Integrable pseudo-Euclidean Toda-like systems in multidimensional cosmology with multicomponent perfect fluid

Abstract

The multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of multicomponent perfect fluid is considered. When the vectors corresponding to the equations of state of the components are orthogonal with respect to the minisuperspace metric, the Einstein equations are integrated and a Kasner-like form of the solutions is presented. For special sets of parameters the cosmological model is reduced to the Euclidean Toda-like system connected with some Lie algebra G. For G=A2 exact solutions are explicitly written. A certain family of wormhole solutions is also obtained.

Multidimensional cosmological models: Cosmological and astrophysical implications and constraints

“…The latter can be achieved if the decay rate becomes larger. However, a fast decay in the regime of a broad parametric resonance [62] may not be realized for gravexcitons since it requires the condition Γ >> H at the beginning of the decay (H ∼ m ψ ) which is not satisfied (see estimate (34)). …”

“…gauge fields and scalar fields 6 . In some models these matter fields can be considered phenomenologically as a perfect fluid with energy density ρ and corresponding equation of state [20,21,34,35]. This provides, for example, an efficient way to take into account the Casimir effect [36], Freund-Rubin monopoles [24,37,38] or other hypothetical potentials [20,39].…”

“…where Im is proportional either to the trace of the EMT of matter on the world-brane (in brane-world scenarios [17]), or to the energy density of matter in our 4D Universe (in the Kaluza-Klein approach [9,21,34,46]). The behavior of the source term Im is defined not only by the red-shifting EMT of matter but also by gravexcitons' interactions with it, e.g.…”

“…(34). n ψ(eq) denotes the gravexciton number density in thermal equilibrium (The subscript is not to be mixed with that of the characteristic time of matter/radiation equality).…”

On Observational Predictions from Multidimensional Gravity

“…Other possible manifestations of extra dimensions are monopole modes in gravitational waves, various predictions for standard cosmological tests and generation of the cosmological constant [10], and numerous effects connected with local field sources, some of them being the subject of the present paper. These include, in particular, deviations from the Newton and Coulomb laws [11,4,5,12] and properties of black holes.…”