Generalized G-Inflation: --Inflation with the Most General Second-Order Field Equations--

The Tolman-Ehrenfest criterion of thermal equilibrium in scalar-tensor gravity

The Tolman-Ehrenfest criterion for the thermal equilibrium of a fluid at rest in a static general-relativistic geometry is generalized to scalar-tensor gravity. Surprisingly, the gravitational scalar field, which fixes the strength of the effective gravitational coupling, does not play a role in determining thermal equilibrium. As a result, heat does not sink more in a gravitational field where gravity is stronger.

More on the first-order thermodynamics of scalar-tensor and Horndeski gravity

Two issues in the first-order thermodynamics of scalar-tensor (including "viable" Horndeski) gravity are elucidated. The application of this new formalism to FLRW cosmology is shown to be fully legitimate and then extended to all Bianchi universes. It is shown that the formalism holds thanks to the almost miraculous fact that the constitutive relations of Eckart's thermodynamics are satisfied, while writing the field equations as effective Einstein equations with an effective dissipative fluid does not contain new physics.

Teleparallel gravity: from theory to cosmology

Teleparallel gravity (TG) has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we give a comprehensive introduction to how teleparallel geometry is developed as a gauge theory of translations together with all the other properties of gauge field theory. This relates the geometry to the broader metric-affine approach to forming gravitational theories where we describe a systematic way of constructing consistent teleparallel theories that respect certain physical conditions such as local Lorentz invariance. We first use TG to formulate a teleparallel equivalent of general relativity (GR) which is dynamically equivalent to GR but which may have different behaviors for other scenarios, such as quantum gravity. After setting this foundation, we describe the plethora of modified teleparallel theories of gravity that have been proposed in the literature. We attempt to connect them together into general classes of covariant gravitational theories. Of particular interest, we highlight the recent proposal of a teleparallel analogue of Horndeski gravity which offers the possibility of reviving all of the regular Horndeski contributions. In the second part of the Review, we first survey works in teleparallel astrophysics literature where we focus on the open questions in this regime of physics. We then discuss the cosmological consequences for the various formulations of TG. We do this at background level by exploring works using various approaches ranging from dynamical systems to Noether symmetries, and more. Naturally, we then discuss perturbation theory, firstly by giving a concise approach in which this can be applied in TG theories and then apply it to a number of important theories in the literature. Finally, we examine works in observational and precision cosmology across the plethora of proposal theories. This is done using some of the latest observations and is used to tackle cosmological tensions which may be alleviated in teleparallel cosmology. We also introduce a number of recent works in the application of machine learning to gravity, we do this through deep learning and Gaussian processes, together with discussions about other approaches in the literature.

Avoidance of Strong Coupling in General Relativity Solutions with a Timelike Scalar Profile in a Class of Ghost-Free Scalar-Tensor Theories

Modified gravity theories can accommodate exact solutions, for which the metric has the same form as the one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is that perturbations around them exhibit strong coupling when the solutions are realized in degenerate higher-order scalar-tensor theories. We show that the strong coupling problem can be circumvented in the framework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a way that higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect is built-in in U-DHOST theories in general. There is an apparent Ostrogradsky mode in U-DHOST theories, but it does not propagate as it satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface. We also clarify how this nonpropagating mode, i.e., the "shadowy" mode shows up at the nonlinear level.

Reformulating scalar-tensor field theories as scalar-scalar field theories using a novel geometry

In this paper, I shall show how the notions of Finsler geometry can be used to construct a similar geometry using a scalar field, f, on the cotangent bundle of a differentiable manifold M. This will enable me to use the second vertical derivatives of f, along with the differential of a scalar field φ on M, to construct a Lorentzian metric on M that depends upon φ. I refer to a field theory based upon a manifold with such a Lorentzian structure as a scalar-scalar field theory. We shall study such a theory when f is chosen so that the resultant metric on M has the form of a Friedmann-Lemaître-Robertson-Walker metric, and the Lagrangian has a particularly simple form. It will be shown that the scalar-scalar theory determined by the Lagrangian can generate self-inflating universes, which can be pieced together to form multiverses with non-Hausdorff topologies, in which the global time function multifurcates at t = 0. Some of the universes in these multiverses begin explosively, and then settle down to a period of much quieter accelerated expansion, which can be followed by a collapse to its original, pre-expansion state. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.

Search for Dark Higgs Inflation with Curvature Corrections at LHC Experiments

We analyse the dark Higgs inflation model with curvature corrections and explore the possibility to test its predictions by the particle physics experiments at LHC. We show that the dark Higgs inflation model with curvature corrections is strongly favoured by the present cosmological observation. The cosmological predictions of this model, including the quantum corrections of dark Higgs coupling constants and the uncertainty in estimation of the reheating temperature, lead to the dark Higgs mass mφ=0.919± 0.211 GeV and the mixing angle (at 68% CL). We evaluate the FASER and MAPP-1 experiments reach for dark Higgs inflation mass and mixing angle in the 95% CL cosmological confidence region for an integrated luminosity of 3ab−1 at 13 TeV LHC, assuming 100% detection efficiency. We conclude that the dark Higgs inflation model with curvature corrections is a compelling inflation scenario based on particle physics theory favoured by the present cosmological measurements that can leave imprints in the dark Higgs boson searchers at LHC.

Why Must Primordial Non-Gaussianity Be Very Small?

One-loop correction to the power spectrum in generic single-field inflation is calculated by using standard perturbation theory. Because of the enhancement inversely proportional to the observed red tilt of the spectral index of curvature perturbation, the correction turns out to be much larger than previously anticipated. As a result, the primordial non-Gaussianity must be much smaller than the current observational bound in order to warrant the validity of cosmological perturbation theory.

Cosmological Tests of Gravity: A Future Perspective

In this review, we outline the expected tests of gravity that will be achieved at cosmological scales in the upcoming decades. We focus mainly on constraints on phenomenologically parameterized deviations from general relativity, which allow to test gravity in a model-independent way, but also review some of the expected constraints obtained with more physically motivated approaches. After reviewing the state-of-the-art for such constraints, we outline the expected improvement that future cosmological surveys will achieve, focusing mainly on future large-scale structures and cosmic microwave background surveys but also looking into novel probes on the nature of gravity. We will also highlight the necessity of overcoming accuracy issues in our theoretical predictions, issues that become relevant due to the expected sensitivity of future experiments.

Dynamics of Screening in Modified Gravity

Gravitational theories differing from general relativity may explain the accelerated expansion of the Universe without a cosmological constant. However, to pass local gravitational tests, a "screening mechanism" is needed to suppress, on small scales, the fifth force driving the cosmological acceleration. We consider the simplest of these theories, i.e., a scalar-tensor theory with first-order derivative self-interactions, and study isolated (static and spherically symmetric) nonrelativistic and relativistic stars. We produce screened solutions and use them as initial data for nonlinear numerical evolutions in spherical symmetry. We find that these solutions are stable under large initial perturbations, as long as they do not cause gravitational collapse. When gravitational collapse is triggered, the characteristic speeds of the scalar evolution equation diverge, even before apparent black-hole or sound horizons form. This casts doubts on whether the dynamical evolution of screened stars may be predicted in these effective field theories.

Sound Speed Resonance of the Stochastic Gravitational-Wave Background

We propose a novel mechanism to test time variation of the propagation speed of gravitational waves (GWs) in light of GWs astronomy. As the stochastic GWs experience the whole history of cosmic expansion, they encode potential observational evidence of such variation. We report that, one feature of a varying GWs speed is that the energy spectrum of GWs will present resonantly enhanced peaks if the GWs speed oscillates in time at high-energy scales. Such oscillatory behavior arises in a wide class of modified gravity theories. The amplitude of these peaks can be at reach by current and forthcoming GWs instruments, hence making the underlying theories falsifiable. This mechanism reveals that probing the variation of GWs speed can be a promising way to search for new physics beyond general relativity.

Extremal Cosmological Black Holes in Horndeski Gravity and the Anti-Evaporation Regime

Extremal cosmological black holes are analysed in the framework of the most general second order scalar-tensor theory, the so-called Horndeski gravity. Such extremal black holes are a particular case of Schwarzschild-De Sitter black holes that arises when the black hole horizon and the cosmological one coincide. Such metric is induced by a particular value of the effective cosmological constant and is known as Nariai spacetime. The existence of this type of solutions is studied when considering the Horndeski Lagrangian and its stability is analysed, where the so-called anti-evaporation regime is studied. Contrary to other frameworks, the radius of the horizon remains stable for some cases of the Horndeski Lagrangian when considering perturbations at linear order.

Inflation with Scalar-Tensor Theory of Gravity

The latest released data from Planck in 2018 put up tighter constraints on inflationary parameters. In the present article, the in-built symmetry of the non-minimally coupled scalar-tensor theory of gravity is used to fix the coupling parameter, the functional Brans–Dicke parameter, and the potential of the theory. It is found that all the three different power-law potentials and one exponential pass these constraints comfortably, and also gracefully exit from inflation.

Dynamically Generated Inflationary ΛCDM

Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden, nonlinear Noether symmetry which produces an energy-momentum tensor identified as the sum of a dynamically generated cosmological constant and dust-like dark matter. The non-Riemannian volume-element in the initial Einstein–Hilbert action upon passage to the physical Einstein-frame creates, dynamically, a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data.

Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity

We study a theory of gravity of the form f ( G ) where G is the Gauss–Bonnet topological invariant without considering the standard Einstein–Hilbert term as common in the literature, in arbitrary ( d + 1 ) dimensions. The approach is motivated by the fact that, in particular conditions, the Ricci curvature scalar can be easily recovered and then a pure f ( G ) gravity can be considered a further generalization of General Relativity like f ( R ) gravity. Searching for Noether symmetries, we specify the functional forms invariant under point transformations in a static and spherically symmetric spacetime and, with the help of these symmetries, we find exact solutions showing that Gauss–Bonnet gravity is significant without assuming the Ricci scalar in the action.

Gravity and Nonlinear Symmetry Realization

Application of nonlinear symmetry realization technique to gravity is studied. We identify the simplest extensions of the Poincare group suitable for nonlinear realization at the level of physical fields. Two simple models are proposed. The first one introduces additional scalar degrees of freedom that may be suitable for driving inflation. The second one describes states with well-defined mass that lack a linear interaction with matter states. We argue that this phenomenon points out a necessity to draw a distinction between gravitational states with well-defined masses and states that participate in interaction with matter.

Horndeski theory and beyond: a review

This article is intended to review the recent developments in the Horndeski theory and its generalization, which provide us with a systematic understanding of scalar-tensor theories of gravity as well as a powerful tool to explore astrophysics and cosmology beyond general relativity. This review covers the generalized Galileons, (the rediscovery of) the Horndeski theory, cosmological perturbations in the Horndeski theory, cosmology with a violation of the null energy condition, degenerate higher-order scalar-tensor theories and their status after GW170817, the Vainshtein screening mechanism in the Horndeski theory and beyond, and hairy black hole solutions.

Disformal Transformations in Scalar–Torsion Gravity

We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar–torsion actions which is invariant under disformal transformations, and which possesses different invariant subclasses. For the most simple of these subclasses we explicitly derive all terms that may appear in the action. We propose to study actions from this class as possible teleparallel analogues of healthy beyond Horndeski theories.

Einstein-Gauss-Bonnet Gravity with Extra Dimensions

We consider a theory of modified gravity possessing d extra spatial dimensions with a maximally symmetric metric and a scale factor, whose ( 4 + d ) -dimensional gravitational action contains terms proportional to quadratic curvature scalars. Constructing the 4D effective field theory by dimensional reduction, we find that a special case of our action where the additional terms appear in the well-known Gauss-Bonnet combination is of special interest as it uniquely produces a Horndeski scalar-tensor theory in the 4D effective action. We further consider the possibility of achieving stabilised extra dimensions in this scenario, as a function of the number and curvature of extra dimensions, as well as the strength of the Gauss-Bonnet coupling. Further questions that remain to be answered such as the influence of matter-coupling are briefly discussed.

Dark Energy after GW170817 Revisited

We revisit the status of scalar-tensor theories with applications to dark energy in the aftermath of the gravitational wave signal GW170817 and its optical counterpart GRB170817A. At the level of the cosmological background, we identify a class of theories, previously declared unviable in this context, whose anomalous gravitational wave speed is proportional to the scalar equation of motion. As long as the scalar field is assumed not to couple directly to matter, this raises the possibility of compatibility with the gravitational wave data, for any cosmological sources, thanks to the scalar dynamics. This newly "rescued" class of theories includes examples of generalized quintic Galileons from Horndeski theories. Despite the promise of this leading order result, we show that the loophole ultimately fails when we include the effect of large scale inhomogeneities.