Modified gravity. Problems and observational manifestations

Some models of modified gravity and their observational manifestations are considered. It is shown, that gravitating systems with mass density rising with time evolve to a singular state with infinite curvature scalar. The universe evolution during the radiation dominated epoch is studied in $R^2$-extended gravity theory. Particle production rate by the oscillating curvature is calculated. Possible implications of the model for cosmological creation of non-thermal dark matter are discussed.Comment: 8 pages, 4 figures, talk presented at Les Rencontres de Physique de la Vallee d'Aoste, 26 February - 3 March, 201

New Options for SUSY-kind Dark Matter

In the conventional cosmology masses of the stable supersymmetric relics, candidates for the dark matter (DM) particles, should be typically below 1 TeV. This is in conflict with the LHC bounds on the low energy SUSY. However, in $R^2$-gravity the masses of the stable particles with the interaction strength typical for SUSY could be much higher depending upon the dominant decay mode of the scalaron. We discuss the bounds on the masses of DM particles for the following dominant decay modes: to minimally coupled massless scalars, to massive fermions, and to gauge bosons.Comment: 5 pages, 1 table. Talk presented at 20th Lomonosov Conference on Elementary Particle Physics, Moscow, MSU, 19-25 August, 202

On Influence of Intensive Stationary Electromagnetic Field on the Behavior of Fermionic Systems

Exact solutions of Schroedinger and Pauli equations for charged particles in an external stationary electromagnetic field of an arbitrary configuration are constructed. Green functions of scalar and spinor particles are calculated in this field. The corresponding equations for complex energy of particles bounded by short range potential are deduced. Boundary condition typical for delta - potential is not used in the treatment. Explicit analytical expressions are given for the shift and width of a quasistationary level for different configurations of the external field. The critical value of electric field in which the idea of quasistationary level becomes meaningless is calculated. It is shown that the common view on the stabilizing role of magnetic field concerns only scalar particles.Comment: 15 pages, no figures, LaTeX2

Jeans Instability in Classical and Modified Gravity

Gravitational instability in classical Jeans theory, General Relativity, and modified gravity is considered. The background density increase leads to a faster growth of perturbations in comparison with the standard theory. The transition to the Newtonian gauge in the case of coordinate dependent background metric functions is studied. For modified gravity a new high frequency stable solution is found

Curvature Oscillations in Modified Gravity and High Energy Cosmic Rays

It is shown that F(R)-modified gravitational theories lead to curvature oscillations in astrophysical systems with rising energy density. The frequency and the amplitude of such oscillations could be very high and would lead to noticeable production of energetic cosmic ray particles.Comment: 7 pages, 2 figures, author's affiliation is correcte