Perturbations in higher derivative gravity beyond maximally symmetric spacetimes

We study (covariant) scalar-vector-tensor (SVT) perturbations of infinite derivative gravity (IDG), at the quadratic level of the action, around conformally-flat, covariantly constant curvature backgrounds which are not maximally symmetric spacetimes (MSS). This extends a previous analysis of perturbations done around MSS, which were shown to be ghost-free. We motivate our choice of backgrounds which arise as solutions of IDG in the UV, avoiding big bang and black hole singularities. Contrary to MSS, in this paper we show that, generically, all SVT modes are coupled to each other at the quadratic level of the action. We consider simple examples of the full IDG action, and illustrate this mixing and also a case where the action can be diagonalized and ghost-free solutions constructed. Our study is widely applicable for both non-singular cosmology and black hole physics where backgrounds depart from MSS. In appendices, we provide SVT perturbations around conformally-flat and arbitrary backgrounds which can serve as a compendium of useful results when studying SVT perturbations of various higher derivative gravity models.Comment: 36 pages, 1 figur

R2R^2 inflation to probe non-perturbative quantum gravity

It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, $R+R^2$, or shortly $R^2$, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local $R^2$ model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index ($n_s$), a tensor-to-scalar ratio ($r$) and a tensor tilt ($n_t$). It appears that $n_s$ remains the same as in the local $R^2$ inflation in the leading slow-roll approximation, while $r$ and $n_t$ get modified due to modification of the tensor power spectrum. This class of models allows for any value of $r<0.07$ with a modified consistency relation which can be fixed by future observations of primordial $B$-modes of the CMB polarization. This makes the UV complete $R^2$ gravity a natural target for future CMB probes.Comment: 37 page

Towards a unitary formulation of quantum field theory in curved space-time II: the case of Schwarzschild black hole

We argue that the origin of unitarity violation and information loss paradox in our understanding of black holes (BH) lies in the standard way of doing quantum field theory in curved space-time (QFTCS), which is heavily biased on intuition borrowed from classical General Relativity. In this paper, with the quantum first approach, we formulate a so-called direct sum QFT (DQFT) in BH space-time based on a novel formulation of discrete space-time transformations in gravity that potentially restores unitarity. By invoking the quantum effects associated with the gravitational backreaction, we show that the Hawking quanta emerging outside of the Schwarzschild radius ($r_S=2GM$) cannot be independent of the quanta that continue to be inside $r_S$. This enables the information to be carried by Hawking quanta, but in the BH DQFT formalism, we do not get any firewalls. Furthermore, BH DQFT does not create any entanglement between interior and exterior Hawking quanta which implies there is no entanglement entropy and the BH evaporation happens involving only pure states. Finally, we discuss the ways our framework leaves important clues for formulating a scattering matrix and probing the nature of quantum gravity.Comment: 31 pages, 4 figures. Any comments are welcom

Unitary quantum gravitational physics and the CMB parity asymmetry

The proposal of Direct-Sum Quantum Field Theory (DQFT) offers a new perspective for quantum fields by combining parity and time reversal operations, blurring the distinction between quantum past and future while preserving causality. This approach provides a unitary QFT in curved spacetime, resolving the information-loss paradox. When applied to inflationary quantum fluctuations, DQFT predicts variations in CMB measurements, explaining longstanding anomalies as a result of parity asymmetry. The data strongly supports the unitary treatment of quantum fluctuations, with a probability over 650 times greater than the standard prediction. This significant discrepancy underscores the validity and importance of the DQFT approach in understanding the intricate relationship between gravity and quantum mechanics.Comment: 6 pages, 6 figure

Dark matter and Standard Model reheating from conformal GUT inflation

Spontaneous breaking of conformal symmetry has been widely exploited in successful model building of both inflationary cosmology and particle physics phenomenology. Conformal Grand Unified Theory (CGUT) inflation provides the same scalar tilt and tensor-to-scalar ratio as of Starobinsky and Higgs inflation. Moreover, it predicts a proton life time compatible with the current experimental bound. In this paper, we extend CGUT to account for the production of dark matter and the reheating of the Standard Model. To this end, we introduce a hidden sector directly coupled to the inflaton, whereas the reheating of the visible sector is realized through a portal coupling between the dark particles and the Higgs boson. The masses and interactions of the dark particles and the Higgs boson are determined by the form of the conformal potential and the non-vanishing VEV of the inflaton. We provide benchmark points in the parameter space of the model that give the observed dark matter relic density and reheating temperatures compatible with the Big Bang nucleosynthesis.Comment: 38 pages, 9 figures, matches published versio

Gravitational waves in α−\alpha-attractors

We study inflation in the $\alpha-$attractor model under a non-slow-roll dynamics with an ansatz proposed by Gong \& Sasaki \cite{Gong:2015ypa} of assuming $N=N\left(\phi\right)$. Under this approach, we construct a class of local shapes of inflaton potential that are different from the T-models. We find this type of inflationary scenario predicts an attractor at $n_{s}\sim0.967$ and $r\sim0.00055$. In our approach, the non-slow-roll inflaton dynamics are related to the $\alpha-$parameter which is the curvature of K\"ahler geometry in the SUGRA embedding of this model.Comment: 6 pages, 2 figures. Contribution to the proceedings of "The Fourtheenth Marcel Grossmann Meeting on General Relativity", University of Rome "La Sapienza", Rome, July 12-18, 2015, based on a talk delivered at the ST4 parallel sessio

Finite quantum gravity in dS and AdS spacetimes

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.Comment: 24 pages, final version with journal correction