Effective inhomogeneous inflation: curvature inhomogeneities of the Einstein vacuum

We consider spatially averaged inhomogeneous universe models and argue that, already in the absence of sources, an effective scalar field arises through foliating and spatially averaging inhomogeneous geometrical curvature invariants of the Einstein vacuum. This scalar field (the `morphon') acts as an inflaton, if we prescribe a potential of some generic form. We show that, for any initially negative average spatial curvature, the morphon is driven through an inflationary phase and leads - on average - to a spatially flat, homogeneous and isotropic universe model, providing initial conditions for pre-heating and, by the same mechanism, a possibly natural self-exit.Comment: 9 pages, 2 figures, to appear in Class. Quant. Grav. as Fast Track Communicatio

The Spatial Averaging Limit of Covariant Macroscopic Gravity - Scalar Corrections to the Cosmological Equations

It is known that any explicit averaging scheme of the type essential for describing the large scale behaviour of the Universe, must necessarily yield corrections to the Einstein equations applied in the Cosmological setting. The question of whether or not the resulting corrections to the Einstein equations are significant, is still a subject of debate, partly due to possible ambiguities in the averaging schemes available. In particular, it has been argued in the literature that the effects of averaging could be gauge artifacts. We apply the formalism of Zalaletdinov's Macroscopic Gravity (MG) which is a fully covariant and nonperturbative averaging scheme, in an attempt to construct gauge independent corrections to the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) equations. We find that whereas one cannot escape the problem of dependence on \emph{one} gauge choice -- which is inherent in the assumption of large scale homogeneity and isotropy -- it is however possible to construct \emph{spacetime scalar} corrections to the standard FLRW equations. This partially addresses the criticism concerning the corrections being gauge artifacts. For a particular initial choice of gauge which simplifies the formalism, we explicitly construct these scalars in terms of the underlying inhomogeneous geometry, and incidentally demonstrate that the formal structure of the corrections with this gauge choice is identical to that of analogous corrections derived by Buchert in the context of spatial averaging of scalars.Comment: 18 pages, no figures, revtex4; v2 - minor clarifications added; v3 - minor changes in presentation to improve clarity, reference added, to appear in Phys. Rev.

Exchange-correlation orbital functionals in current-density-functional theory: Application to a quantum dot in magnetic fields

The description of interacting many-electron systems in external magnetic fields is considered in the framework of the optimized effective potential method extended to current-spin-density functional theory. As a case study, a two-dimensional quantum dot in external magnetic fields is investigated. Excellent agreement with quantum Monte Carlo results is obtained when self-interaction corrected correlation energies from the standard local spin-density approximation are added to exact-exchange results. Full self-consistency within the complete current-spin-density-functional framework is found to be of minor importance.Comment: 5 pages, 2 figures, submitted to PR

Geometric and impurity effects on quantum rings in magnetic fields

We investigate the effects of impurities and changing ring geometry on the energetics of quantum rings under different magnetic field strengths. We show that as the magnetic field and/or the electron number are/is increased, both the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become insensitive to whether the ring is circular or square in shape. This is in qualitative agreement with experiments. However, we also find that the Aharonov-Bohm oscillation can be greatly phase-shifted by only a few impurities and can be completely obliterated by a high level of impurity density. In the many-electron calculations we use a recently developed fourth-order imaginary time projection algorithm that can exactly compute the density matrix of a free-electron in a uniform magnetic field.Comment: 8 pages, 7 figures, to appear in PR

Becke-Johnson-type exchange potential for two-dimensional systems

We extend the Becke-Johnson approximation [J. Chem. Phys. 124, 221101 (2006)] of the exchange potential to two dimensions. We prove and demonstrate that a direct extension of the underlying formalism may lead to divergent behavior of the potential. We derive a cure to the approach by enforcing the gauge invariance and correct asymptotic behavior of the exchange potential. The procedure leads to an approximation which is shown, in various quasi-two-dimensional test systems, to be very accurate in comparison with the exact exchange potential, and thus a considerable improvement over the commonly applied local-density approximation.Comment: submitted to Phys. Rev. B on July 9th, 200

A cosmic equation of state for the inhomogeneous Universe: can a global far-from-equilibrium state explain Dark Energy?

A system of effective Einstein equations for spatially averaged scalar variables of inhomogeneous cosmological models can be solved by providing a `cosmic equation of state'. Recent efforts to explain Dark Energy focus on `backreaction effects' of inhomogeneities on the effective evolution of cosmological parameters in our Hubble volume, avoiding a cosmological constant in the equation of state. In this Letter it is argued that, if kinematical backreaction effects are indeed of the order of the averaged density (or larger as needed for an accelerating domain of the Universe), then the state of our regional Hubble volume would have to be in the vicinity of a far-from-equilibrium state that balances kinematical backreaction and average density. This property, if interpreted globally, is shared by a stationary cosmos with effective equation of state $p_{\rm eff} = -1/3 \rho_{\rm eff}$. It is concluded that a confirmed explanation of Dark Energy by kinematical backreaction may imply a paradigmatic change of cosmology.Comment: 7 pages, matches published version in Class. Quant. Gra

Averaging anisotropic cosmologies

We examine the effects of spatial inhomogeneities on irrotational anisotropic cosmologies by looking at the average properties of anisotropic pressure-free models. Adopting the Buchert scheme, we recast the averaged scalar equations in Bianchi-type form and close the standard system by introducing a propagation formula for the average shear magnitude. We then investigate the evolution of anisotropic average vacuum models and those filled with pressureless matter. In the latter case we show that the backreaction effects can modify the familiar Kasner-like singularity and potentially remove Mixmaster-type oscillations. The presence of nonzero average shear in our equations also allows us to examine the constraints that a phase of backreaction-driven accelerated expansion might put on the anisotropy of the averaged domain. We close by assessing the status of these and other attempts to define and calculate `average' spacetime behaviour in general relativity.Comment: revised version, to appear in CQ

Back-reaction and effective acceleration in generic LTB dust models

We provide a thorough examination of the conditions for the existence of back-reaction and an "effective" acceleration (in the context of Buchert's averaging formalism) in regular generic spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. By considering arbitrary spherical comoving domains, we verify rigorously the fulfillment of these conditions expressed in terms of suitable scalar variables that are evaluated at the boundary of every domain. Effective deceleration necessarily occurs in all domains in: (a) the asymptotic radial range of models converging to a FLRW background, (b) the asymptotic time range of non-vacuum hyperbolic models, (c) LTB self-similar solutions and (d) near a simultaneous big bang. Accelerating domains are proven to exist in the following scenarios: (i) central vacuum regions, (ii) central (non-vacuum) density voids, (iii) the intermediate radial range of models converging to a FLRW background, (iv) the asymptotic radial range of models converging to a Minkowski vacuum and (v) domains near and/or intersecting a non-simultaneous big bang. All these scenarios occur in hyperbolic models with negative averaged and local spatial curvature, though scenarios (iv) and (v) are also possible in low density regions of a class of elliptic models in which local spatial curvature is negative but its average is positive. Rough numerical estimates between -0.003 and -0.5 were found for the effective deceleration parameter. While the existence of accelerating domains cannot be ruled out in models converging to an Einstein de Sitter background and in domains undergoing gravitational collapse, the conditions for this are very restrictive. The results obtained may provide important theoretical clues on the effects of back-reaction and averaging in more general non-spherical models.Comment: Final version accepted for publication in Classical and Quantum Gravity. 47 pages in IOP LaTeX macros, 12 pdf figure

Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust

In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.Comment: 18 pages. Matches published version in CQ

Average observational quantities in the timescape cosmology

We examine the properties of a recently proposed observationally viable alternative to homogeneous cosmology with smooth dark energy, the timescape cosmology. In the timescape model cosmic acceleration is realized as an apparent effect related to the calibration of clocks and rods of observers in bound systems relative to volume-average observers in an inhomogeneous geometry in ordinary general relativity. The model is based on an exact solution to a Buchert average of the Einstein equations with backreaction. The present paper examines a number of observational tests which will enable the timescape model to be distinguished from homogeneous cosmologies with a cosmological constant or other smooth dark energy, in current and future generations of dark energy experiments. Predictions are presented for: comoving distance measures; H(z); the equivalent of the dark energy equation of state, w(z); the Om(z) measure of Sahni, Shafieloo and Starobinsky; the Alcock-Paczynski test; the baryon acoustic oscillation measure, D_v; the inhomogeneity test of Clarkson, Bassett and Lu; and the time drift of cosmological redshifts. Where possible, the predictions are compared to recent independent studies of similar measures in homogeneous cosmologies with dark energy. Three separate tests with indications of results in possible tension with the Lambda CDM model are found to be consistent with the expectations of the timescape cosmology.Comment: 22 pages, 12 figures; v2 discussion, references added, matches published versio