Anisotropy and inflation in Bianchi I brane worlds

After a more general assumption on the influence of the bulk on the brane, we extend some conclusions by Maartens et al. and Santos et al. on the asymptotic behavior of Bianchi I brane worlds. As a consequence of the nonlocal anisotropic stresses induced by the bulk, in most of our models, the brane does not isotropize and the nonlocal energy does not vanish in the limit in which the mean radius goes to infinity. We have also found the intriguing possibility that the inflation due to the cosmological constant might be prevented by the interaction with the bulk. We show that the problem for the mean radius can be completely solved in our models, which include as particular cases those in the references above.Comment: 10 pages, improved discussion on the likeliness of non-isotropization, completed list of references, matches version to appear in Class. Quantum Gra

On A Cosmological Invariant as an Observational Probe in the Early Universe

k-essence scalar field models are usually taken to have lagrangians of the form ${\mathcal L}=-V(\phi)F(X)$ with $F$ some general function of $X=\nabla_{\mu}\phi\nabla^{\mu}\phi$. Under certain conditions this lagrangian in the context of the early universe can take the form of that of an oscillator with time dependent frequency. The Ermakov invariant for a time dependent oscillator in a cosmological scenario then leads to an invariant quadratic form involving the Hubble parameter and the logarithm of the scale factor. In principle, this invariant can lead to further observational probes for the early universe. Moreover, if such an invariant can be observationally verified then the presence of dark energy will also be indirectly confirmed.Comment: 4 pages, Revte

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

SO(1,1) dark energy model and the universe transition

We suggest a scalar model of dark energy with the SO(1,1) symmetry. The model may be reformulated in terms of a real scalar field $\Phi$ and the scale factor $a$ so that the Lagrangian may be decomposed as that of the real quintessence model plus the negative coupling energy term of $\Phi$ to $a$. The existence of the coupling term $L^c$ leads to a wider range of $w_{\Phi}$ and overcomes the problem of negative kinetic energy in the phantom universe model. We propose a power-law expansion model of univese with time-dependent power, which can describe the phantom universe and the universe transition from ordinary acceleration to super acceleration.Comment: 12 pages. submitted to CQ

Cosmology with exponential potentials

We examine in the context of general relativity the dynamics of a spatially flat Robertson-Walker universe filled with a classical minimally coupled scalar field \phi of exponential potential ~ e^{-\mu\phi} plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation, providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints on the present values of \Omega_{m}, w_{\phi} provide, independently of initial conditions and other parameters, necessary conditions on \mu. Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w_{\phi} ~ -1, as well as, for the generic late-times evolution, the general relation \Omega_{\phi}(w_{\phi}) is obtained.Comment: RevTex4, 9 pages, 2 figures, References adde

Dilatonic ghost condensate as dark energy

We explore a dark energy model with a ghost scalar field in the context of the runaway dilaton scenario in low-energy effective string theory. We address the problem of vacuum stability by implementing higher-order derivative terms and show that a cosmologically viable model of ``phantomized'' dark energy can be constructed without violating the stability of quantum fluctuations. We also analytically derive the condition under which cosmological scaling solutions exist starting from a general Lagrangian including the phantom type scalar field. We apply this method to the case where the dilaton is coupled to non-relativistic dark matter and find that the system tends to become quantum mechanically unstable when a constant coupling is always present. Nevertheless, it is possible to obtain a viable cosmological solution in which the energy density of the dilaton eventually approaches the present value of dark energy provided that the coupling rapidly grows during the transition to the scalar field dominated era.Comment: 26 pages, 6 figure

Coupled dark energy: Towards a general description of the dynamics

In dark energy models of scalar-field coupled to a barotropic perfect fluid, the existence of cosmological scaling solutions restricts the Lagrangian of the field \vp to p=X g(Xe^{\lambda \vp}), where X=-g^{\mu\nu} \partial_\mu \vp \partial_\nu \vp /2, $\lambda$ is a constant and $g$ is an arbitrary function. We derive general evolution equations in an autonomous form for this Lagrangian and investigate the stability of fixed points for several different dark energy models--(i) ordinary (phantom) field, (ii) dilatonic ghost condensate, and (iii) (phantom) tachyon. We find the existence of scalar-field dominant fixed points (\Omega_\vp=1) with an accelerated expansion in all models irrespective of the presence of the coupling $Q$ between dark energy and dark matter. These fixed points are always classically stable for a phantom field, implying that the universe is eventually dominated by the energy density of a scalar field if phantom is responsible for dark energy. When the equation of state w_\vp for the field \vp is larger than -1, we find that scaling solutions are stable if the scalar-field dominant solution is unstable, and vice versa. Therefore in this case the final attractor is either a scaling solution with constant \Omega_\vp satisfying 0<\Omega_\vp<1 or a scalar-field dominant solution with \Omega_\vp=1.Comment: 21 pages, 5 figures; minor clarifications added, typos corrected and references updated; final version to appear in JCA

Two Loop Scalar Self-Mass during Inflation

We work in the locally de Sitter background of an inflating universe and consider a massless, minimally coupled scalar with a quartic self-interaction. We use dimensional regularization to compute the fully renormalized scalar self-mass-squared at one and two loop order for a state which is released in Bunch-Davies vacuum at t=0. Although the field strength and coupling constant renormalizations are identical to those of lfat space, the geometry induces a non-zero mass renormalization. The finite part also shows a sort of growing mass that competes with the classical force in eventually turning off this system's super-acceleration.Comment: 31 pages, 5 figures, revtex4, revised for publication with extended list of reference

Cosmological constraints on the dark energy equation of state and its evolution

We have calculated constraints on the evolution of the equation of state of the dark energy, w(z), from a joint analysis of data from the cosmic microwave background, large scale structure and type-Ia supernovae. In order to probe the time-evolution of w we propose a new, simple parametrization of w, which has the advantage of being transparent and simple to extend to more parameters as better data becomes available. Furthermore it is well behaved in all asymptotic limits. Based on this parametrization we find that w(z=0)=-1.43^{+0.16}_{-0.38} and dw/dz(z=0) = 1.0^{+1.0}_{-0.8}. For a constant w we find that -1.34 < w < -0.79 at 95% C.L. Thus, allowing for a time-varying w shifts the best fit present day value of w down. However, even though models with time variation in w yield a lower chi^2 than pure LambdaCDM models, they do not have a better goodness-of-fit. Rank correlation tests on SNI-a data also do not show any need for a time-varying w.Comment: 19 pages, 11 figures, JCAP format, typos corrected, references update

Brane-World Gravity

The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the \textit{d} extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($\sim$ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.Comment: A major update of Living Reviews in Relativity 7:7 (2004) "Brane-World Gravity", 119 pages, 28 figures, the update contains new material on RS perturbations, including full numerical solutions of gravitational waves and scalar perturbations, on DGP models, and also on 6D models. A published version in Living Reviews in Relativit