Remo Garattini

Particle propagation and effective space-time in Gravity's Rainbow

Based on the results obtained in our previous study on gravity’s rainbow, we determine the quantum corrections to the space-time metric for the Schwarzschild and the de Sitter background, respectively. We analyze how quantum fluctuations alter these metrics, inducing modifications on the propagation of test particles. Significantly enough, we find that quantum corrections can become relevant not only for particles approaching the Planck energy but, due to the one-loop contribution, even for low-energy particles as far as Planckian length scales are considered. We briefly compare our results with others obtained in similar studies and with the recent experimental OPERA announcement of superluminal neutrino propagation.

Self-sustained phantom wormholes in semi-classical gravity

A possible candidate for the late time accelerated expanding universe is phantom energy, which possesses rather bizarre properties, such as the prediction of a Big Rip singularity and the violation of the null energy condition. The latter is a fundamental ingredient of traversable wormholes, and it has been shown that phantom energy may indeed sustain these exotic geometries. Inspired by the evolving dark energy parameter crossing the phantom divide, we consider in this work a varying equation of state parameter dependent on the radial coordinate, i.e., ω(r) = p(r)/ρ(r). We shall impose that phantom energy is concentrated in the neighbourhood of the throat, to ensure the flaring out condition, and several models are analysed. We shall also consider the possibility that these phantom wormholes be sustained by their own quantum fluctuations. The energy density of the graviton one-loop contribution to a classical energy in a phantom wormhole background and the finite one-loop energy density are considered as a self-consistent source for these wormhole geometries. The latter semi-classical approach prohibits solutions with a constant equation of state parameter, which further motivates the imposition of a radial dependent parameter, ω(r), and only permits solutions with a steep positive slope proportional to the radial derivative of the equation of state parameter, evaluated at the throat. The size of the wormhole throat as a function of the relevant parameters is also explored.

The cosmological constant as an eigenvalue of f(R)-gravity Hamiltonian constraint

In the framework of ADM formalism, it is possible to find out eigenvalues of the WDW equation with the meaning of vacuum states, i.e. cosmological constants, for f(R) theories of gravity, where f(R) is a generic analytic function of the Ricci curvature scalar R. The explicit calculation is performed for a Schwarzschild metric where one-loop energy is derived by the zeta function regularization method and a renormalized running Λ0 constant is obtained.

Self-sustained traversable wormholes in noncommutative geometry

Abstract In this work, we find exact wormhole solutions in the context of noncommutative geometry, and further explore their physical properties and characteristics. The energy density of these wormhole geometries is a smeared and particle-like gravitational source, where the mass is diffused throughout a region of linear dimension α due to the intrinsic uncertainty encoded in the coordinate commutator. Furthermore, we also analyze these wormhole geometries considering that the equation governing quantum fluctuations behaves as a backreaction equation. In particular, the energy density of the graviton one loop contribution to a classical energy in a traversable wormhole background and the finite one loop energy density is considered as a self-consistent source for these wormhole geometries. Interesting solutions are found for an appropriate range of the parameters, validating the perturbative computation introduced in this semi-classical approach.

Noncommutative approach to the cosmological constant problem

In this paper, we study the cosmological constant emerging from the Wheeler-DeWitt equation as an eigenvalue of the related Sturm-Liouville problem. We employ Gaussian trial functionals and we perform a mode decomposition to extract the transverse-traceless component, namely, the graviton contribution, at one loop. We implement a noncommutative-geometry-induced minimal length to calculate the number of graviton modes. As a result, we find regular graviton fluctuation energies for the Schwarzschild, de Sitter, and anti-de Sitter backgrounds. No renormalization scheme is necessary to remove infinities, in contrast to what happens in conventional approaches.

Self-sustained wormholes in modified dispersion relations

In this work, we consider the possibility that wormhole geometries are sustained by their own quantum fluctuations, in the context of modified dispersion relations. More specifically, the energy density of the graviton one-loop contribution to a classical energy in a wormhole background is considered as a self-consistent source for wormholes. In this semiclassical context, we consider specific choices for the rainbow’s functions and find solutions for wormhole geometries in the cis-Planckian and trans-Planckian regimes. In the former regime, the wormhole spacetimes are not asymptotically flat and need to be matched to an exterior vacuum solution. In the latter trans-Planckian regime, we find that the quantum corrections are exponentially suppressed, which provide asymptotically flat wormhole geometries with a constant shape function, i.e., b(r)=rt, where rt is the wormhole throat. In addition to this analysis, we also fix the geometry by considering the behavior of a specific shape function through a variational approach which imposes a local analysis to the problem at the wormhole throat. We further explore the respective parameter range of the rainbow’s functions, and find a good agreement with previous work.

The Cosmological constant as an eigenvalue of the Hamiltonian constraint in Horava-Lifshits theory

In the framework of Hořava-Lifshitz theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. The explicit calculation is performed with the help of a variational procedure with trial wave functionals of the Gaussian type. We analyze both the case with the detailed balanced condition and the case without it. In the case without the detailed balance, we find the existence of an eigenvalue depending on the set of coupling constants (g2, g3) and (g4, g5, g6), respectively, and on the physical scale.

Gravity’s Rainbow induces topology change

In this work, we explore the possibility that quantum fluctuations induce a topology change, in the context of Gravity’s Rainbow. A semiclassical approach is adopted, where the graviton one-loop contribution to a classical energy in a background spacetime is computed through a variational approach with Gaussian trial wave functionals. The energy density of the graviton one-loop contribution, or equivalently the background spacetime, is then let to evolve, and consequently the classical energy is determined. More specifically, the background metric is fixed to be Minkowskian in the equation governing the quantum fluctuations, which behaves essentially as a backreaction equation, and the quantum fluctuations are let to evolve; the classical energy, which depends on the evolved metric functions, is then evaluated. Analyzing this procedure, a natural ultraviolet cutoff is obtained, which forbids the presence of an interior spacetime region, and this may result in a multiply connected spacetime. Thus, in the context of Gravity’s Rainbow, this process may be interpreted as a change in topology, and in principle it results in the presence of a planckian wormhole.

Self sustained traversable wormholes

We compute the graviton one-loop contribution to a classical energy in a traversable wormhole background. Such a contribution is evaluated by means of a variational approach with Gaussian trial wavefunctionals. A zeta function regularization is involved to handle divergences. A renormalization procedure is introduced and the finite one-loop energy is considered as a self-consistent source for the traversable wormhole.

Linearized stability analysis of gravastars in noncommutative geometry

A bstractIn this work, we find exact gravastar solutions in the context of noncommutative geometry, and explore their physical properties and characteristics. The energy density of these geometries is a smeared and particle-like gravitational source, where the mass is diffused throughout a region of linear dimension