Constraints for warped branes

We investigate singular geometries which can be associated with warped branes in arbitrary dimensions. If the brane tension is allowed to be variable, the extremum condition for the action requires additional constraints beyond the solution of the field equations. In a higher dimensional world, such constraints arise from variations of the metric which are local in the usual four-dimensional spacetime, without changing the geometry of internal space. As a consequence, continuous families of singular solutions of the field equations, with arbitrary integration constants, are generically reduced to a discrete subset of extrema of the action, similar to regular spaces. As an example, no static extrema of the action with effective four-dimensional gravity exist for six-dimensional gravity with a cosmological constant. These findings explain why the field equations of the reduced four-dimensional theory are not consistent with arbitrary solutions of the higher dimensional field equations - consistency requires the additional constraints. The characteristic solutions for variable tension branes are non-static runaway solutions where the effective four-dimensional cosmological constant vanishes as time goes to infinity.Comment: 25 page

Gravitational excitons from extra dimensions

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces near minima of an effective potential have a form of massive scalar fields in the external space-time. Parameters of models which ensure minima of the effective potentials are obtained for particular cases and masses of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20 pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97

1/R multidimensional gravity with form-fields: stabilization of extra dimensions, cosmic acceleration and domain walls

We study multidimensional gravitational models with scalar curvature nonlinearity of the type 1/R and with form-fields (fluxes) as a matter source. It is assumed that the higher dimensional space-time undergoes Freund-Rubin-like spontaneous compactification to a warped product manifold. It is shown that for certain parameter regions the model allows for a freezing stabilization of the internal space near the positive minimum of the effective potential which plays the role of the positive cosmological constant. This cosmological constant provides the observable late-time accelerating expansion of the Universe if parameters of the model is fine tuned. Additionally, the effective potential has the saddle point. It results in domain walls in the Universe. We show that these domain walls do not undergo inflation.Comment: 10 pages, revtex, 5 eps figures, footnotes and references adde

AdS and stabilized extra dimensions in multidimensional gravitational models with nonlinear scalar curvature terms 1/R and R^4

We study multidimensional gravitational models with scalar curvature nonlinearities of the type 1/R and R^4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with warped product structure. Special attention is paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the 1/R model that configurations with stabilized extra dimensions do not provide a late-time acceleration (they are AdS), whereas the solution branch which allows for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R^4 model, we obtain that the stability region in parameter space depends on the total dimension D=dim(M) of the higher dimensional spacetime M. For D>8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singularity (and an antigravity sector beyond it) by a potential barrier of infinite height and width. This sector is smoothly connected with the stability region of a curvature-linear model. For D<8 an additional (metastable) sector exists which is separated from the conformal singularity by a potential barrier of finite height and width so that systems in this sector are prone to collapse into the conformal singularity. This second sector is not smoothly connected with the first (absolutely stable) one. Several limiting cases and the possibility for inflation are discussed for the R^4 model.Comment: 28 pages, minor cosmetic improvements, Refs. added; to appear in Class. Quantum Gra

On singular solutions in multidimensional gravity

It is proved that the Riemann tensor squared is divergent as \tau \ra 0 for a wide class of cosmological metrics with non-exceptional Kasner-like behaviour of scale factors as \tau \ra 0, where $\tau$ is synchronous time. Using this result it is shown that any non-trivial generalization of the spherically-symmetric Tangherlini solution to the case of $n$ Ricci-flat internal spaces \cite{FIM} has a divergent Riemann tensor squared as R \ra R_0, where $R_0$ is parameter of length of the solution. Multitemporal naked singularities are also considered.Comment: 16 pages, LaTex. Submitted to Gravitation and Cosmology (new Russian journal