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The recent direct detection of gravitational waves have been successfully used to examine the basic properties of the gravitational degrees of freedom. They set an upper bound on their mass and constrain their speed of propagation with unprecedented accuracy. Within the current realm of observational and theoretical constraints, we explore the possibility for gravity to depart from general relativity (GR) in the infrared and derive the implications on our observable Universe. We also investigate whether these types of models could ever enjoy a standard analytic UV completion. [ABSTRACT FROM AUTHOR]

The EFT coefficients in any gapped, scalar, Lorentz invariant field theory must satisfy positivity requirements if there is to exist a local, analytic Wilsonian UV completion. We apply these bounds to the tree level scattering amplitudes for a massive Galileon. The addition of a mass term, which does not spoil the non-renormalization theorem of the Galileon and preserves the Galileon symmetry at loop level, is necessary to satisfy the lowest order positivity bound. We further show that a careful choice of successively higher derivative corrections are necessary to satisfy the higher order positivity bounds. There is then no obstruction to a local UV completion from considerations of tree level 2-to-2 scattering alone. To demonstrate this we give an explicit example of such a UV completion. [ABSTRACT FROM AUTHOR]

The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there exist stable solutions in this class of models. This result also has important implications for Lorentz–invariant massive gravity: There exist stable nontrivial vacua in massive gravity that are free from any linear vDVZ-discontinuity and a Λ 2 decoupling limit can be defined on these vacua. [ABSTRACT FROM AUTHOR]

We present exact Friedmann Lemaítre Robertson Walkers (FLRW) solutions in generalized massive gravity where the mass parameters are naturally promoted to Lorentz-invariant functions of the Stückelberg fields. This new dependence relaxes the constraint that would otherwise prevent massive gravity from possessing exact FLRW solutions. It does so without the need to introduce additional degrees of freedom. We find self-accelerating cosmological solutions and show that, with a mild restriction on the region of phase space, these cosmological solutions exhibit full stability, i.e. absence of ghosts and gradient instabilities for all the tensor, vector and scalar modes, for all cosmic time. We perform the full decoupling limit analysis, including vector degrees of freedom, which can be used to confirm the existence of an active Vainshtein mechanism about these solutions. [ABSTRACT FROM AUTHOR]

Abstract: We show that every Galileon theory admits a dual formulation as a Galileon theory with new operator coefficients. In n dimensions a free scalar field in Minkowski spacetime is dual to a -th order Galileon theory which exhibits the Vainshtein mechanism when coupled to sources and superluminal propagation even on-shell. This demonstrates that superluminal propagation at low energies is compatible with an analytic S-matrix and causality. For point sources, the duality interchanges the strongly coupled Vainshtein regime with the weakly coupled asymptotic regime. [Copyright &y& Elsevier]

We show that the ghost-free models of massive gravity and their multi-graviton extensions follow from considering higher dimensional General Relativity in Einstein–Cartan form on a discrete extra dimension, according to the dimensional deconstruction paradigm. We show that dimensional deconstruction is equivalent to a truncation of the Kaluza–Klein tower at the nonlinear level. Higher dimensional gravity is not recovered from a lower dimensional multi-graviton theory in the limit of a continuous extra dimension (infinite Kaluza–Klein tower) due to the appearance of a low strong coupling scale that depends on IR physics. This strong coupling scale, which is associated with the mass of the lowest Kaluza–Klein mode, controls the onset of the Vainshtein mechanism and is crucial to the theoretical and observational viability of the truncated theory. [ABSTRACT FROM AUTHOR]

ABSTRACT We examine the mode functions of the electromagnetic field on spherically symmetric backgrounds with special attention to the subclass which allows for a foliation as open Friedmann-Lemaître (FL) space-time. It is well known that in certain scalar field theories on open FL background there can exist so-called supercurvature modes, their existence depending on parameters of the theory. Looking at specific open universe models, such as open inflation and the Milne universe, we find that no supercurvature modes are present in the spectrum of the electromagnetic field. This excludes the possibility for superadiabatic evolution of cosmological magnetic fields within these models without relying on new physics or breaking the conformal invariance of electromagnetism. [ABSTRACT FROM AUTHOR]

Abstract: Massive gravity in 4 dimensions has been shown to be free of the Boulware–Deser (BD) ghost in the ADM language for a specific choice of mass terms. We show here how this is consistent with the Stückelberg language beyond the decoupling limit, and how the constraint required to remove the BD ghost arises in this framework non-perturbatively, without the use of field redefinitions. We emphasize a subtlety in obtaining this constraint, that has been overlooked in previous literature. In both the ADM and Stückelberg formalisms the vanishing of the determinant of a Hessian guarantees the absence of the BD ghost. [Copyright &y& Elsevier]

Abstract: We calculate the cubic order terms in a covariant theory that gives a nonlinear completion of the Fierz–Pauli massive spin-2 action. The resulting terms have specially tuned coefficients guarantying the absence of a ghost at this order in the decoupling limit. We show in this limit that: (1) The quadratic theory propagates helicity-2, 1, and helicity-0 states of massive spin-2. (2) The cubic terms with six derivatives – which would give ghosts on local backgrounds – cancel out automatically. (3) There is a four-derivative cubic term for the helicity-0 field, that has been known to be ghost-free on any local background. (4) There are four-derivative cubic terms that mix two helicity-0 fields with one helicity-2, or two helicity-1 fields with one helicity-0; none of them give ghosts on local backgrounds. (5) In the absence of external sources, all the cubic mixing terms can be removed by nonlinear redefinitions of the helicity-2 and helicity-1 fields. Notably, the helicity-2 redefinition generates the quartic Galileon term. These findings hint to an underlying nonlinearly realized symmetry, that should be responsible for what appears as the accidental cancellation of the ghost. [Copyright &y& Elsevier]

Abstract: We propose an explicit non-linear realization of massive gravity, which relies on the introduction of a spurious compact extra dimension, on which we impose half-Newmann and half-Dirichlet boundary conditions. At the linearized level, we recover the expected gravitational exchange amplitude between two sources mediated by a massive Fierz–Pauli spin-2 field, while cubic interactions in the additional helicity-0 mode give rise to the expected Vainshtein mechanism. We also show that this framework can accommodate for a flat four-dimensional geometry in the presence of a cosmological constant, putting this framework on a good footing for the study of degravitation. [Copyright &y& Elsevier]

S-matrix bootstrap and positivity bounds are usually viewed as constraints on low-energy theories imposed by the requirement of a standard UV completion. By considering graviton-photon scattering in the standard model, we argue that the low-energy theory can be used to put constraints on the UV behavior of the gravitational scattering amplitudes. [ABSTRACT FROM AUTHOR]

We reconsider the construction of general derivative self-interactions for a massive Proca field. The constructed Lagrangian is such that the vector field propagates at most three degrees of freedom, thus avoiding the ghostly nature of a fourth polarisation. The construction makes use of the well-known condition for constrained systems of having a degenerate Hessian. We briefly discuss the casuistry according to the nature of the existing constraints algebra. We also explore various classes of interesting new interactions that have been recently raised in the literature. For the sixth order Lagrangian that satisfies the constraints by itself we prove its topological character, making such a term irrelevant. There is however a window of opportunity for exploring other classes of fully-nonlinear interactions that satisfy the constraint algebra by mixing terms of various order. [ABSTRACT FROM AUTHOR]

The recent direct detection of gravitational waves from a neutron star merger with optical counterpart has been used to severely constrain models of dark energy that typically predict a modification of the gravitational wave speed. However, the energy scales observed at LIGO, and the particular frequency of the neutron star event, lie very close to the strong coupling scale or cutoff associated with many dark energy models. While it is true that at very low energies one expects gravitational waves to travel at a speed different than light in these models, the same is no longer necessarily true as one reaches energy scales close to the cutoff. We show explicitly how this occurs in a simple model with a known partial UV completion. Within the context of Horndeski, we show how the operators that naturally lie at the cutoff scale can affect the speed of propagation of gravitational waves and bring it back to unity at LIGO scales. We discuss how further missions including LISA and PTAs could play an essential role in testing such models. [ABSTRACT FROM AUTHOR]

Cascading gravity is an explicit realization of the idea of degravitation, where gravity behaves as a high-pass filter. This could explain why a large cosmological constant does not backreact as much as anticipated from standard General Relativity. The model relies on the presence of at least two infinite extra dimensions while our world is confined on a four-dimensional brane. Gravity is then four-dimensional at short distances and becomes weaker and weaker at larger distances. [ABSTRACT FROM AUTHOR]

We show that there can be no new Lorentz invariant kinetic interactions free from the Boulware–Deser ghost in four dimensions in the metric formulation of gravity, beyond the standard Einstein–Hilbert, up to total derivatives. We use dimensional deconstruction as a way to motivate a non-linear ansatz for potential new ghost-free kinetic interactions for massive gravity, bi-gravity and multi-gravity in four and higher dimensions. These interactions descend from Lovelock terms, and so naively one might expect the interactions to be ghost-free. However, we show that these new interactions inevitably lead to more than five propagating degrees of freedom. We then perform a general perturbative analysis in four dimensions, and show that the only term with two derivatives that does not introduce a ghost is the Einstein–Hilbert term. This result extends to all orders in perturbations. [ABSTRACT FROM AUTHOR]

Euclid is a European Space Agency medium-class mission selected for launch in 2019 within the Cosmic Vision 2015 - 2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss ive broad topics: dark energy and modiied gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientiic themes that will underlie the activity of the group during the preparation of the Euclid mission. [ABSTRACT FROM AUTHOR]

The metric of a spacetime can be greatly simplified if the spacetime is circular. We prove that in generic effective theories of gravity, the spacetime of a stationary, axisymmetric, and asymptotically flat solution must be circular if the solution can be obtained perturbatively from a solution in the general relativity limit. This result applies to a broad class of gravitational theories that include arbitrary scalars and vectors in their light sector, so long as their nonstandard kinetic terms and nonmininal couplings to gravity are treated perturbatively. [ABSTRACT FROM AUTHOR]

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015-2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission. [ABSTRACT FROM AUTHOR]