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We study the Hamiltonian structure of tri-gravity and four-gravity in the framework of ADM decomposition of the corresponding metrics. Hence we can deduce the general structure of the constraint system of multi-gravity. We will show it is…
The existence of a ghost free theory of massive gravity begs for an interpretation as a Higgs phase of General Relativity. We revisit the study of massive gravity as a Higgs phase. Absent a compelling microphysical model of spontaneous…
We perform the Hamiltonian analysis of general bimetric gravity. We determine four first class constraints that are generators of the diagonal diffeomorphism. We further analyze the remaining constraints and we present an evidence that…
In this paper we study the most general covariant action of gravity up to terms that are quadratic in curvature. In particular this includes non-local, infinite derivative theories of gravity which are ghost-free and exhibit asymptotic…
We give an introduction to massive spin-2 theories and the problem of their non-linear completion. We review the Boulware-Deser ghost problem and two ways to circumvent classic no-go theorems. In turn, massive spin-2 theories are not…
Coupling the galileons to a curved background has been a tradeoff between maintaining second order equations of motion, maintaining the galilean shift symmetries, and allowing the background metric to be dynamical. We propose a construction…
We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended…
We find unitary and local theories of higher curvature gravity in the vielbein formalism, known as the Poincar\'{e} gauge theory by utilizing the equivalence to the ghost-free massive bigravity. We especially focus on three and four…
I consider an extension of General Relativity by an auxiliary non-dynamical dimension that enables our space-time to acquire an extrinsic curvature. Obtained gravitational equations, without or with a cosmological constant, have a…
Adding terms quadratic in the curvature to the Einstein-Hilbert action renders gravity renormalizable. This property is preserved in the presence of the most general renormalizable couplings with (and of) a generic quantum field theory…
A ghost free massive deformation of unimodular gravity (UG), in the spirit of {\em mimetic massive gravity}, is shown to exist. This construction avoids the no-go theorem for a Fierz-Pauli type of mass term in UG by giving up on Lorentz…
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…
We consider Einstein-Maxwell-dilaton gravity with charged dust and interaction of the form $P(\chi) F_{\mu\nu} F^{\mu\nu}$, where $P(\chi)$ is an arbitrary function of the dilaton field $\chi$ that can be normal or phantom. For any regular…
A crucial building block of the ghost free massive gravity is the square root function of a matrix. This is a problematic entity from the viewpoint of existence and uniqueness properties. We accurately describe the freedom of choosing a…
We explore dilaton gravity with general dilaton potentials in the semi-classical limit viewed both as a gas of blunt defects and also as a semi-classical theory in its own right. We compare the exact defect gas picture with that obtained by…
The unimodular version of the ghost-free higher derivative gravity is obtained. It is the unimodular reduction of some particular lagrangians quadratic in curvature.
Non-linear partially massless (PM) gravity, if it exists, is a theory of massive gravity in which the graviton has four propagating degrees of freedom. In PM gravity, a scalar gauge symmetry removes one of the five modes of the massive…
We propose and study a new first order version of the ghost-free massive gravity. Instead of metrics or tetrads, it uses a connection together with Plebanski's chiral 2-forms as fundamental variables, rendering the phase space structure…
We present the construction of a gravitational action including an infinite series of higher derivative terms. The outcome is a classically consistent completion of a well-studied quadratic curvature theory. The closed form for the full…
The quantum cosmology of two-dimensional dilaton-gravity models is investigated. A class of models is mapped onto the constrained oscillator-ghost-oscillator model. A number of exact and approximate solutions to the corresponding…