divides the inflationary stage into two parts; the Lorentz violating stage and the standard slow roll stage. We show that the universe is expanding as an exact de Sitter spacetime in the Lorentz violating stage although the inflaton field is rolling down the potential. Much more interestingly, we find exact Lorentz violating inflationary solutions in the absence of the inflaton potential. In this case, the inflation is completely associated with the Lorentz violation. We also mention some consequences of Lorentz violating inflation which can be tested by observations.Comment: 7 pages, 1 figur