Generalized Fibonacci Numbers, Cosmological Analogies, and an Invariant

Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing a spatially homogeneous and isotropic cosmology in general relativity. These analogies are presented together with their Lagrangian and Hamiltonian formulations and with an invariant of the Fibonacci sequence.

Hubble parameter in f(R)-gravity

In view of the famous problem with the “Hubble constant tension” there is a number of approaches to modify the cosmological equations and correspondingly modify Hubble parameter H(z) in order to to relieve the tension between the “early” and “late” Hubble constants. f(R)– gravity is one of such possible modifications. We discuss how to choose the Lagrangian in the f(R)– gravity on account of observational data within the homogeneous isotropic cosmology. The equation is obtained that enable us to derive f(R) for given Hubble parameter H(z). This yields a second order differential equation with corresponding degrees of freedom. If H(z) corresponds to that obtained from usual Friedmann equations, this equation yields a condition for f(R) to mimic the observable quantities of the standard ΛCDM with the above-mentioned freedom. To reduce this freedom on needs additional considerations, which involve the other observable quantities, such as those which appear in considerations of cosmological perturbations on the isotropic and homogeneous background. Also, we consider the reverse problem to find for given f(R). This is fulfilled within an approximation in case of small deviation of f(R) from the General Relativity value.

ON THEORY OF REGULAR ACCELERATING UNIVERSE IN RIEMANN–CARTAN SPACETIME

Isotropic cosmology built in the Riemann–Cartan spacetime is investigated. Properties of homogeneous isotropic cosmological models filled with usual gravitating matter and scalar fields are studied in the beginning of cosmological expansion near the limiting energy density. It is shown that cosmological models are regular not only with respect to the Hubble parameter and the energy density but also with respect to the torsion and curvature tensors.

Reconstruction of the equation of state for the cyclic universes in homogeneous and isotropic cosmology

We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) space-time. In particular, we reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic functions. It is explicitly illustrated that in several models the universe always stays in the non-phantom (quintessence) phase, whereas there also exist models in which the crossing of the phantom divide can be realized in the reconstructed cyclic universes.

DE SITTER SPACETIME WITH TORSION AS PHYSICAL SPACETIME IN THE VACUUM AND ISOTROPIC COSMOLOGY

Homogeneous isotropic models with two torsion functions built in the framework of the Poincaré gauge theory of gravity (PGTG) based on general expression of gravitational Lagrangian without cosmological constant are analyzed. It is shown that the physical spacetime in the vacuum in the framework of PGTG can have the structure of flat de Sitter spacetime with torsion. Some physical consequences of obtained conclusion are discussed.

A NOTE ON THE COSMOLOGICAL DYNAMICS IN FINITE-RANGE GRAVITY

In this note we consider the homogeneous and isotropic cosmology in the finite-range gravity theory recently proposed by Babak and Grishchuk. In this scenario the universe undergoes late time accelerated expansion if both the massive gravitons present in the model are tachyons. We carry out the phase space analysis of the system and show that the late-time acceleration is an attractor of the model.