Narrow Results

We discuss the brane cosmology in the 5D anti de Sitter Reissner–Nordstrom (AdSRN₅) space–time. A brane with tension σ is defined as the edge of an AdSRN₅ space with mass M and charge Q. In this case we get the CFT-radiation term (ρ_CFT) from M and the charged dust from Q² in the Friedmann-like equation. However, this equation is not justified because it contains -term with the negative sign. This is unconventional in view of the standard cosmology. In order to resolve this problem, we introduce a localized dust matter which satisfies P_dm = 0. If , the unwanted is cancelled against and thus one recovers a standard Friedmann–Robertson–Walker universe with CFT-radiation and dust matter. For the stiff matter consideration, we can set ρ_csti ~ Q² with the negative sign. Here we introduce a massless scalar which plays the role of a stiff matter with P_sca = ρ_sca to cancel -ρ_csti. In this case, however, we find a mixed version of the standard and brane cosmologies.

The most remarkable and interesting feature of brane world scenario is the use of bulk's curvature to localize gravity on the brane, albeit with fine tuning of the brane and bulk parameters. For FRW expanding universe on the brane, it is a moving hypersurface in Schwarzschild anti de Sitter bulk spacetime. We show that zero mass gravitons have bound state on the brane for suitable values of brane and bulk parameters. There occur various cases giving rise to different cosmological models, in particular we discuss a model with positive cosmological constant on the brane.

We investigate a model of brane cosmology to find a unified description of the radiation-matter-dark energy universe. It is of the interacting holographic dark energy with a bulk-holographic matter χ. This is a five-dimensional cold dark matter, which plays a role of radiation on the brane. Using the effective equations of state instead of the native equations of state ω_Λ, we show that this model cannot accommodate any transition from the dark energy with to the phantom regime . Furthermore, the case of interaction between four-dimensional cold dark matter and five-dimensional cold dark matter is considered for completeness. Here we find that the redshift of matter-radiation equality z_eq is the same order as . Finally, we obtain a general decay rate Γ which is suitable for describing all interactions.

A Brans–Dicke brane cosmology with two scalar fields inspired from string theories and phenomenological effective cosmological constant is investigated and some features are described in some details, in particular the low and high energies limit.

We find exact solution of the Einstein equations in the context of the braneworld scenario. We assumed a generalized Chaplygin gas equation of state for bulk. This study displays a constant energy density and pressure for bulk in late time. It is shown that our assumptions impose a specific equation of state on brane. In this work, we obtain a decelerate universe in early time and late time. In the end, it is shown that under some assumption we can obtain equation of state of cosmological constant for bulk.

We study the dynamical equations for extra-dimensional dependence of a warp factor and a bulk scalar in 5D brane world scenarios with 3+1 de Sitter slices. We show that these equations are similar to the equations for 4D scalar field cosmology, but with the sign of the scalar field potential reversed. We construct three dimensional phase portraits for this system for a variety of potentials. We show that for many potentials there will be an unavoidable singularity occuring a finite distance from the brane. This singularity can be shielded by the addition of a second brane. The properties of these branes will generally fix the inter-brane separation and effective 4D cosmological constants, thus providing a possible mechanism for stabilizing the braneworld. Some of these results were previously known for some models, but we bring together a variety of results and show how they can all be easily seen using phase portraits.

Thermodynamics of 5d SdS black hole is considered. Thermal fluctuations define the (sub-dominant) logarithmic corrections to black hole entropy and then to Cardy–Verlinde formula and to FRW brane cosmology. We demonstrate that logarithmic terms (which play the role of effective cosmological constant) change the behavior of 4d spherical brane in dS, SdS or Nariai bulk. In particularly, bounce Universe occurs or 4d dS brane expands to its maximum and then shrinks. The entropy bounds are also modified by next-to-leading terms. Out of braneworld context the logarithmic terms may suggest slight modification of standard FRW cosmology.

We analyze possible cosmological scenarios on a brane where the brane acts as a dynamical boundary of various black holes with anti-de Sitter or de Sitter asymptotic. In many cases, the brane is found to describe the completely nonsingular universe. In some cases, quantum gravity era of the brane-universe can also be avoided by properly tuning bulk parameters. We further discuss the creation of a brane-universe by studying its wave function. This is done by employing Wheeler–De Witt equation in the mini superspace formalism.

The semiclassical corrections to the Cardy–Verlinde entropy of a five-dimensional Schwarzschild de-Sitter black hole (SdS₅) are explicitly evaluated. These corrections are considered within the context of KKW analysis and arise as a result of the self-gravitation effect. In addition, a four-dimensional spacelike brane is considered as the boundary of the SdS₅ bulk background. It is already known that the induced geometry of the brane is exactly given by that of a radiation-dominated FRW universe. By exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of SdS₅ bulk black hole as the source for stiff matter. Furthermore, we rewrite the Friedmann-like equation in such a way that it represents the conservation equation of energy of a point particle moving in a one-dimensional effective potential. The self-gravitational corrections to the effective potential and, consequently, to the point particle's motion are obtained. A short analysis on the asymptotic behavior of the four-dimensional brane is presented.

The relativistic Friedmann Lemaitre cosmology model (FLCM) is very sucessful in describing the evolution history of the Universe from the "First three Minutes". Any alternative model should be consistent with the FLCM explanations to the later stage evolutions of the Universe at certain points. A noncompact extra dimension model was recently proposed by Randall and Sundrum. Binetruy et al. obtained the modified Friedmann equation, in which the energy density of the brane appears quadratically in contrast with the linear behavior of the standard Friedmann equation. We investigate various kinds of classical cosmological effects of the new models and get a general solution of the cosmic evolution for this extended model, with more detail discussions of the brane tension parameter on these cosmological tests.

We analyze the implications of the Wilkinson Microwave Anisotropy Probe (WMAP) results for a braneworld tachyonic model of inflation. We find that WMAP bounds on n_s allow us to constrain significantly the parameter space of the model; in particular, extremely weak string coupling is required, g_s~10^-15. Moreover, our analysis shows that the running of the scalar spectral index is within the bounds determined by WMAP for the allowed range of model parameters; however, it is not possible to obtain n_s>1 on large scales and n_s<1 on small scales.

The Cosmic no hair theorem is studied in anisotropic Bianchi brane models which admit power law inflation with a scalar field. We note that all Bianchi models except Bianchi type IX transit to an inflationary regime and the anisotropy washes out at a later epoch. It is found that in the brane world, the anisotropic universe approaches the isotropic phase via inflation much faster than that in the general theory of relativity. The modification in the Einstein field equations on the brane is helpful for a quick transition to an isotropic era from the anisotropic brane. We note a case where the curvature term in the field equation initially drives power law inflation on the isotropic brane which is however not permitted without the brane framework.

We consider a brane-world of co-dimension one without reflection symmetry. Through it, we give a possible explanation of the great discrepancy between the vacuum energy and the observed cosmological constant without contradiction to the knowledge we have about our Universe. We also show the gravity observed will be standard four-dimensional gravity as long as the discrepancy of the bulk cosmological constant at different sides of the brane is small enough.

By studying a tachyon field on the DGP brane model, in order to embed the 4D standard Friedmann equation with a brane tachyon field in the 5D bulk, we present the metric of the 5D space–time. Then, adopting the inverse square potential of the tachyon field, we obtain an expanding universe with a power law on the brane and an exact 5D solution.

In the standard picture of cosmology it is predicted that a phase transition, associated with chiral symmetry breaking after the electroweak transition, has occurred at approximately 10μ seconds after the Big Bang to convert a plasma of free quarks and gluons into hadrons. We consider the quark-hadron phase transition in a Dvali, Gabadadze and Porrati (DGP) brane world scenario within an effective model of QCD. We study the evolution of the physical quantities useful for the study of the early universe, namely, the energy density, temperature and the scale factor before, during and after the phase transition. Also, due to the high energy density in the early universe, we consider the quadratic energy density term that appears in the Friedmann equation. In DGP brane models such a term corresponds to the negative branch (ϵ = -1) of the Friedmann equation when the Hubble radius is much smaller than the crossover length in 4D and 5D regimes. We show that for different values of the cosmological constant on a brane, λ, phase transition occurs and results in decreasing the effective temperature of the quark-gluon plasma and of the hadronic fluid. We then consider the quark-hadron transition in the smooth crossover regime at high and low temperatures and show that such a transition occurs along with decreasing the effective temperature of the quark-gluon plasma during the process of the phase transition.

We found cosmological solution of the 6D standing wave braneworld model generated by gravity coupled to a massless scalar phantom-like field. By obtaining a full exact solution of the model, we found a novel dynamical mechanism in which the anisotropic nature of the primordial metric gives rise to expansion of three spatial brane dimensions and affectively reduction of other spatial directions. This dynamical mechanism can be relevant for dimensional reduction in string and other higher-dimensional theories in the attempt of getting a 4D isotropic expanding spacetime.

We study the wave equation for the gravitational fluctuations in the Randall–Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some L¹-L^∞, L²-L^∞ decay estimates and global L^p Strichartz type inequalities. We develop the complete scattering theory: existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.

We consider a five dimensional DGP-brane scenario endowed with a non-minimally coupled scalar field within the context of Brans-Dicke theory. We consider the effective four dimensional field equations on a 3+1 dimensional brane where the fifth dimension is assumed to have an orbifold symmetry. Finally, we discuss the cosmological implications of this setup, predicting an accelerated expanding universe with a value of the Brans-Dicke parameter ω consistent with values resulting from the solar system observations.