Decaying Dark Energy in Higher-Dimensional Gravity

We use data from observational cosmology to put constraints on higher-dimensional extensions of general relativity in which the effective four-dimensional dark-energy density (or cosmological "constant") decays with time. In particular we study the implications of this decaying dark energy for the age of the universe, large-scale structure formation, big-bang nucleosynthesis and the magnitude-redshift relation for Type Ia supernovae. Two of these tests (age and the magnitude-redshift relation) place modest lower limits on the free parameter of the theory, a cosmological length scale L akin to the de Sitter radius. These limits will improve if experimental uncertainties on supernova magnitudes can be reduced around z=1.Comment: 11 pages, 5 figures, submitted to A&

Cosmic Acceleration With A Positive Cosmological Constant

We have considered a cosmological model with a phenomenological model for the cosmological constant of the form \Lambda=\bt\fr{\ddot R}{R}, \bt is a constant. For age parameter consistent with observational data the Universe must be accelerating in the presence of a positive cosmological constant. The minimum age of the Universe is $H_0^{-1}$, where $H_0$ is the present Hubble constant. The cosmological constant is found to decrease as $t^{-2}$. Allowing the gravitational constant to change with time leads to an ever increasing gravitational constant at the present epoch. In the presence of a viscous fluid this decay law for $\Lambda$ is equivalent to the one with $\Lambda=3\alpha H^2$ ($\alpha=\rm const.$) provided \alpha=\fr{\bt}{3(\bt-2)}. The inflationary solution obtained from this model is that of the de-Sitter type.Comment: a more revised versio

Renormalization group improved gravitational actions: a Brans-Dicke approach

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG-framework, $G$ and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields $G$ and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure

Cosmology with Self-Adjusting Vacuum Energy Density from a Renormalization Group Fixed Point

Cosmologies with a time dependent Newton constant and cosmological constant are investigated. The scale dependence of $G$ and $\Lambda$ is governed by a set of renormalization group equations which is coupled to Einstein's equation in a consistent way. The existence of an infrared attractive renormalization group fixed point is postulated, and the cosmological implications of this assumption are explored. It turns out that in the late Universe the vacuum energy density is automatically adjusted so as to equal precisely the matter energy density, and that the deceleration parameter approaches $q = -1/4$. This scenario might explain the data from recent observations of high redshift type Ia Supernovae and the cosmic microwave background radiation without introducing a quintessence field.Comment: v2: published version, two references update

Nucleosynthesis Constraints on Scalar-Tensor Theories of Gravity

We study the cosmological evolution of massless single-field scalar-tensor theories of gravitation from the time before the onset of $e^+e^-$ annihilation and nucleosynthesis up to the present. The cosmological evolution together with the observational bounds on the abundances of the lightest elements (those mostly produced in the early universe) place constraints on the coefficients of the Taylor series expansion of $a(\phi)$, which specifies the coupling of the scalar field to matter and is the only free function in the theory. In the case when $a(\phi)$ has a minimum (i.e., when the theory evolves towards general relativity) these constraints translate into a stronger limit on the Post-Newtonian parameters $\gamma$ and $\beta$ than any other observational test. Moreover, our bounds imply that, even at the epoch of annihilation and nucleosynthesis, the evolution of the universe must be very close to that predicted by general relativity if we do not want to over- or underproduce $^{4}$He. Thus the amount of scalar field contribution to gravity is very small even at such an early epoch.Comment: 15 pages, 2 figures, ReVTeX 3.1, submitted to Phys. Rev. D1

Exact Black Hole and Cosmological Solutions in a Two-Dimensional Dilaton-Spectator Theory of Gravity

Exact black hole and cosmological solutions are obtained for a special two-dimensional dilaton-spectator ($\phi-\psi$) theory of gravity. We show how in this context any desired spacetime behaviour can be determined by an appropriate choice of a dilaton potential function $V(\phi)$ and a ``coupling function'' $l(\phi)$ in the action. We illustrate several black hole solutions as examples. In particular, asymptotically flat double- and multiple- horizon black hole solutions are obtained. One solution bears an interesting resemblance to the $2D$ string-theoretic black hole and contains the same thermodynamic properties; another resembles the $4D$ Reissner-Nordstrom solution. We find two characteristic features of all the black hole solutions. First the coupling constants in $l(\phi)$ must be set equal to constants of integration (typically the mass). Second, the spectator field $\psi$ and its derivative $\psi^{'}$ both diverge at any event horizon. A test particle with ``spectator charge" ({\it i.e.} one coupled either to $\psi$ or $\psi^{'}$), will therefore encounter an infinite tidal force at the horizon or an ``infinite potential barrier'' located outside the horizon respectively. We also compute the Hawking temperature and entropy for our solutions. In $2D$ $FRW$ cosmology, two non-singular solutions which resemble two exact solutions in $4D$ string-motivated cosmology are obtained. In addition, we construct a singular model which describes the $4D$ standard non-inflationary big bang cosmology ($big-bang\rightarrow radiation\rightarrow dust$). Motivated by the similaritiesbetween $2D$ and $4D$ gravitational field equations in $FRW$ cosmology, we briefly discuss a special $4D$ dilaton-spectator action constructed from the bosonic part of the low energy heterotic string action andComment: 34 pgs. Plain Tex, revised version contains some clarifying comments concerning the relationship between the constants of integration and the coupling constants

Stars in five dimensional Kaluza Klein gravity

In the five dimensional Kaluza Klein (KK) theory there is a well known class of static and electromagnetic--free KK--equations characterized by a naked singularity behavior, namely the Generalized Schwarzschild solution (GSS). We present here a set of interior solutions of five dimensional KK--equations. These equations have been numerically integrated to match the GSS in the vacuum. The solutions are candidates to describe the possible interior perfect fluid source of the exterior GSS metric and thus they can be models for stars for static, neutral astrophysical objects in the ordinary (four dimensional) spacetime.Comment: 15 pages, 8 figures. To be published in EPJ

Evolution of the Scale Factor with a Variable Cosmological Term

Evolution of the scale factor a(t) in Friedmann models (those with zero pressure and a constant cosmological term Lambda) is well understood, and elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58, 689 (1986)]. Developments in particle physics and inflationary theory, however, increasingly indicate that Lambda ought to be treated as a dynamical quantity. We revisit the evolution of the scale factor with a variable Lambda-term, and also generalize the treatment to include nonzero pressure. New solutions are obtained and evaluated using a variety of observational criteria. Existing arguments for the inevitability of a big bang (ie., an initial state with a=0) are substantially weakened, and can be evaded in some cases with Lambda_0 (the present value of Lambda) well below current experimental limits.Comment: 29 pages, 12 figures (not included), LaTeX, uses Phys Rev D style files (revtex.cls, revtex.sty, aps.sty, aps10.sty, prabib.sty). To appear in Phys Rev

Five Dimensional Cosmological Models in General Relativity

A Five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and $\Lambda$. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as $G \sim t^{-(1-\omega)}$ whereas the variation for the cosmological constant follows as $\Lambda \sim t^{-2}$, $\Lambda \sim (\dot R/R)^2$ and $\Lambda \sim \ddot R/R$ where $\omega$ is the equation of state parameter and $R$ is the scale factor.Comment: 13 pages, 4 figures, accepted in Int. J. Theor. Phy

Modified gravity in a viscous and non-isotropic background

We study the dynamical evolution of an $f(R)$ model of gravity in a viscous and anisotropic background which is given by a Bianchi type-I model of the Universe. We find viable forms of $f(R)$ gravity in which one is exactly the Einsteinian model of gravity with a cosmological constant and other two are power law $f(R)$ models. We show that these two power law models are stable with a suitable choice of parameters. We also examine three potentials which exhibit the potential effect of $f(R)$ models in the context of scalar tensor theory. By solving different aspects of the model and finding the physical quantities in the Jordan frame, we show that the equation of state parameter satisfy the dominant energy condition. At last we show that the two power law $f(R)$ models behave like quintessence model at late times and also the shear coefficient viscosity tends to zero at late times.Comment: 7 pages, 2 figure