Exact Solutions of Five Dimensional Anisotropic Cosmologies

We solve the five dimensional vacuum Einstein equations for several kinds of anisotropic geometries. We consider metrics in which the spatial slices are characterized as Bianchi types-II and V, and the scale factors are dependent both on time and a non-compact fifth coordinate. We examine the behavior of the solutions we find, noting for which parameters they exhibit contraction over time of the fifth scale factor, leading naturally to dimensional reduction. We explore these within the context of the induced matter model: a Kaluza-Klein approach that associates the extra geometric terms due to the fifth coordinate with contributions to the four dimensional stress-energy tensor.Comment: 11 page

Scales of the Extra Dimensions and their Gravitational Wave Backgrounds

Circumstances are described in which symmetry breaking during the formation of our three-dimensional brane within a higher-dimensional space in the early universe excites mesoscopic classical radion or brane-displacement degrees of freedom and produces a detectable stochastic background of gravitational radiation. The spectrum of the background is related to the unification energy scale and the the sizes and numbers of large extra dimensions. It is shown that properties of the background observable by gravitational-wave observatories at frequencies $f\approx 10^{-4}$ Hz to $10^3$ Hz contain information about unification on energy scales from 1 to $10^{10}$ TeV, gravity propagating through extra-dimension sizes from 1 mm to $10^{-18}$mm, and the dynamical history and stabilization of from one to seven extra dimensions.Comment: 6 pages, Latex, 1 figure, submitted to Phys. Re

Gravitational Waves from Mesoscopic Dynamics of the Extra Dimensions

Recent models which describe our world as a brane embedded in a higher dimensional space introduce new geometrical degrees of freedom: the shape and/or size of the extra dimensions, and the position of the brane. These modes can be coherently excited by symmetry breaking in the early universe even on ``mesoscopic'' scales as large as 1 mm, leading to detectable gravitational radiation. Two sources are described: relativistic turbulence caused by a first-order transition of a radion potential, and Kibble excitation of Nambu-Goldstone modes of brane displacement. Characteristic scales and spectral properties are estimated and the prospects for observation by LISA are discussed. Extra dimensions with scale between 10 \AA and 1 mm, which enter the 3+1-D era at cosmic temperatures between 1 and 1000 TeV, produce backgrounds with energy peaked at observed frequencies in the LISA band, between $10^{-1}$ and $10^{-4}$ Hz. The background is detectable above instrument and astrophysical foregrounds if initial metric perturbations are excited to a fractional amplitude of $10^{-3}$ or more, a likely outcome for the Nambu-Goldstone excitations.Comment: Latex, 5 pages, plus one figure, final version to appear in Phys. Rev. Let

Higher Dimensional Cosmological Implications Of A Decay Law For Λ\Lambda Term : Expressions For Some Observable Quantities

Implications of cosmological model with a cosmological term of the form $\Lambda = \beta \frac{\ddot {a}}{a}$, where $\beta$ is a constant, are analyzed in multidimensional space time. The proper distance, the luminosity distance-redshift, the angular diameter distance-redshift, and look back time-redshift for the model are presented. It has been shown that such models are found to be compatible with the recent observations. This work has thus generalized to higher dimensions the well-know result in four dimensional space time. It is found that there may be significant difference in principle at least,from the analogous situation in four dimensional space time.Comment: 11 pages, no figur