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Linearized gravitational waves in Brans-Dicke and scalar-tensor theories carry negative energy. A gauge-invariant analysis shows that the background Minkowski space is stable at the classical level with respect to linear scalar and tensor…

We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark…

We explore in detail a dilatonic scalar-tensor theory of gravity inspired by large extra dimensions, where a radion field from compact extra dimensions gives rise to quintessence in our 4-dimensional world. We show that the model can give…

We use astrophysical data to shed light on fundamental physics by constraining parametrized theoretical cosmological and gravitational models. Gravitational parameters are those constants that parametrize possible departures from Einstein's…

We study a subclass of Horndeski gravity which has both global conformal and shift symmetries. Global symmetries are characterised by the presence of a conserved current which has been shown to be of particular importance for the…

It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric $g_{\mu \nu} \to \Omega^2(\phi)g_{\mu \nu}+\Gamma (\phi,X)…

Various gravity theories beyond general relativity have been rigorously investigated in the literature such as Horndeski and degenerate higher-order scalar-tensor (DHOST) theories. In general, numerous model parameters are involved in such…

We construct gravitational modifications that go beyond Horndeski, namely theories with extended nonminimal derivative couplings, in which the coefficient functions depend not only on the scalar field but also on its kinetic energy. Such…

The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in…

In the context of the effective field theory of dark energy (EFT) we perform agnostic explorations of Horndeski gravity. We choose two parametrizations for the free EFT functions, namely a power law and a dark energy density-like behaviour…

Screening mechanisms are essential features of dark energy models mediating a fifth force on large scales. We study the regime of strong scalar field nonlinearities, known as Vainshtein screening, in the most general scalar-tensor theories…

It is known that the construction of a completely stable solution in Horndeski theory is restricted very strongly by the so-called no-go theorem. Previously, various techniques have been used to avoid the conditions of the theorem. In this…

This contribution reviews scalar-tensor theories whose Lagrangian contains second-order derivatives of a scalar field but nevertheless propagate only one scalar mode (in addition to the usual two tensor modes), and are thus not plagued with…

(abridged) We report the results of a 10-year timing campaign on PSR J1738+0333, a 5.85-ms pulsar in a low-eccentricity 8.5-hour orbit with a low-mass white dwarf companion (...) The measurements of proper motion and parallax allow for a…

We study a class of homogeneous but anisotropic cosmologies within the family of shift-symmetric Horndeski theories, where the scalar field features an inhomogeneous profile but it preserves a translational symmetry that is realised as a…

The detection of an electromagnetic counterpart (GRB 170817A) to the gravitational wave signal (GW170817) from the merger of two neutron stars opens a completely new arena for testing theories of gravity. We show that this measurement…

We review the most general scalar-tensor cosmological models with up to second-order derivatives in the field equations that have a fixed spatially flat de Sitter critical point independent of the material content or vacuum energy. This…

Horndeski's vector-tensor (HVT) gravity is described by a Lagrangian in which the field strength $F_{\mu \nu}=\partial_{\mu} A_{\nu}-\partial_{\nu} A_{\mu}$ of a vector field $A_{\mu}$ interacts with a double dual Riemann tensor $L^{\mu \nu…

We investigate the stability and gravitational waves (GWs) in the four-dimensional general Einstein-vector theory in a cosmological background. The theory accommodates up to six propagating degrees of freedom, comprising two tensor, two…

Neutron stars (NS) offer an exceptional opportunity to investigate gravitational physics in extreme environments. In the context of alternative theories of General Relativity (GR), a scalar field non-minimally coupled to gravity can lead to…