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We consider the cosmology of the Ricci-tensor-squared gravity in the Palatini variational approach. The gravitational action of standard general relativity is modified by adding a function f(R^abR_ab) to the Einstein-Hilbert action, and the…
Barbour's interpretation of Mach's principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, "shapes." Recently, it was shown that the dynamics of General…
This thesis is devoted to the study of gravitational theories which can be seen as modifications or generalisations of General Relativity. The motivation for considering such theories, stemming from Cosmology, High Energy Physics and…
Both muon tomography and gravimetry are geophysical methods that provide information on the density structure of the Earth's subsurface. Muon tomography measures the natural flux of cosmic muons and its attenuation produced by the screening…
In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Typically, the…
Approximate equations are derived for the motion of a gyroscope on the earth's gravitational field using the Einstein, Infeld, Hoffmann surface integral method. This method does not require a knowledge of the energy-momentum-stress tensor…
It is a review paper. General relativity (GR) is presented in the field theoretical form, where gravitational field (metric perturbations) together with other physical fields are propagated in an auxiliary arbitrary curved background…
Many theories of modified gravity, including the well studied Horndeski models, are characterized by a screening mechanism that ensures that standard gravity is recovered near astrophysical bodies. In a recently introduced class of…
We naturally extend the theory of gravity with a conformally coupled scalar field by only requiring conformal invariance of the scalar field equation of motion and not of the action. The classically extended theory incorporates a…
We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear…
Monte Carlo simulations are an essential tool in particle physics data analysis. Events are typically generated alongside weights that redistribute the cross section of the simulated process across the phase space. These weights can be…
We revise general relativity (GR) from the perspective of calculus for moving surfaces (CMS). While GR is intrinsically constructed in pseudo-Riemannian geometry, a complete understanding of moving manifolds requires embedding in a higher…
For the study of cosmological backreacktion an avaragng procedure is required. In this work a covariant and gauge invariant averaging formalism for finite volumes will be developed. This averaging will be applied to the scalar parts of…
Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have been studied in great detail. When considered as complete theories of gravity they…
The effects implied for the structure of compact objects by the modification of General Relativity produced by the generalization of the Lagrangian density to the form f(R)=R+\alpha R^2, where R is the Ricci curvature scalar, have been…
The "external" or "bulk" motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition, and velocity are allowed as long as there is no direct…
For a class of viable cosmological models in $f(R)$ gravity which deviation from the Einstein gravity decreases as a inverse power law of the Ricci scalar $R$ for large $R$, an analytic solution for density perturbations in the matter…
In survey statistics, the usual technique for estimating a population total consists in summing appropriately weighted variable values for the units in the sample. Different weighting systems exit: sampling weights, GREG weights or…
It is known that any explicit averaging scheme of the type essential for describing the large scale behaviour of the Universe, must necessarily yield corrections to the Einstein equations applied in the Cosmological setting. The question of…
The gravitational potential and the gravitational rotation field generated by a thin-disk mass distribution with exponential density are considered in the case when the force between any two mass elements is not the usual Newtonian one, but…