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The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…

Modifications of General Relativity generically contain additional degrees of freedom that can mediate forces between matter particles. One of the common manifestations of a fifth force in alternative gravity theories is a difference…

In recent years Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected.…

A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under…

The dispersion relations in the real and imaginary parts of the meson self-energies are studied to check the consistency of the "renormalization" in cutoff field theory. It is shown that the dispersion relations are preserved by the…

In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions…

The variability of gamma-ray burst (GRB) is thought to be correlated with its absolute peak luminosity, and this relation had been used to derive an estimate of the redshifts of GRBs. Recently Amati et al. presented the results of spectral…

We present the second-order general relativistic description of the observed galaxy number density in a cosmological framework. The observed galaxy number density is affected by the volume and the source effects, both of which arise due to…

Gravitational redshift imprints a slight asymmetry in the observed clustering of galaxies, producing odd multipoles (e.g.\ the dipole) in the cross-correlation function. But there are other sources of asymmetry which must also be considered…

There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The…

Subject of this contribution is to demonstrate that the observed faintness of the supernovae at the high redshift can be considered as a manifestation of quantum effects at cosmological scales. We show that observed redshift distribution of…

We investigate the properties of one--dimensional flux ``voids'' (connected regions in the flux distribution above the mean flux level) by comparing hydrodynamical simulations of large cosmological volumes with a set of observed…

A great number of macroquantum laws connecting gravity and electromagnetism if found empirically. To describe them the model of anisotropic gravitational field is proposed. This field is build as a superposition of planes and force lines…

The quantum model of the homogeneous and isotropic universe predicts logarithmic-law dependence of coordinate distance to source on redshift z which is in good agreement with type Ia supernovae and radio galaxies observations for the…

This note looks at the possibility of a system of free particles presenting decoherence in the total momentum when tracing upon their relative momenta if we take into account a relativistic correction to the expression of the kinetic…

Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…

We consider a new set of effects arising from the quantum gravity corrections to the propagation of fields, associated with fluctuations of the spacetime geometry. Using already existing experimental data, we can put bounds on these effects…

Deformed dispersion relations are considered in the study of equations of state of Fermi gas with applications to compact objects. Different choices of deformed energy relations are used in the formulation of our model. As a first test, we…

The evolution of density perturbations is analysed in a modified theory of gravity with a nonminimal coupling between curvature and matter. We consider the broken degeneracy between the choices of matter Lagrangian for a perfect fluid,…

Starting from the luminosity-redshift relation recently given up to second order in the Poisson gauge, we calculate the effects of the realistic stochastic background of perturbations of the so-called concordance model on the combined…