Multidimensional cosmological models: Cosmological and astrophysical implications and constraints

Abstract

We investigate four-dimensional effective theories which are obtained by dimensional reduction of multidimensional cosmological models with factorizable geometry and consider the interaction between conformal excitations of the internal space (geometrical moduli excitations) and Abelian gauge fields. It is assumed that the internal space background can be stabilized by minima of an effective potential. The conformal excitations over such a background have the form of massive scalar fields (gravitational excitons) propagating in the external spacetime. We discuss cosmological and astrophysical implications of the interaction between gravexcitons and four-dimensional photons as well as constraints arising on multidimensional models of the type considered in our paper. In particular, we show that due to the experimental bounds on the variation of the fine structure constant, gravexcitons should decay before nucleosynthesis starts. For a successful nucleosynthesis the masses of the decaying gravexcitons should be m > ∼ 10 4 GeV. Furthermore, we discuss the possible contribution of gravexcitons to UHECR. It is shown that, at energies E ∼ 10 20 eV, the decay length of gravexcitons with masses m > ∼ 10 4 GeV is very small, but that for m < ∼ 10 2 GeV it becomes much larger than the Greisen-Zatsepin-Kuzmin cut-off distance. Finally, we investigate the possibility for gravexciton-photon oscillations in strong magnetic fields of astrophysical objects. The corresponding estimates indicate that even the high magnetic field strengths B of magnetars (special types of pulsars with B > B critical ∼ 4.4 × 10 13 Gauss) are not sufficient for an efficient and copious production of gravexcitons.

Extra dimensions and Lorentz invariance violation

“…Eq. (3) together with Bianchi identity (which is preserved in the considered model due to gaugeinvariance of the tensor, F µν [17]) defines a complete set 1 In the brane-world model the prefactor κ 0 in the expression for κ 0 ψ is replaced by the parameter proportional to M −1 EW [14]. Thus, the smallness condition holds for ψ < M EW .…”

“…In Kaluza-Klein models the term f(ψ)F 2 has the pure geometrical origin, and it appears in the effective, dimensionally reduced, four dimensional action (see e.g. [16,17]). In particular, in reduced Einstein-Yang-Mills theories, the function f (ψ) coincides (up to a numerical prefactor) with the volume of the internal space.…”

“…These demands lead to a certain constrains for gravexcitons (see Refs. [17,19]). We use the time delay effect, caused by the interaction between photons and gravexcitons, to get additional bounds on the parameters of gravexcitons.…”

“…Dimensional reduction of the action (1) results in the following effective D 0 -dimensional action [17] …”

“…[18]. To be more specific, we consider the model which is based on the reduced Einstein-Yang-Mills theory [17], where the term ∝ ψF 2 describes the interaction between the conformal excitations of the internal space (gravexcitons) and photons. It is clear that the similar LV effect exists for all types of interactions of the form f(ψ)F 2 mentioned above.…”