Minimally modified theories of gravity: a playground for testing the uniqueness of general relativity

Abstract

In a recent paper [1], it was introduced a new class of gravitational theories with two local degrees of freedom. The existence of these theories apparently challenges the distinctive role of general relativity as the unique non-linear theory of massless spin-2 particles. Here we perform a comprehensive analysis of these theories with the aim of (i) understanding whether or not these are actually equivalent to general relativity, and (ii) finding the root of the variance in case these are not. We have found that a broad set of seemingly different theories actually pass all the possible tests of equivalence to general relativity (in vacuum) that we were able to devise, including the analysis of scattering amplitudes using on-shell techniques. These results are complemented with the observation that the only examples which are manifestly not equivalent to general relativity either do not contain gravitons in their spectrum, or are not guaranteed to include only two local degrees of freedom once radiative corrections are taken into account. Coupling to matter is also considered: we show that coupling these theories to matter in a consistent way is not as straightforward as one could expect. Minimal coupling, as well as the most straightforward non-minimal couplings, cannot be used. Therefore, before being able to address any issues in the presence of matter, it would be necessary to find a consistent (and in any case rather peculiar) coupling scheme.

Deformed General Relativity and Quantum Black Holes Interior

“…Phenomenological implications were explored both for inhomogeneous cosmological backgrounds as well as for black holes in [69][70][71]. More recently, exact solutions for black holes interior in a very large class of gravitational systems with deformed covariance were found in [72,73], and relations between these deformed theories and modified gravity (in the framework of scalartensor theories) have been investigated in [74][75][76][77][78][79][80].…”

Distinguishing general relativity from Chern-Simons gravity using gravitational wave polarizations

“…Even if waveforms for the numerous modifications to gravity [9][10][11] can be obtained, it is imperative to obtain a handful of parameters that can be used as a consistency test of GR. Specifically, it is essential to find a dimensionless, model-independent parameter which vanishes for GR and finite for modified gravity theories.…”

Rainbow-Like Black-Hole Metric from Loop Quantum Gravity

“…(8), the time reparametrization of the theory needs to be modified, leading to a rescaling of the lapse function N in Eq. (9) as…”

“…Various attempts, which seemed particularly promising at their birth, got stuck with insurmountable obstacles in the form of several formal complexities [1][2][3][4][5][6][7]. In the light of this, a more pragmatic approach to the problem of quantum gravity (QG) consisted in looking for simplified (or, better to say, effective) models able to encode a few characteristics of what we expect to be the theory of QG [3,[8][9][10][11]. Of course these models could not provide us with the "final theory" but may capture some key ingredients of QG, optimistically those that may allow us to perform experimental tests needed to guide our intuition as well as the construction of more reliable formal approaches to the problem.…”

“…Remarkably, at least in symmetry-reduced LQG models, it has been shown that the modified constraints still form a closed set of Poisson brackets, which is alternatively deformed with respect to the case of ADM GR [24,[26][27][28][29][30][31]. These first studies, performed within the framework of effective LQG, attracted renewed interest in the possibility of QG-induced symmetry deformations and inspired further analyses in other approaches beyond general relativity, namely: the gravity sector of multi-fractional models [32], a certain class of (minimally) modified theories of gravity in the canonical formulation [9], and finally canonical noncommutative gravity with ⋆-product deformations of the algebra [33]. Thus, this gave additional support to claim that QG may require a deformation of GR covariance.…”