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Several extensions of General Relativity and high energy physics include scalar fields as extra degrees of freedom. In the search for predictions in the non-linear regime of cosmological evolution, the community makes use of numerical…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
Starting with Maxwell's equations and defining normal variables in the Fourier space, we write the equations of temporal evolution of the electromagnetic field with sources in the Hamiltonian and Lagrangian forms, making explicit all…
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular…
It is a general belief that the only possible way to consistently deform the Pauli-Fierz action, changing also the gauge algebra, is general relativity. Here we show that a different type of deformation exists in three dimensions if one…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
We discuss some general characteristics of modifications of the 4D Einstein-Hilbert action that become important for low space-time curvatures. In particular we focus on the chameleon-like behaviour of the massive gravitational degrees of…
We discuss a mechanism which generates a mass term for a scalar field in an expanding universe. The mass of this field turns out to be generated by the cosmological constant and can be naturally small if protected by a conformal symmetry…
We study multidimensional cosmological models with a higher-dimensional product manifold, that consists of spherical and flat spaces, in the presence of a minimal free scalar field. Dynamical behaviour of the model is analyzed both in…
Degenerate scalar-tensor theories of gravity extend general relativity by a single degree of freedom, despite their equations of motion being higher than second order. In some cases, this is a mere consequence of a disformal field…
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…
The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…
A suitable deformation of the Hopf algebra of the creation and annihilation operators for a complex scalar field, initially quantized in Minkowski space--time, induces the canonical quantization of the same field in a generic gravitational…
We explore a comprehensive analysis of the formalism governing the gravitational field equations in degenerate higher-order scalar-tensor theories. The propagation of these theories in the vacuum has a maximum of three degrees of freedom…
We consider the quantum dynamics of a massless scalar field in de Sitter space-time. The classical evolution is represented by a canonical transformation on the phase space for the field theory. By studying the corresponding Bogoliubov…
Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many…
A modified-gravity theory with a four-form field strength $F$, a variable gravitational coupling parameter $G(F)$, and a standard matter action is considered here. Maxwell and Einstein equations are now derived when including to action also…
We solve Einstein's equation with Robertson-Walker metric as an initial-value problem, using as the source of gravity a Halpern-Huang real scalar field, which was derived from renormalization-group analysis, with a potential that exhibits…
We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in arXiv:1404.6495. As they generalize Horndeski theories, or "generalized" galileons, we call them G$^3$. These theories…
We study the evolution of cosmological perturbations, using a hybrid approximation scheme which upgrades the weak-field limit of Einstein's field equations to account for post-Newtonian scalar and vector metric perturbations and for…