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Out of several possible extensions of general relativity, the scalar-tensor theory is the most popular for several reasons. Since the quantum description of gravity is yet to be formulated properly, the understanding of a gravitational…
We reflect on the possibility of having a matter action that is invariant only under transverse diffeomorphisms. This possibility is particularly interesting for the dark sector, where no restrictions arise based on the weak equivalence…
We consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. Since two of these invariants possess odd parity, they naturally allow…
Due to its underlying gauge structure, teleparallel gravity achieves a separation between inertial and gravitational effects. It can, in consequence, describe the isolated gravitational interaction without resorting to the equivalence…
As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form…
Based on the recent result that, if the masses of timelike fields are point-dependent fields themselves, the action of matter fields is conformal form-invariant in its standard form, and on the active and passive approaches to conformal…
We extend the class of recently formulated scalar-nonmetricity theories by coupling a five-parameter nonmetricity scalar to a scalar field and considering a mixed kinetic term between the metric and the scalar field. The symmetric…
Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge…
Motivated by the two-dimensional massive gravity description of $T\overline{T}$ deformations, we propose a direct generalization in $d$ dimensions. Our methodology indicates that all terms up to order $d$ are present in the deformation. In…
It is shown that extensions to General Relativity, which introduce a strongly coupled scalar field, can be viable if the interaction has a non-conformal form. Such disformal coupling depends upon the gradients of the scalar field. Thus, if…
We put forward the idea that in addition to diffeomorphism invariance of general relativity (GR) the gravitational interaction is invariant under arbitrary scale-deformations of the metric field. In addition, we assume that the scaling…
The general relativistic perturbations of scalar-tensor theories (STT) of gravity are studied in a manifestly gauge invariant Hamiltonian formalism. After the derivation of the Hamiltonian equations of motion in this framework, the gauge…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
Horndeski gravity was highly constrained from the recent gravitational wave observations by the LIGO Collaboration down to $|c_{g}/c-1|\gtrsim 10^{-15}$. In this Letter we study the tensorial perturbations in a flat cosmological background…
General relativity dynamics can be derived from different actions -- which depart from the Einstein-Hilbert action in boundary terms -- and for different choices of the dynamical variables. Among them, the teleparallel equivalent of general…
Teleparallel gravity offers a new avenue in which to construct gravitational models beyond general relativity. While teleparallel gravity can be framed in a way to be dynamically equivalent to general relativity, its modifications are…
In this Note we show that Einstein's equations for gravity are generically invariant under 'disformations'. We also show that the particular subclass when this is not true yields the equations of motion of 'Mimetic Gravity'. Finally we give…
Horndeski gravity is the most general scalar-tensor theory with one scalar field leading to second-order Euler-Lagrange field equations for the metric and scalar field, and it is based on Riemannian geometry. In this paper, we formulate an…
We write down the teleparallel equivalent to Hassan-Rosen bigravity, which is written using a torsionful but curvature-free connection. The theories only differ by a boundary term. The equivalence was proven, both by using perturbation…
We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory,…