Black holes, cosmology and Brans-Dicke theories in 4+1 dimensional universe

Abstract

We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-Brans-Dicke theory. We show that exponentially growing and power law scale factors are implied. We solve the Brans-Dicke equations and we realize that only a linear warp factor satisfies these equations. In both exponentially expanding and power law expanding cases we find out that the scalar field is a function of the warp factor and the scale factor. Whereas the 4 + 1 dimensional scalar field is approximately constant for each case, the effective 3 + 1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor. We calculate the effective gravitational constant and realize that same results are valid. We construct a static solution for 4 + 1 dimensional bulk such that the 3 + 1 dimensional world has a linear warp factor and describes the Schwarzschild-dS4 black hole. The 4 + 1 dimensional space-time is taken to be flat. For zero mass this four dimensional universe and Friedmann-Robertson-Walker universe are related with an explicit coordinate transformation. Also we realize that if there is a contribution from the mass term, both energy momentum and cosmological constant vanish in the bulk. We explain the four dimensional cosmological constant originates from the hidden brane and its effects cause the localized mass densities in our visible brane. Using hierarchy between the Planck mass and electroweak energy scale, we obtain the size of the extra dimension as close to Hubble length but smaller than it. We emphasize that for linear warp factors the effect of bulk on the brane world shows up as the dS4 background which is favored by the Big Bang cosmology.