Asymmetric embedding in brane cosmology

We derive a system of cosmological equations for a braneworld with induced curvature which is a junction between several bulk spaces. The permutation symmetry of the bulk spaces is not imposed, and the values of the fundamental constants, and even the signatures of the extra dimension, may be different on different sides of the brane. We then consider the usual partial case of two asymmetric bulk spaces and derive an exact closed system of scalar equations on the brane. We apply this result to the cosmological evolution on such a brane and describe its various partial cases.Comment: 10 page

Determination of Wave Function Functionals: The Constrained-Search--Variational Method

In a recent paper [Phys. Rev. Lett. \textbf{93}, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. The space of variations is expanded because a search over the functions $\chi$ can in principle lead to the true wave function. As the space of such variations is large, we proposed the constrained-search-- variational method whereby a constrained search is first performed over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a physical constraint such as normalization or the Fermi-Coulomb hole sum rule, or leads to the known value of an observable such as the diamagnetic susceptibility, nuclear magnetic constant or Fermi contact term. A rigorous upper bound to the energy is then obtained by application of the variational principle. A key attribute of the method is that the wave function functional is accurate throughout space, in contrast to the standard variational method for which the wave function is accurate only in those regions of space contributing principally to the energy. In this paper we generalize the equations of the method to the determination of arbitrary Hermitian single-particle operators as applied to two-electron atomic and ionic systems. The description is general and applicable to both ground and excited states. A discussion on excited states in conjunction with the theorem of Theophilou is provided.Comment: 26 pages, 4 figures, 5 table

Probing the Coupling between Dark Components of the Universe

We place observational constraints on a coupling between dark energy and dark matter by using 71 Type Ia supernovae (SNe Ia) from the first year of the five-year Supernova Legacy Survey (SNLS), the cosmic microwave background (CMB) shift parameter from the three-year Wilkinson Microwave Anisotropy Probe (WMAP), and the baryon acoustic oscillation (BAO) peak found in the Sloan Digital Sky Survey (SDSS). The interactions we study are (i) constant coupling delta and (ii) varying coupling delta(z) that depends on a redshift z, both of which have simple parametrizations of the Hubble parameter to confront with observational data. We find that the combination of the three databases marginalized over a present dark energy density gives stringent constraints on the coupling, -0.08 < delta < 0.03 (95% CL) in the constant coupling model and -0.4 < delta_0 < 0.1 (95% CL) in the varying coupling model, where delta_0 is a present value. The uncoupled LambdaCDM model (w_X = -1 and delta = 0) still remains a good fit to the data, but the negative coupling (delta < 0) with the equation of state of dark energy w_X < -1 is slightly favoured over the LambdaCDM model.Comment: 9 pages, 7 figures, RevTeX, minor corrections, references added, accepted for publication in Phys. Rev.

Evolution of perturbations in distinct classes of canonical scalar field models of dark energy

Dark energy must cluster in order to be consistent with the equivalence principle. The background evolution can be effectively modelled by either a scalar field or by a barotropic fluid.The fluid model can be used to emulate perturbations in a scalar field model of dark energy, though this model breaks down at large scales. In this paper we study evolution of dark energy perturbations in canonical scalar field models: the classes of thawing and freezing models.The dark energy equation of state evolves differently in these classes.In freezing models, the equation of state deviates from that of a cosmological constant at early times.For thawing models, the dark energy equation of state remains near that of the cosmological constant at early times and begins to deviate from it only at late times.Since the dark energy equation of state evolves differently in these classes,the dark energy perturbations too evolve differently. In freezing models, since the equation of state deviates from that of a cosmological constant at early times, there is a significant difference in evolution of matter perturbations from those in the cosmological constant model.In comparison, matter perturbations in thawing models differ from the cosmological constant only at late times. This difference provides an additional handle to distinguish between these classes of models and this difference should manifest itself in the ISW effect.Comment: 11 pages, 6 figures, accepted for publication in Phys. Rev.

Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology

We examine a class of braneworld models in which the expanding universe encounters a "quiescent" future singularity. At a quiescent singularity, the energy density and pressure of the cosmic fluid as well as the Hubble parameter remain finite while all derivatives of the Hubble parameter diverge (i.e., ${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariant diverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expects quantum effects to play an important role as the quiescent singularity is approached. We explore the effects of vacuum polarization due to massless conformally coupled fields near the singularity and show that these can either cause the universe to recollapse or, else, lead to a softer singularity at which $H$, ${\dot H}$, and ${\ddot H}$ remain finite while ${\dddot H}$ and higher derivatives of the Hubble parameter diverge. An important aspect of the quiescent singularity is that it is encountered in regions of low density, which has obvious implications for a universe consisting of a cosmic web of high and low density regions -- superclusters and voids. In addition to vacuum polarization, the effects of quantum particle production of non-conformal fields are also likely to be important. A preliminary examination shows that intense particle production can lead to an accelerating universe whose Hubble parameter shows oscillations about a constant value.Comment: 19 pages, 3 figures, text slightly improved and references added. Accepted for publication in Classical and Quantum Gravit

The Evolution of Voids in the Adhesion Approximation

We apply the adhesion approximation to study the formation and evolution of voids in the Universe. Our simulations -- carried out using 128$^3$ particles in a cubical box with side 128 Mpc -- indicate that the void spectrum evolves with time and that the mean void size in the standard COBE-normalised Cold Dark Matter (hereafter CDM) model with $h_{50} = 1,$ scales approximately as $\bar D(z) = {\bar D_0\over \sqrt {1+z}},$ where $\bar D_0 \simeq 10.5$ Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way towards reconstructing the form of the primordial potential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in $k$-space cutoff we find that, the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments merge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitational potential. A central result of this paper is thatComment: Plain TeX, 38 pages Plus 16 Figures (available on request from the first author), IUCAA-28 To appear in The Astrophysical Journal, July 199

APSIS - an Artificial Planetary System in Space to probe extra-dimensional gravity and MOND

A proposal is made to test Newton's inverse-square law using the perihelion shift of test masses (planets) in free fall within a spacecraft located at the Earth-Sun L2 point. Such an Artificial Planetary System In Space (APSIS) will operate in a drag-free environment with controlled experimental conditions and minimal interference from terrestrial sources of contamination. We demonstrate that such a space experiment can probe the presence of a "hidden" fifth dimension on the scale of a micron, if the perihelion shift of a "planet" can be measured to sub-arc-second accuracy. Some suggestions for spacecraft design are made.Comment: 17 pages, revtex, references added. To appear in Special issue of IJMP

Dark energy models toward observational tests and data

A huge amount of good quality astrophysical data converges towards the picture of a spatially flat universe undergoing the today observed phase of accelerated expansion. This new observational trend is commonly addressed as Precision Cosmology. Despite of the quality of astrophysical surveys, the nature of dark energy dominating the matter-energy content of the universe is still unknown and a lot of different scenarios are viable candidates to explain cosmic acceleration. Methods to test these cosmological models are based on distance measurements and lookback time toward astronomical objects used as standard candles. I discuss the characterizing parameters and constraints of three different classes of dark energy models pointing out the related degeneracy problem which is the signal that more data at low (z= 0- 1), medium (1<z<10) and high (10 <z< 1000) redshift are needed to definitively select realistic models.Comment: 17 pages, 9 figures, Lectures for 42nd Karpacz Winter School of Theoretical Physics: Current Mathematical Topics in Gravitation and Cosmology, Ladek, Poland, 6-11 Feb 200

Statefinder diagnostic for cosmology with the abnormally weighting energy hypothesis

In this paper, we apply the statefinder diagnostic to the cosmology with the Abnormally Weighting Energy hypothesis (AWE cosmology), in which dark energy in the observational (ordinary matter) frame results from the violation of weak equivalence principle (WEP) by pressureless matter. It is found that there exist closed loops in the statefinder plane, which is an interesting characteristic of the evolution trajectories of statefinder parameters and can be used to distinguish AWE cosmology from the other cosmological models.Comment: 5 pages, 4 figures, accepted by PR

Fine Tuning Free Paradigm of Two Measures Theory: K-Essence, Absence of Initial Singularity of the Curvature and Inflation with Graceful Exit to Zero Cosmological Constant State

The dilaton-gravity sector of the Two Measures Field Theory (TMT)is explored in detail in the context of cosmology. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. The effective model represents an explicit example of the effective k-essence resulting from first principles without any exotic term in the fundamental action. Depending of the choice of regions in the parameter space, TMT exhibits different possible outputs for cosmological dynamics: a) Absence of initial singularity of the curvature while its time derivative is singular. This is a sort of "sudden" singularities studied by Barrow on purely kinematic grounds. b) Power law inflation in the subsequent stage of evolution. Depending on the region in the parameter space (but without fine tuning) the inflation ends with a graceful exit either into the state with zero cosmological constant (CC) or into the state driven by both a small CC and the field phi with a quintessence-like potential. c) Possibility of resolution of the old CC problem. From the point of view of TMT, it becomes clear why the old CC problem cannot be solved (without fine tuning) in conventional field theories. d) TMT enables two ways for achieving small CC without fine tuning of dimensionfull parameters: either by a seesaw type mechanism or due to a correspondence principle between TMT and conventional field theories (i.e theories with only the measure of integration sqrt{-g} in the action. e) There is a wide range of the parameters such that in the late time universe: the equation-of-state w=p/\rho <-1; w asymptotically (as t\to\infty) approaches -1 from below; \rho approaches a constant, the smallness of which does not require fine tuning of dimensionfull parameters.Comment: 37 pages, 20 figures. Minor misprints corrected, reference added. The final version published in Phys. Rev.