p-Adic and Adelic Harmonic Oscillator with Time-Dependent Frequency

The classical and quantum formalism for a p-adic and adelic harmonic oscillator with time-dependent frequency is developed, and general formulae for main theoretical quantities are obtained. In particular, the p-adic propagator is calculated, and the existence of a simple vacuum state as well as adelic quantum dynamics is shown. Space discreteness and p-adic quantum-mechanical phase are noted.Comment: 10 page

On the Schwarzschild-de Sitter metric of nonlocal de Sitter gravity

Earlier constructed a simple nonlocal de Sitter gravity model has a cosmological solution in a very good agreement with astronomical observations. In this paper, we continue the investigation of the nonlocal de Sitter model of gravity, focusing on finding an appropriate solution for the Schwarzschild-de Sitter metric. We succeeded to solve the equations of motion in a certain approximation. The obtained approximate solution is of particular interest for examining the possible role of non-local de Sitter gravity in describing the effects in galactic dynamics that are usually attributed to dark matter.Comment: 10 page

On Modified Gravity

We consider some aspects of nonlocal modified gravity, where nonlocality is of the type $R \mathcal{F}(\Box) R$. In particular, using ansatz of the form $\Box R = c R^\gamma,$ we find a few $R(t)$ solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is decelerated. R (t) = 0 satisfies all equations when k = -1.Comment: added references; made some clarifications; 8 page