arXiv subjects
Publications and source records attributed to Leonardo Modesto.
We hereby derive the Newtonian metric potentials for the fourth-derivative gravity including the one-loop logarithm quantum corrections. It is explicitly shown that the behavior of the modified Newtonian potential near the origin is improved respect to the classical one, but this is not enough to remove the curvature singularity in $r=0$. Our result is grounded on a rigorous proof based on numerical and analytic computations.
We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is finite. In particular, the non-local scalar and gravitational theories with exponential operators are characterized by, respectively, two and four initial conditions in any dimension and, respectively, by one and eight degrees of freedom in four dimensions. The fully covariant equations of motion are written in a form convenient to find analytic non-perturbative solutions.
Based on the ultraviolet asymptotic freedom of nonlocal quantum gravity, we show that the trans-Planckian energy regime is unattainable in laboratory experiments. As physical implications, it turns out that the violation of causality, typical of nonlocal field theories, can never be detected in particle accelerators, while the asymptotic freedom of the theory provides an elegant solution to the so called trans-Planckian cosmological problem.
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signalling, entanglement monogamy, and the equivalence principle. We here provide a quantum model for Hawking pair black hole evaporation within which these principles are all respected. The model does not involve exotic new physics, but rather uses quantum theory and general relativity. The black hole and radiation are in a joint superposition of different energy states at any stage of the evaporation process. In the particular branch where the black hole mass is 0, the radiation state is pure and one-to-one with the initial state forming the black hole. Thus there is no information loss upon full evaporation. The original Hawking's pair entanglement between infalling and outgoing particles gets transferred to outgoing particles via entanglement swapping, without violation of no-signalling or the entanglement's monogamy. The final state after the full black hole evaporation is pure, without loss of information, violation of monogamy, or the equivalence principle.
We consider the family of singularity-free rotating black hole solutions in Einstein's conformal gravity found in Bambi, Modesto & Rachwal (2017) and we constrain the value of the conformal parameter $L$ from the analysis of a 30 ks NuSTAR observation of the stellar-mass black hole in GS 1354-645 during its outburst in 2015. Our new constraint is much stronger than that found in previous work. Here we obtain $L/M < 0.12$ (99% confidence level, statistical uncertainty only).
We investigate the non-perturbative degrees of freedom of a class of weakly non-local gravitational theories that have been proposed as an ultraviolet completion of general relativity. At the perturbative level, it is known that the degrees of freedom of non-local gravity are the same of the Einstein--Hilbert theory around any maximally symmetric spacetime. We prove that, at the non-perturbative level, the degrees of freedom are actually eight in four dimensions, contrary to what one might guess on the basis of the "infinite number of derivatives" present in the action. It is shown that six of these degrees of freedom do not propagate on Minkowski spacetime, but they might play a role at large scales on curved backgrounds. We also propose a criterion to select the form factor almost uniquely.
We prove that the Minkowski spacetime is stable at nonlinear level and to all perturbative orders in the gravitational perturbation in a general class of nonlocal gravitational theories that are unitary and finite at quantum level.
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic completion of the spacetime when it is probed by massive, massless, and conformally coupled particles. As a universal feature of the regular metric, nothing can reach the singularity located in t=0 in a finite amount of proper time (for massive particles and conformally coupled particles) or for finite values of the affine parameter (for massless particles).
We show quantitatively that an exact solution of Einstein's conformal gravity can explain very well the galactic rotation curves for a sample of 104 galaxies without need for dark matter or other exotic modification of gravity. The metric is an overall rescaling of the Schwarzschild-de Sitter spacetime as required by Weyl conformal invariance, which has to be spontaneously broken, and the velocity of the stars depends only on two universal parameters determined on the base of the observational data.
We prove the unitarity of the Euclidean nonlocal scalar field theory to all perturbative orders in the loop expansion. The amplitudes in the Euclidean space are calculated assuming that all the particles have purely imaginary energies, and afterwards they are analytically continued to real energies. We show that such amplitudes satisfy the Cutkowsky rules and that only the cut diagrams corresponding to normal thresholds contribute to their imaginary part. This implies that the theory is unitary. This analysis is then exported to nonlocal gauge and gravity theories by means of Becchi-Rouet-Stora-Tyutin or diffeomorphism invariance, and Ward identities.
We address the stability issue of Ricci-flat and maximally symmetric spacetimes in nonlocal gravity to all perturbative orders in the gravitational perturbation. Assuming a potential at least cubic in curvature tensors but quadratic in the Ricci tensor, our proof consists on a mapping of the stability analysis in nonlocal gravity to the same problem in Einstein-Hilbert theory. One of the consequences is that only the graviton field can propagate and the theory is ghost-free at all perturbative orders. All the results known in Einstein gravity in vacuum with or without a cosmological constant can be exported to the case of nonlocal gravity: if a spacetime is stable at all perturbative orders in Einstein gravity, it is stable also in nonlocal gravity. Minkowski and de Sitter spacetimes are particular examples. We also study how the theory affects the propagation of gravitational waves in a cosmological background.
Analytic infinite derivative (AID) non-local quadratic curvature gravity in Weyl basis is known to be ghost free, superrenormalizable or finite and perturbatively Unitary and as such it is Ultra-Violet (UV) complete. Recently $R+R^2$ ("Starobinsky") inflation was successfully embedded in AID non-local gravity and the corresponding observables were computed. Here in this paper, we derive the form factors compatible within near de Sitter aproaximation and prove that the theory must contain a scalaron that drives inflationary expansion. Further more we consider the form factors (AID non-local operators) proposed by Tomboulis in hep-th/9702146 and compute the corresponding predictions of tensor to scalar ratio and tensor tilt $\left( n_t,\,r \right)$ where the scalar tilt remains the same as the local Starobinsky model. Anticipating future CMB probes such will be able to test non-local Starobinsky inflation we constrain the scale of non-locality to be $10^{14}\,GeV\lesssim\mathcal{M}\lesssim 5\times 10^{14}\,GeV$ and $10^{-7}\lesssim r \lesssim 0.07$ for different form factors. We found that it possible to have a blue or red tensor tilt $\left( n_t\gtrless 0 \right)$ depending on the scale of non-locality and the form factor. We also comment on Higgs inflation in non-local context.
We hereby study the properties of a large class of weakly nonlocal gravitational theories around the (anti-) de Sitter spacetime background. In particular, we explicitly prove that the kinetic operator for the graviton field has the same structure as the one in Einstein-Hilbert theory around any maximally symmetric spacetime. Therefore, the perturbative spectrum is the same of standard general relativity, while the propagator on any maximally symmetric spacetime is a mere generalization of the one from Einstein's gravity derived and extensively studied in several previous papers. At quantum level the range of theories here presented is superrenormalizable or finite when proper (non affecting the propagator) terms cubic or higher in curvatures are added. Finally, it is proven that for a large class of nonlocal theories, which in their actions do involve neither the Weyl nor the Riemann tensor, the theory is classically equivalent to the Einstein-Hilbert one with cosmological constant by means of a metric field redefinition at any perturbative order.
One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton constant by using the Barvinsky-Vilkovisky trace technology. The result is well-defined in a large class of models of gravity in the sense that the renormalization group beta functions do not depend on the gauge-fixing condition. Finally, we discuss the possibility to apply the results to a large class of nonlocal gravitational theories which are free of massive ghost-like states at the tree-level.
We prove that Ricci-flat vacuum exact solutions are stable under linear perturbations in a new class of weakly non-local gravitational theories finite at the quantum level.
We study some general properties of two black hole solutions in Einstein's conformal gravity. Both solutions can be obtained from the Kerr metric with a suitable conformal rescaling, which leads, respectively, to a regular and a singular spacetime. In addition to the mass $M$ and the spin angular momentum $J$ of the black hole, these solutions are characterized by a new parameter, $L$, which may be expected to be of the order of the black hole mass. We study the geodesic motion and we calculate the radiative efficiency of a putative accretion disk around these black holes, which allows us to get an estimate of an upper bound on the value of $L$. Lastly, we explore the possibility of "destroying" the event horizon of these black holes. Within our approach, we are not able to destroy the event horizon of the regular black hole solution, while we can in the case of the singular one.
We compute the area term contribution to black holes' entanglement entropy (using the conical technique) for a class of local or weakly non-local super-renormalizable gravitational theories coupled to matter. For the first time, we explicitly prove that all the beta functions in the proposed theory, except for the cosmological constant, are identically zero in cut-off regularization scheme and not only in dimensional regularization scheme. In particular, we show that there is no divergence quadratic in cut-off and hence there is no contribution to the beta function of the Newton constant. As a consequence of this result, we argue that in these theories of gravity conical entropy is a sensible definition of physical entropy, in particular, it is positive-definite and gauge-independent. On top of this the conical entropy, being expressed only in terms of the classical Newton constant, turns out to be finite and naturally coincides with Bekenstein-Hawking entropy. Finally, we propose a theory in which the renormalization of the Newton constant is entirely due to the Standard Model matter, arguing that such a contribution does not give the usual interpretational problems of conical entropy discussed in the literature.
Contrary to recent claims in the literature, a simple test for reflection positivite, which we call perturbative reflection positivity in the coincidence limit, is shown to be satisfied for nonlocal field theories. Particular attention is given to weakly nonlocal gravity and gauge theories.