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In the light of recent experimental and theoretical data, we go back to the studies tackled in previous publications [1] and develop some of their consequences. Some of their main aspects will be studied in further detail. Yet this text…
This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…
Does relativistic gravity provide arguments against the existence of a preferred frame? Our answer is negative. We define a viable theory of gravity with preferred frame. In this theory, the EEP holds exactly, and the Einstein equations of…
The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content…
Spacetime geometry is described by two -- {\em a priori} independent -- geometric structures: the symmetric connection $\Gamma$ and the metric tensor $g$. Metricity condition of $\Gamma$ (i.e. $\nabla g = 0$) is implied by the Palatini…
Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. In particular, we argue that previous…
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. Galilean or Lorentz space-time…
Modifications of gravity generated by a multiplicative coupling of a scalar field to the electromagnetic Lagrangian lead to a breaking of Einstein equivalence principle (EEPB) as well as to variations of fundamental constants. In these…
The disformal transformation of metric $g_{\mu \nu} \to \Omega^2 (\phi)g_{\mu \nu}+\Gamma(\phi,X) \partial_{\mu}\phi \partial_{\nu}\phi$, where $\phi$ is a scalar field with the kinetic energy $X= \partial_{\mu}\phi \partial^{\mu}\phi/2$,…
A class of homogeneous isotropic space-time models including pseudo-Euclidean space as a special case is considered. Such a model is chosen, where the particle motion is described in the most adequate way. It means that the world tubes of…
To explain the recently reported large-scale spatial variations of the fine structure constant $\alpha$, we apply some models of curvature-nonlinear multidimensional gravity. Under the reasonable assumption of slow changes of all quantities…
The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects…
We consider the quantum effects of matter fields in scalar-tensor theories and clarify the role of trace anomaly when switching between conformally related `frames'. We exploit the property that the couplings between the scalar and the…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
The Standard Cosmological Model assumes that the Universe is, on average, homogeneous and isotropic for large scales (z>1), but this principle has been questioned from the results about Cosmic Microwave Background. This radiation has…
In 1981, Mermin published a now famous paper titled, "Bringing home the atomic world: Quantum mysteries for anybody" that Feynman called, "One of the most beautiful papers in physics that I know." Therein, he presented the "Mermin device"…
Eigenvectors of stress-energy tensor (the source in Einstein's equations) form privileged bases in description of the corresponding space-times. When one or more of these vector fields are rotating (the property well determined in…
A scalar theory of gravity with a preferred reference frame is presented. It is insisted on the dynamics, which involves a (non-trivial) extension of Newton's second law, and on the new version (v2) with isotropic space metric. We display…
Bianchi cosmologies are ``natural'' anisotropic extensions of the Friedmann universes and they have long been used to investigate the cosmological implications of anisotropy. The latter introduces new ingredients to the standard scenarios,…
Large-scale bulk peculiar motions introduce a characteristic length scale, inside which the local kinematics are dominated by peculiar-velocity perturbations rather than by the background Hubble expansion. Regions smaller than the…