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It is known that very distant galaxies, much like our own, show remarkably high receding velocities, the magnitude of which increases with distance. Therefore, in this study, a gravitational analog of the photoelectric effect was investigated by replacing the classical (wave) theory of gravity with a gravity quanta hypothesis. The significance of this concept regarding the motion of distant galaxies is evaluated by comparing the results obtained for a photon traveling through a Planck lattice model of spacetime to the observational data for both the cosmological redshift and time dilation effects of light from distant Type Ia supernovae. The photogravity effect does not necessarily invalidate the standard big bang cosmology and may in fact add a layer of fidelity to its conclusions concerning the evolution and age of the universe.

Number counts observations available with new surveys such as the Euclid mission will be an important source of information about the metric of the Universe. We compute the low red-shift expansion for the density contrast using an exact spherically symmetric solution in presence of a cosmological constant. At low red-shift the expansion is more precise than linear perturbation theory prediction. We then use the local expansion to reconstruct the metric from the monopole of the density contrast. We test the inversion method using numerical calculations and find a good agreement within the regime of validity of the red-shift expansion. The method could be applied to observational data to reconstruct the metric of the local Universe with a level of precision higher than the one achievable using perturbation theory.

The Hamiltonian formulation of modified dispersion relations (MDRs) allows for their implementation on generic curved spacetimes. In turn it is possible to derive phenomenological effects. I will present how to construct the kappa-Poincare dispersion relation on curved spacetimes, its spherically symmetric realizations, among them the kappa deformation of Schwarzschild spacetime, and its implementation on Friedmann-Lemaître-Robertson-Walker spacetimes with arbitrary scale factor. In addition we will construct the general first order modifications of the general relativistic dispersion relation. After-wards we will use the perturbative MDRs to calculate specific observables such as the redshift, lateshift and photon circular orbits.

Nature of photon trajectories in a curved spacetime around black holes are studied without constraining their motion to any plane. Impacts of photon bending are separately scrutinized for Keplerian and CENBOL components of Two Component Advective Flow (TCAF) model. Parameters like Red shift, Bolometric Flux, temperature profile and time of arrival of photons are also computed.