3 research outputs found
Isotropic singularity in inhomogeneous brane cosmological models
We discuss the asymptotic dynamical evolution of spatially inhomogeneous
brane-world cosmological models close to the initial singularity. By
introducing suitable scale-invariant dependent variables and a suitable gauge,
we write the evolution equations of the spatially inhomogeneous brane
cosmological models with one spatial degree of freedom as a system of
autonomous first-order partial differential equations. We study the system
numerically, and we find that there always exists an initial singularity, which
is characterized by the fact that spatial derivatives are dynamically
negligible. More importantly, from the numerical analysis we conclude that
there is an initial isotropic singularity in all of these spatially
inhomogeneous brane cosmologies for a range of parameter values which include
the physically important cases of radiation and a scalar field source. The
numerical results are supported by a qualitative dynamical analysis and a
calculation of the past asymptotic decay rates. Although the analysis is local
in nature, the numerics indicates that the singularity is isotropic for all
relevant initial conditions. Therefore this analysis, and a preliminary
investigation of general inhomogeneous () models, indicates that it is
plausible that the initial singularity is isotropic in spatially inhomogeneous
brane-world cosmological models and consequently that brane cosmology naturally
gives rise to a set of initial data that provide the conditions for inflation
to subsequently take place.Comment: 32 pages with 8 pictures. submitted to Class. Quant. Gra
Anisotropy in Bianchi-type brane cosmologies
The behavior near the initial singular state of the anisotropy parameter of
the arbitrary type, homogeneous and anisotropic Bianchi models is considered in
the framework of the brane world cosmological models. The matter content on the
brane is assumed to be an isotropic perfect cosmological fluid, obeying a
barotropic equation of state. To obtain the value of the anisotropy parameter
at an arbitrary moment an evolution equation is derived, describing the
dynamics of the anisotropy as a function of the volume scale factor of the
Universe. The general solution of this equation can be obtained in an exact
analytical form for the Bianchi I and V types and in a closed form for all
other homogeneous and anisotropic geometries. The study of the values of the
anisotropy in the limit of small times shows that for all Bianchi type
space-times filled with a non-zero pressure cosmological fluid, obeying a
linear barotropic equation of state, the initial singular state on the brane is
isotropic. This result is obtained by assuming that in the limit of small times
the asymptotic behavior of the scale factors is of Kasner-type. For brane
worlds filled with dust, the initial values of the anisotropy coincide in both
brane world and standard four-dimensional general relativistic cosmologies.Comment: 12 pages, no figures, to appear in Class. Quantum Gra