Global and local gravitational redshifts in cosmology and their consequences for theory and observations

A consistent theory of gravitational redshift in cosmology (GRC) is formulated. The global GRC arises due to weakening of gravitational time dilation due to decreasing of matter density during the propagation time of photons. In the expanding world the local GRC arises due to the weakening of gravity of the sphere between observer and source, since photons emitted at a smaller radius arrive at a larger one. In static world there is no GRC at the exchange of photons at the periphery of this sphere. In any case photons from observer to source have the same GRC as photons from source to observer, which is in agreement with the cosmological principle. Consequences of the local and global GRC for cosmological models and their parameters, as well as corrections to data on distant objects and CMB, are considered. In Appendix the inconsistency of two former treatments of the gravitational frequency shift in cosmology is shown. They: a) did not take into account the global GRC; b) derived the local GRC not from the field of the sphere between the source and observer, but from the field of spheres around one of them; c) contradicted each other (the signs of shifts are opposite); d) violated cosmological principle (changing the propagation direction changes the sign of shift) and e) were based on the delusion that the Friedmann model supposedly contains the gravitational shift.

Big-Bang nucleosynthesis: Constraints on nuclear reaction rates, neutrino degeneracy, inhomogeneous and Brans–Dicke models

We review the recent progress in the Big-Bang nucleosynthesis which includes the standard and nonstandard theory of cosmology, effects of neutrino degeneracy, and inhomogeneous nucleosynthesis within the framework of a Friedmann model. As for a nonstandard theory of gravitation, we adopt a Brans–Dicke theory which incorporates a cosmological constant. We constrain various parameters associated with each subject.

ON THE DISTRIBUTION OF LUMINOUS MATTER IN A FRIEDMANN UNIVERSE

The Friedmann model is considered through stereographic projection of the Friedmann-Roberson-Walker metric for open, flat and closed matter-dominated universe. A relation between redshift and number density of galaxies is derived on the platform of this metric while neglecting the effects of dark matter and dark energy. The derived relation is observed to have the potential to test the fractal-homogeneous nature of our universe based on accurate future observational data.

Geometry of the Universe and Its Relation to Entropy and Information

In an effort to investigate a possible relation between geometry and information, we establish a relation of the Ricci scalar in the Robertson-Walker metric of the cosmological Friedmann model to the number of informationNand entropyS. This is with the help of a previously derived result that relates the Hubble parameter to the number of informationN. We find that the Ricci scalar has a dependence which is inversely proportional to the number of informationNand entropyS. Similarly, a nonzero number of information would imply a finite Ricci scalar, and therefore space time will unfold. Finally, using the maximum number of information existing in the universe, we obtain a numerical value for the Ricci scalar to beO(10-52) m-2.

THE BIANCHI TYPE I MODEL WITH TWO INTERACTING SCALAR FIELDS

The flat anisotropic model of the early Universe is considered. Two interacting scalar fields with a special form of potential energy are a source of matter fields. Analytic solutions for stages of inflation and preheating are found. It is shown that the solutions tend asymptotically to an isotropic Friedmann model.