Classical evolution of subspaces

Abstract

We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. A number of final metrics describing our Universe is quite poor if we limit ourselves with a maximally symmetric extra space. We show that the initial conditions can be a reason of nontrivial solutions (funnels) and study their properties.

Cosmology and Matter-Induced Branes

“…Action (1) is firmly confirmed at the energies lower than ∼ 10TeV. A variety of modified gravitational actions are studied at higher scales, [7,8]. The necessary condition for all of them is the reduction to the standard form (1) at the low energies.…”

Inhomogeneous compact extra dimensions and de Sitter cosmology

“…Let us briefly discuss the observational manifestations of such solutions. As was shown in [16], there exist such extra-dimensional metrics that lead to the 4D cosmological constant Λ 4 arbitrarily close to zero. This effect is a result of interference between the gravitational and scalar field parts of the Lagrangian.…”

“…in addition to r (u) and φ(u). As three independent equations for this system, we can take, for example, (13), (12) and a combination of (16) and 12:…”

“…a e-mail: kb20@yandex.ru b e-mail: arkady_popov@mail.ru c e-mail: sergeirubin@list.ru (corresponding author) In this paper, we study the possible influence of a matter field on the metric of extra dimensions. Previous results concerning multidimensional gravity with 4D Minkowski factor space are published in [13][14][15][16][17], where the importance of inhomogeneous extra dimensions was discussed. In particular, the scalar field localization on deformed extra space.…”

Sub-Planckian Scale and Limits for f(R) Models

“…Other attempts were undertaken to describe the whole period of evolution of the universe with the multiparametric f (R) function; see References [12][13][14][15][16][17].…”