On the validity of power functionals for the homogeneous electron gas in reduced.density-matrix-functional theory

Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced density-matrix functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form $f(n,n')=(n n')^\alpha$ for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power $\alpha$ to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition $n({\mathbf k})<1$ for all wave vectors ${\mathbf k}$. The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for $\alpha$ that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at $\alpha\gtrsim 0.6$ and at $r_s\gtrsim 10$ for the density parameter, corresponding to relatively low densities.Comment: Phys. Rev. A (in print, 2016

Do Large-Scale Inhomogeneities Explain Away Dark Energy?

Recently, new arguments (astro-ph/0501152, hep-th/0503117) for how corrections from super-Hubble modes can explain the present-day acceleration of the universe have appeared in the literature. However, in this letter, we argue that, to second order in spatial gradients, these corrections only amount to a renormalization of local spatial curvature, and thus cannot account for the negative deceleration. Moreover, cosmological observations already put severe bounds on such corrections, at the level of a few percent, while in the context of inflationary models, these corrections are typically limited to ~ 10^{-5}. Currently there is no general constraint on the possible correction from higher order gradient terms, but we argue that such corrections are even more constrained in the context of inflationary models.Comment: 4 Pages, no figures. Minor modifications, added reference

Light-cone averaging in cosmology: formalism and applications

We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted "geodesic light-cone" coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called "redshift drift" in a generic inhomogeneous Universe.Comment: 20 pages, 2 figures. Comments and references added, typos corrected. Version accepted for publication in JCA

Gauges and Cosmological Backreaction

We present a formalism for spatial averaging in cosmology applicable to general spacetimes and coordinates, and allowing the easy incorporation of a wide variety of matter sources. We apply this formalism to a Friedmann-LeMaitre-Robertson-Walker universe perturbed to second-order and present the corrections to the background in an unfixed gauge. We then present the corrections that arise in uniform curvature and conformal Newtonian gauges.Comment: 13 pages. Updated: reference added, typos corrected, exposition clarified. Version 3: Replaced with version published by JCA

The Hubble rate in averaged cosmology

The calculation of the averaged Hubble expansion rate in an averaged perturbed Friedmann-Lemaitre-Robertson-Walker cosmology leads to small corrections to the background value of the expansion rate, which could be important for measuring the Hubble constant from local observations. It also predicts an intrinsic variance associated with the finite scale of any measurement of H_0, the Hubble rate today. Both the mean Hubble rate and its variance depend on both the definition of the Hubble rate and the spatial surface on which the average is performed. We quantitatively study different definitions of the averaged Hubble rate encountered in the literature by consistently calculating the backreaction effect at second order in perturbation theory, and compare the results. We employ for the first time a recently developed gauge-invariant definition of an averaged scalar. We also discuss the variance of the Hubble rate for the different definitions.Comment: 12 pages, 25 figures, references added, clarity improved, frame switching subtlety fixed, results unchanged, v3 minor typos fixe

Averaging Robertson-Walker Cosmologies

The cosmological backreaction arises when one directly averages the Einstein equations to recover an effective Robertson-Walker cosmology, rather than assuming a background a priori. While usually discussed in the context of dark energy, strictly speaking any cosmological model should be recovered from such a procedure. We apply the Buchert averaging formalism to linear Robertson-Walker universes containing matter, radiation and dark energy and evaluate numerically the discrepancies between the assumed and the averaged behaviour, finding the largest deviations for an Einstein-de Sitter universe, increasing rapidly with Hubble rate to a 0.01% effect for h=0.701. For the LCDM concordance model, the backreaction is of the order of Omega_eff~4x10^-6, with those for dark energy models being within a factor of two or three. The impacts at recombination are of the order of 10^-8 and those in deep radiation domination asymptote to a constant value. While the effective equations of state of the backreactions in Einstein-de Sitter, concordance and quintessence models are generally dust-like, a backreaction with an equation of state w_eff<-1/3 can be found for strongly phantom models.Comment: 18 pages, 11 figures, ReVTeX. Updated to version accepted by JCA

A covariant and gauge invariant formulation of the cosmological "backreaction"

Using our recent proposal for defining gauge invariant averages we give a general-covariant formulation of the so-called cosmological "backreaction". Our effective covariant equations allow us to describe in explicitly gauge invariant form the way classical or quantum inhomogeneities affect the average evolution of our Universe.Comment: 12 pages, no figures. Typos corrected, matches version to appear in JCA

Light Propagation and Large-Scale Inhomogeneities

We consider the effect on the propagation of light of inhomogeneities with sizes of order 10 Mpc or larger. The Universe is approximated through a variation of the Swiss-cheese model. The spherical inhomogeneities are void-like, with central underdensities surrounded by compensating overdense shells. We study the propagation of light in this background, assuming that the source and the observer occupy random positions, so that each beam travels through several inhomogeneities at random angles. The distribution of luminosity distances for sources with the same redshift is asymmetric, with a peak at a value larger than the average one. The width of the distribution and the location of the maximum increase with increasing redshift and length scale of the inhomogeneities. We compute the induced dispersion and bias on cosmological parameters derived from the supernova data. They are too small to explain the perceived acceleration without dark energy, even when the length scale of the inhomogeneities is comparable to the horizon distance. Moreover, the dispersion and bias induced by gravitational lensing at the scales of galaxies or clusters of galaxies are larger by at least an order of magnitude.Comment: 27 pages, 9 figures, revised version to appear in JCAP, analytical estimate included, typos correcte

Cosmological Solutions in Macroscopic Gravity

In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the equations of macroscopic gravity for a spatially homogeneous and isotropic macroscopic space-time and find that the correlation tensor is of the form of a spatial curvature term. We briefly discuss the physical consequences of these results.Comment: 5 page

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result