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Usually when applying the mimetic model to the early universe, higher derivative terms are needed to promote the mimetic field to be dynamical. However such models suffer from the ghost and/or the gradient instabilities and simple…
We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on "seed" scalar-tensor theories which may be nondegenerate, we can…
The main goal of this thesis is to quantize the Einstein-Hilbert action extended by the quadratic curvature terms within the canonical quantization approach, thus formulating quantum geometrodynamics of the higher derivative theories. The…
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type,…
We investigate higher-derivative extensions of Einstein-Maxwell theory that are invariant under electromagnetic duality rotations, allowing for non-minimal couplings between gravity and the gauge field. Working in a derivative expansion of…
We consider a maximal extension of the Hilbert-Einstein action and analyze several interesting features of the theory. More specifically, the motion is non-geodesic and takes place in the presence of an extra force. These models could lead…
The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…
The effective approach is applied to the analysis of inflationary magnetogenesis. Rather than assuming a particular underlying description, all the generally covariant terms potentially appearing with four space-time derivatives in the…
Higher-derivative operators are central elements of any effective field theory. In supersymmetric theories, these operators include terms with derivatives in the K\"ahler potential. We develop a toolkit for coupling such supersymmetric…
We classify higher-order Maxwell-Einstein theories linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength whose kinetic matrices are degenerate. This provides a generalisation of quadratic…
During inflation, higher derivative terms in the gravitational action may play a significant role. Building on new stable formulations of four-derivative scalar-tensor theories, we study the impact of these corrections in the case where the…
Einstein-aether theory is extended by allowing for spinning degrees of freedom of the aether. In addition to the acceleration, shear, expansion, and vorticity of the aether velocity field, a spin rotation describing the dynamics of a…
Modified theories of gravity usually present new degrees of freedom, as well as higher order derivatives, wrong signs in certain terms and complicated couplings already present in the Lagrangian from the beginning or originated by the field…
We study various aspects of higher-curvature theories of gravity built from contractions of the metric, the Riemann tensor and the covariant derivative, $\mathcal{L}(g^{ab},R_{abcd},\nabla_a)$. We characterise the linearized spectrum of…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
We study next-to-leading corrections to the effective action of the curvature perturbation obtained by integrating out the coupled heavy isocurvature perturbation. These corrections result from including higher order derivative operators,…
I discuss the relation between arbitrarily high-order theories of gravity and scalar-tensor gravity at the level of the field equations and the action. I show that $(2n+4)$-order gravity is dynamically equivalent to Brans-Dicke gravity with…
In this work a study of the gravity is made using Einstein's equation in the post-Newtonian approach. This is a method to linearise the General Relativity indicated to treat non-relativistic objects. It enables us to construct, from…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…