Brane singularities with mixtures in the bulk

Abstract

By extending previous analysis of the authors, a systematic study of the singularity structure and possible asymptotic behaviors of five-dimensional braneworld solutions is performed in the case where the bulk is a mixture of an analog of perfect fluid (with a density and pressure depending on the extra coordinate) and a massless scalar field. The two bulk components interact by exchanging energy so that the total energy is conserved. In a particular range of the interaction parameters, we find flat brane general solutions avoiding the singularity at finite distance from the brane, in the same region of the equation of state constant parameter $\gamma=P/\rho$ that we found previously in the absence of the bulk scalar field $(-1<\gamma<-1/2)$.Comment: 48 page

Infinity in string cosmology: A review through open problems

“…There are at least two areas here where interesting research programs may be grounded. The first is the extension of the works [68,69] (see next Section for a brief description of that work) from Minkowski (or dS or AdS) branes to general RobertsonWalker ones (for a background on the latter cf. [70], where embeddings, geodesics and fluctuations are worked out in detail).…”

The Singularity Problem in Brane Cosmology

“…This is an on-going project with many open problems, the non-interacting, co-existing fluid case is treated in detail in Reference [8]. For the massless scalar, we then take an energy-momentum tensor of the form T 1 AB = (ρ 1 + P 1 )u A u B − P 1 g AB , where A, B = 1, 2, 3, 4, 5, u A = (0, 0, 0, 0, 1) and ρ 1 , P 1 are its density and pressure, which we take as P 1 = ρ 1 = λφ 2 /2, with λ a parameter.…”

“…In Reference [8], it was noticed that suitably choosing the exchange parameters ν, σ, and analyzing the resulting dynamical system has the effect of moving these singular points to infinity. There is an intricate structure of the eigenvalues of the asymptotic matrix that controls the behaviour of the solutions in this case, and this structure leads to the interesting result that for the same interval of the fluid parameter as in the massless dilaton case-namely, γ ∈ (−1, −1/2)-the singularities are seen to move to infinity.…”

“…In this paper we provide a concise overview of the various ramifications and results that have been obtained in recent years about the singularity problem in such contexts, basically using the methods developed in References [6][7][8][9]. Previous work on this subject can be found in [10].…”

Curved branes with regular support

“…(2.10) gives the following relation between the density and the warp factor: 12) and after setting C = 2/3Ac 1 (note that the sign of C is the same as the sign of ρ), we have the Friedman constraint in the form…”