Brane singularities and their avoidance

The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, it is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved. In the case where the bulk field content is parametrized by an analogue of perfect fluid with an arbitrary equation of state P=\gamma\rho between the `pressure' P and the `density' \rho, our results depend crucially on the constant fluid parameter \gamma: (i) For \gamma>-1/2, the flat brane solution suffers from a collapse singularity at finite distance, that disappears in the curved case. (ii) For \gamma<-1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For -1<\gamma< or = -1/2, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility for a revival of the self-tuning proposal.Comment: 37 pages, latex, merged version of arXiv:1005.3221 and arXiv:1004.3379, to appear in Class.Quant.Gra

New Isotropic and Anisotropic Sudden Singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.Comment: Typos corrected. Published versio

Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday

We discuss the modified gravity which includes negative and positive powers of the curvature and which provides the gravitational dark energy. It is shown that in GR plus the term containing negative power of the curvature the cosmic speed-up may be achieved, while the effective phantom phase (with $w$ less than -1) follows when such term contains the fractional positive power of the curvature. The minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fliud may describe the (effective phantom) dark energy. The account of $R^2$ term (consistent modified gravity) may help to escape of cosmic doomsday.Comment: LaTeX file, 9 pages, based on the talk given by S.D. Odintsov (Int. Conference Mathematical Methods in Physics, Rio de Janeiro, Augest, 2004), to appear in CQG, Letter

DYNAMICS AND ASYMPTOTICS OF BRANE-WORLDS

The self-tuning mechanism aims to provide a way to address the cosmological constant problem by guarantying the existence of flat brane solutions independently of the brane tension value. In recent work we have studied the asymptotics of different models of brane-worlds, and here we highlight certain interesting behaviors we have encountered in our search for appropriate conditions to avoid finite-distance singularities in flat brane solutions. Finding such conditions offers a framework within which the self-tuning mechanism could be realized

Regular braneworlds with nonlinear bulk-fluids

We construct a regular five-dimensional brane-world with localised gravity on a flat 3-brane. The matter content in the bulk is parametrised by an analog of a non-linear fluid with equation of state p= γρλ between the ‘pressure’ p and the ‘density’ ρ dependent on the 5th dimension. For γ negative and λ&gt; 1 , the null energy condition is satisfied and the geometry is free of singularities within finite distance from the brane, while the induced four-dimensional Planck mass is finite. © 2021, The Author(s)