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In this chapter, we will review the field-theoretic treatment of General Relativity based on an effective field theory extension of the Einstein-Hilbert action. This pragmatic route to low-energy quantum effects in gravity critically underpins miscellaneous investigations of phenomenological and quantum extensions of General Relativity. We discuss how it allows quantum field theory to be a theoretical laboratory for testing Einstein's theory of gravity and demonstrate the current state of the art of an efficient and practical scheme for evaluating the classical components of perturbative weak-field scattering amplitudes until the fourth post-Minkowskian order. Such results complement numerical predictions in Einstein's theory of gravity., Comment: 42 pages. 12 figures. Invited chapter for the Section "Effective Quantum Gravity" edited by C. Burgess and J. Donoghue of the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Nature, expected in 2023)

We have taken a modified version of the Einstein Hilbert action, $ f(R, T^\phi) $ gravity under consideration, where $T^\phi$ is the energy-momentum tensor trace for the scalar field under consideration. The structural behaviour of the scalar field considered varies with the form of the potential. The number of polarization modes of gravitational waves in modified theories has been studied extensively for the corresponding fields. There are two additional scalar modes, in addition to the usual two transverse-traceless tensor modes found in general relativity: a massive longitudinal mode and a massless transverse mode (the breathing mode)., Comment: Prepared for Proceedings of XXIV Bled Workshop

The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context. In this brief review, we focus on the post-Minkowskian expansion as applied to the two-body problem in general relativity without spin, and we describe how relativistic quantum field theory can be used to greatly simplify analytical calculations based on the Einstein-Hilbert action. Subtleties related to the extraction of classical physics from such quantum mechanical calculations highlight the care which must be taken when both positive and negative powers of Planck's constant are at play. In the process of obtaining classical results in both Einstein gravity and supergravity, one learns new aspects of quantum field theory that are obscured when using units in which Planck's constant is set to unity. The scattering amplitude approach provides a self-contained framework for deriving the two-body scattering valid in all regimes of energy. There is hope that the full impact of amplitude computations in this field may significantly alter the way in which gravitational wave predictions will advance in the coming years., Comment: 35 pages, see also the overview article. v2: minor corrections, published version

The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein--Hilbert action reduces to a one-dimensional mechanical model. We have shown in [SciPost Phys. 10, 022 (2021), [2010.07059]] that this model exhibits a symmetry under the $(2+1)$-dimensional Poincar\'e group. Here we explain how this can be understood as a broken infinite-dimensional BMS$_3$ symmetry. This is done by reinterpreting the action for the model as a geometric action for BMS$_3$, where the configuration space variables are elements of the algebra $\mathfrak{bms}_3$ and the equations of motion transform as coadjoint vectors. The Poincar\'e subgroup then arises as the stabilizer of the vacuum orbit. This symmetry breaking is analogous to what happens with the Schwarzian action in AdS$_2$ JT gravity, although in the present case there is no direct interpretation in terms of boundary symmetries. This observation, together with the fact that other lower-dimensional gravitational models (such as the BTZ black hole) possess the same broken BMS$_3$ symmetries, provides yet another illustration of the ubiquitous role played by this group., Comment: 32 pages

International audience; We present a novel and remarkably simple formulation of degenerate higher-order scalar-tensor (DHOST) theories whose Lagrangian is quadratic in the second derivatives of some scalar field. Using disformal transformations of the metric, we identify a special “frame” (or metric) for which the Lagrangian of quadratic DHOST theories reduces to the usual Einstein-Hilbert term plus a few terms that depend on simple geometric quantities characterizing the uniform scalar-field hypersurfaces. In particular, for quadratic DHOST theories in the physically interesting class Ia, the Lagrangian simply consists of the Einstein-Hilbert term plus a term proportional to the three-dimensional scalar curvature of the uniform scalar-field hypersurfaces. The classification of all quadratic DHOST theories becomes particularly transparent in this geometric reformulation, which also applies to scalar-tensor theories that are degenerate only in the unitary gauge.

We show that the introduction of two worldline parameters defines a different approach to computations in the effective field theory approach to the two-body problem in General Relativity and present some preliminary evidence for a reduction in computational complexity. These parameters obey a polynomial equation whose perturbative expansion recovers an infinite series of diagrams. Futhermore, we show that our equations define an effective two-body horizon for interacting particles in General Relativity; in the circular orbit case, it corresponds to the smallest conceivable separation up to which the orbit can remain circular. We expect our results to simplify higher-order computations in the two-body problem, as well as to give insights on the nonperturbative properties of interacting binaries., 16 pages, 6 figures. More detailed version accepted in PRD

We study string loop corrections to the gravity kinetic terms in type IIB compactifications on Calabi-Yau threefolds or their orbifold limits, in the presence of $D7$-branes and orientifold planes. We show that they exhibit in general a logarithmic behaviour in the large volume limit transverse to the $D7$-branes, induced by a localised four-dimensional Einstein-Hilbert action that appears at a lower order in the closed string sector, found in the past. Here, we compute the coefficient of the logarithmic corrections and use them to provide an explicit realisation of a mechanism for K\"ahler moduli stabilisation that we have proposed recently, which does not rely on non-perturbative effects and lead to de Sitter vacua. Our result avoids no-go theorems of perturbative stabilisation due to runaway potentials, in a way similar to the Coleman-Weinberg mechanism, and provides a counter example to one of the swampland conjectures concerning de Sitter vacua in quantum gravity, once string loop effects are taken into account; it thus paves the way for embedding the Standard Model of particle physics and cosmology in string theory., Comment: 18 pages, 4 figures; published version

Physics letters / B 807, 135496 - (2020). doi:10.1016/j.physletb.2020.135496, We calculate the motion of binary mass systems in gravity up to the sixth post–Newtonian order to the GN3 terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates. For these contributions we construct a canonical transformation to isotropic and to EOB coordinates at 5PN and agree with the results in the literature [1,2] by Bern et al. and Damour. At 6PN we compare to the Hamiltonians in isotropic coordinates either given in [1] or resulting from the scattering angle. We find a canonical transformation from our Hamiltonian in harmonic coordinates to [1] , but not to [2] . This implies that we also agree on all observables with [1] to the sixth post–Newtonian order to GN3 ., Published by North-Holland Publ., Amsterdam

We present two cases where the addition of the $R^2$ term to an inflationary model leads to single-field inflation instead of two-field inflation as is usually the case. In both cases we find that the effect of the $R^2$ term is to reduce the value of the tensor-to-scalar ratio $r$., Comment: 18 pages, 7 figures, invited talk given at Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity", 31 August - 25 September 2019, Corfu, Greece

In this paper we show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For doing so we need to introduce an auxiliary, hybrid, manifold whose geometry we construct explicitely. This allows us to find the vector density, constructed out of spacetime quantities only, whose divergence is the exterior derivative of the transgression form. As a consequence we can show how the Einstein-Hilbert, Gauss-Bonnet and, in general, the Euler scalar densities can be written as the divergences of genuine vector densities in the critical dimensions $D=2,4$, etc. As Lovelock gravity is a dimensional continuation of Euler densities, these results are of relevance for Gauss-Bonnet and, in general, Lovelock gravity. Indeed, these vectors which can be called generalized Katz vectors ensure, in particular, a well-posed Dirichlet variational principle., 15 pages

We describe scalar-bimetric theories where the dynamics of the Universe are governed by two separate metrics, each with an Einstein-Hilbert term. In this setting, the baryonic and dark matter components of the Universe couple to metrics which are constructed as functions of these two gravitational metrics. The scalar field, contrary to dark energy models, does not have a potential whose role is to mimic a late-time cosmological constant. The late-time acceleration of the expansion of the Universe can be easily obtained at the background level in these models by appropriately choosing the coupling functions appearing in the decomposition of the vierbeins for the baryonic and dark matter metrics. We explicitly show how the concordance model can be retrieved with negligible scalar kinetic energy. This requires the scalar coupling functions to show variations of order unity during the accelerated expansion era. This leads in turn to deviations of order unity for the effective Newton constants and a fifth force that is of the same order as Newtonian gravity, with peculiar features. The baryonic and dark matter self-gravities are amplified although the gravitational force between baryons and dark matter is reduced and even becomes repulsive at low redshift. This slows down the growth of baryonic density perturbations on cosmological scales, while dark matter perturbations are enhanced. In our local environment, the upper bound on the time evolution of Newton's constant requires an efficient screening mechanism that both damps the fifth force on small scales and decouples the local value of Newton constant from its cosmological value. This cannot be achieved by a quasi-static chameleon mechanism, and requires going beyond the quasi-static regime and probably using derivative screenings, such as Kmouflage or Vainshtein screening, on small scales., 35 pages

We consider the consequences of the leading quartic corrections to the Einstein–Hilbert action of gravity at low energy. Using the equivalence between the scalar [Formula: see text] contribution and a scalar-tensor field theory, we analyze the possible ways of detecting the associated scalaron and suggest that short distance tests of gravity, and in particular future tests of Newton’s law aboard satellites, would provide the best environment to detect such a modification of gravity. We also analyze the regimes for which the [Formula: see text] theory would result as a low energy manifestation of putative high energy UV completions involving extra dimensions. In the four-dimensional [Formula: see text] supergravity limit of such extra-dimensional models, the [Formula: see text] models would emerge from the stabilization of a nearly no-scale superfield such as the ones associated to the Kähler modulus corresponding to the breathing mode of a six-dimensional compactification.

We determine a consistent phase space for a theory consisting in the Einstein-Hilbert action coupled to matter fields (dilaton, one-form, two-form) and containing three-dimensional black strings (the Horne-Horowitz solution and generalizations thereof). The theory at hand is the low energy effective action for the bosonic sector of heterotic string theory. We find a consistent set of boundary conditions whose algebra of asymptotic charges consist in a single Virasoro algebra supplemented by three global u(1) generators. We also discuss the thermodynamics of the zero-mode solutions and point out some peculiar features of this system., SCOPUS: ar.j, info:eu-repo/semantics/published

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlator can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum., 21 pages, matches JCAP version

A set of novel derivative terms for spin-2 fields are proposed. They are the wedge products of curvature two-forms and vielbeins. In this work, we investigate the properties of novel two-derivative terms in the context of bi-gravity. Based on a minisuperspace analysis, we identify a large class of bi-gravity models where the Boulware-Deser ghost could be absent. We give a new perspective that Weyl Gravity and New Massive Gravity belong to this class of bi-gravity models involving novel derivative terms. In addition, we discuss the UV cut-off scales, dynamical symmetric conditions and novel higher-derivative terms., Comment: 19 pages, two columns, v3.1; a reference is added