"Swiss-Cheese" Inhomogeneous Cosmology & the Dark Energy Problem

We study an exact swiss-cheese model of the Universe, where inhomogeneous LTB patches are embedded in a flat FLRW background, in order to see how observations of distant sources are affected. We find negligible integrated effect, suppressed by (L/R_{H})^3 (where L is the size of one patch, and R_{H} is the Hubble radius), both perturbatively and non-perturbatively. We disentangle this effect from the Doppler term (which is much larger and has been used recently \cite{BMN} to try to fit the SN curve without dark energy) by making contact with cosmological perturbation theory.Comment: 35 pages, 6 figure

Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics

We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and indicator functions allow us to treat fractional factorial designs without distinction between regular designs and non-regular designs. For the purpose of analysis of data from fractional factorial designs, the techniques of Markov bases allow us to handle discrete observations. Thus the approach of computational algebraic statistics greatly enlarges the scope of fractional factorial designs.Comment: 16 page

Large-scale magnetic fields from density perturbations

We derive the minimal seed magnetic field which unavoidably arises in the radiation and matter eras, prior to recombination, by the rotational velocity of ions and electrons, gravitationally induced by the non-linear evolution of primordial density perturbations. The resulting magnetic field power-spectrum is fully determined by the amplitude and spectral index of density perturbations. The rms amplitude of the seed-field at recombination is B ~ 10^{-23} (\lambda/Mpc)^{-2} G, on comoving scales larger than about 1 Mpc.Comment: 7 pages, 1 figur

Cosmological Backreaction from Perturbations

We reformulate the averaged Einstein equations in a form suitable for use with Newtonian gauge linear perturbation theory and track the size of the modifications to standard Robertson-Walker evolution on the largest scales as a function of redshift for both Einstein de-Sitter and Lambda CDM cosmologies. In both cases the effective energy density arising from linear perturbations is of the order of 10^-5 the matter density, as would be expected, with an effective equation of state w ~ -1/19. Employing a modified Halofit code to extend our results to quasilinear scales, we find that, while larger, the deviations from Robertson-Walker behaviour remain of the order of 10^-5.Comment: 15 pages, 8 figures; replaced by version accepted by JCA

Cosmic Microwave Background, Accelerating Universe and Inhomogeneous Cosmology

We consider a cosmology in which a spherically symmetric large scale inhomogeneous enhancement or a void are described by an inhomogeneous metric and Einstein's gravitational equations. For a flat matter dominated universe the inhomogeneous equations lead to luminosity distance and Hubble constant formulas that depend on the location of the observer. For a general inhomogeneous solution, it is possible for the deceleration parameter to differ significantly from the FLRW result. The deceleration parameter $q_0$ can be interpreted as $q_0 > 0$ ($q_0=1/2$ for a flat matter dominated universe) in a FLRW universe and be $q_0 < 0$ as inferred from the inhomogeneous enhancement that is embedded in a FLRW universe. A spatial volume averaging of local regions in the backward light cone has to be performed for the inhomogeneous solution at late times to decide whether the decelerating parameter $q$ can be negative for a positive energy condition. The CMB temperature fluctuations across the sky can be unevenly distributed in the northern and southern hemispheres in the inhomogeneous matter dominated solution, in agreement with the analysis of the WMAP power spectrum data by several authors. The model can possibly explain the anomalous alignment of the quadrupole and octopole moments observed in the WMAP data.Comment: 20 pages, no figures, LaTex file. Equations and typos corrected and references added. Additional material and some conclusions changed. Final published versio

Is backreaction really small within concordance cosmology?

Smoothing over structures in general relativity leads to a renormalisation of the background, and potentially many other effects which are poorly understood. Observables such as the distance-redshift relation when averaged on the sky do not necessarily yield the same smooth model which arises when performing spatial averages. These issues are thought to be of technical interest only in the standard model of cosmology, giving only tiny corrections. However, when we try to calculate observable quantities such as the all-sky average of the distance-redshift relation, we find that perturbation theory delivers divergent answers in the UV and corrections to the background of order unity. There are further problems. Second-order perturbations are the same size as first-order, and fourth-order at least the same as second, and possibly much larger, owing to the divergences. Much hinges on a coincidental balance of 2 numbers: the primordial power, and the ratio between the comoving Hubble scales at matter-radiation equality and today. Consequently, it is far from obvious that backreaction is irrelevant even in the concordance model, however natural it intuitively seems.Comment: 28 pages. Invited contribution to Classical and Quantum Gravity special issue "Inhomogeneous Cosmological Models and Averaging in Cosmology

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

Non-chaotic dynamics in general-relativistic and scalar-tensor cosmology

In the context of scalar-tensor models of dark energy and inflation, the dynamics of vacuum scalar-tensor cosmology are analysed without specifying the coupling function or the scalar field potential. A conformal transformation to the Einstein frame is used and the dynamics of general relativity with a minimally coupled scalar field are derived for a generic potential. It is shown that the dynamics are non-chaotic, thus settling an existing debate.Comment: 20 pages, LaTeX, to appear in Class. Quantum Gra

Can the Acceleration of Our Universe Be Explained by the Effects of Inhomogeneities?

No. It is simply not plausible that cosmic acceleration could arise within the context of general relativity from a back-reaction effect of inhomogeneities in our universe, without the presence of a cosmological constant or ``dark energy.'' We point out that our universe appears to be described very accurately on all scales by a Newtonianly perturbed FLRW metric. (This assertion is entirely consistent with the fact that we commonly encounter $\delta \rho/\rho > 10^{30}$.) If the universe is accurately described by a Newtonianly perturbed FLRW metric, then the back-reaction of inhomogeneities on the dynamics of the universe is negligible. If not, then it is the burden of an alternative model to account for the observed properties of our universe. We emphasize with concrete examples that it is {\it not} adequate to attempt to justify a model by merely showing that some spatially averaged quantities behave the same way as in FLRW models with acceleration. A quantity representing the ``scale factor'' may ``accelerate'' without there being any physically observable consequences of this acceleration. It also is {\it not} adequate to calculate the second-order stress energy tensor and show that it has a form similar to that of a cosmological constant of the appropriate magnitude. The second-order stress energy tensor is gauge dependent, and if it were large, contributions of higher perturbative order could not be neglected. We attempt to clear up the apparent confusion between the second-order stress energy tensor arising in perturbation theory and the ``effective stress energy tensor'' arising in the ``shortwave approximation.''Comment: 20 pages, 1 figure, several footnotes and references added, version accepted for publication in CQG;some clarifying comments adde

LTB solutions in Newtonian gauge: from strong to weak fields

Lemaitre-Tolman-Bondi (LTB) solutions are used frequently to describe the collapse or expansion of spherically symmetric inhomogeneous mass distributions in the Universe. These exact solutions are obtained in the synchronous gauge where nonlinear dynamics (with respect to the FLRW background) induce large deviations from the FLRW metric. In this paper we show explicitly that this is a gauge artefact (for realistic sub-horizon inhomogeneities). We write down the nonlinear gauge transformation from synchronous to Newtonian gauge for a general LTB solution using the fact that the peculiar velocities are small. In the latter gauge we recover the solution in the form of a weakly perturbed FLRW metric that is assumed in standard cosmology. Furthermore we show how to obtain the LTB solutions directly in Newtonian gauge and illustrate how the Newtonian approximation remains valid in the nonlinear regime where cosmological perturbation theory breaks down. Finally we discuss the implications of our results for the backreaction scenario.Comment: 17 page