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.

Correspondence between kinematical backreaction and scalar field cosmologies - the `morphon field'

Spatially averaged inhomogeneous cosmologies in classical general relativity can be written in the form of effective Friedmann equations with sources that include backreaction terms. In this paper we propose to describe these backreaction terms with the help of a homogeneous scalar field evolving in a potential; we call it the `morphon field'. This new field links classical inhomogeneous cosmologies to scalar field cosmologies, allowing to reinterpret, e.g., quintessence scenarios by routing the physical origin of the scalar field source to inhomogeneities in the Universe. We investigate a one-parameter family of scaling solutions to the backreaction problem. Subcases of these solutions (all without an assumed cosmological constant) include scale-dependent models with Friedmannian kinematics that can mimic the presence of a cosmological constant or a time-dependent cosmological term. We explicitly reconstruct the scalar field potential for the scaling solutions, and discuss those cases that provide a solution to the Dark Energy and coincidence problems. In this approach, Dark Energy emerges from morphon fields, a mechanism that can be understood through the proposed correspondence: the averaged cosmology is characterized by a weak decay (quintessence) or growth (phantom quintessence) of kinematical fluctuations, fed by `curvature energy' that is stored in the averaged 3-Ricci curvature. We find that the late-time trajectories of those models approach attractors that lie in the future of a state that is predicted by observational constraints.Comment: 36 pages and 6 Figures, matches published version in Class.Quant.Gra

The Effect of Large-Scale Inhomogeneities on the Luminosity Distance

We study the form of the luminosity distance as a function of redshift in the presence of large scale inhomogeneities, with sizes of order 10 Mpc or larger. We approximate the Universe through the Swiss-cheese model, with each spherical region described by the Tolman-Bondi metric. We study the propagation of light beams in this background, assuming that the locations of the source and the observer are random. We derive the optical equations for the evolution of the beam area and shear. Through their integration we determine the configurations that can lead to an increase of the luminosity distance relative to the homogeneous cosmology. We find that this can be achieved if the Universe is composed of spherical void-like regions, with matter concentrated near their surface. For inhomogeneities consistent with the observed large scale structure, the relative increase of the luminosity distance is of the order of a few percent at redshifts near 1, and falls short of explaining the substantial increase required by the supernova data. On the other hand, the effect we describe is important for the correct determination of the energy content of the Universe from observations.Comment: 27 pages, 5 figures Revised version. References added. Conclusions clarifie

Dark energy as a mirage

Motivated by the observed cosmic matter distribution, we present the following conjecture: due to the formation of voids and opaque structures, the average matter density on the path of the light from the well-observed objects changes from Omega_M ~ 1 in the homogeneous early universe to Omega_M ~ 0 in the clumpy late universe, so that the average expansion rate increases along our line of sight from EdS expansion Ht ~ 2/3 at high redshifts to free expansion Ht ~ 1 at low redshifts. To calculate the modified observable distance-redshift relations, we introduce a generalized Dyer-Roeder method that allows for two crucial physical properties of the universe: inhomogeneities in the expansion rate and the growth of the nonlinear structures. By treating the transition redshift to the void-dominated era as a free parameter, we find a phenomenological fit to the observations from the CMB anisotropy, the position of the baryon oscillation peak, the magnitude-redshift relations of type Ia supernovae, the local Hubble flow and the nucleosynthesis, resulting in a concordant model of the universe with 90% dark matter, 10% baryons, no dark energy, 15 Gyr as the age of the universe and a natural value for the transition redshift z_0=0.35. Unlike a large local void, the model respects the cosmological principle, further offering an explanation for the late onset of the perceived acceleration as a consequence of the forming nonlinear structures. Additional tests, such as quantitative predictions for angular deviations due to an anisotropic void distribution and a theoretical derivation of the model, can vindicate or falsify the interpretation that light propagation in voids is responsible for the perceived acceleration.Comment: 33 pages, 2 figs; v2: minor clarifications, results unchanged; v3: matches the version published in General Relativity and Gravitatio

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure

Accelerated expansion from structure formation

We discuss the physics of backreaction-driven accelerated expansion. Using the exact equations for the behaviour of averages in dust universes, we explain how large-scale smoothness does not imply that the effect of inhomogeneity and anisotropy on the expansion rate is small. We demonstrate with an analytical toy model how gravitational collapse can lead to acceleration. We find that the conjecture of the accelerated expansion being due to structure formation is in agreement with the general observational picture of structures in the universe, and more quantitative work is needed to make a detailed comparison.Comment: 44 pages, 1 figure. Expanded treatment of topics from the Gravity Research Foundation contest essay astro-ph/0605632. v2: Added references, clarified wordings. v3: Published version. Minor changes and corrections, added a referenc

Apparent and average acceleration of the Universe

In this paper we consider the relation between the volume deceleration parameter obtained within the Buchert averaging scheme and the deceleration parameter derived from the supernova observation. This work was motivated by recent findings that showed that there are models which despite $\Lambda=0$ have volume deceleration parameter $q^{vol} < 0$. This opens the possibility that backreaction and averaging effects may be used as an interesting alternative explanation to the dark energy phenomenon. We have calculated $q^{vol}$ in some Lema\^itre--Tolman models. For those models which are chosen to be realistic and which fit the supernova data, we find that $q^{vol} > 0$, while those models which we have been able to find which exhibit $q^{vol} < 0$ turn out to be unrealistic. This indicates that care must be exercised in relating the deceleration parameter to observations.Comment: 15 pages, 5 figures; matches published versio

Expression of Mir-21 and Mir-143 in Cervical Specimens Ranging from Histologically Normal through to Invasive Cervical Cancer

MicroRNA expression is severely disrupted in carcinogenesis, however limited evidence is available validating results from cell-line models in human clinical cancer specimens. MicroRNA-21 (mir-21) and microRNA-143 (mir-143) have previously been identified as significantly deregulated in a range of cancers including cervical cancer. Our goal was to investigate the expression patterns of several well-studied microRNA species in cervical samples and compare the results to cell line samples.We measured the expression of mir-21 and mir-143 in 142 formalin-fixed, paraffin embedded (FFPE) cervical biopsy tissue blocks, collected from Dantec Oncology Clinic, Dakar, Senegal. MicroRNA expression analysis was performed using Taqman-based real-time PCR assays. Protein immunohistochemical staining was also performed to investigate target protein expression on 72 samples. We found that mir-21 expression increased with worsening clinical diagnosis but that mir-143 was not correlated with histology. These observations were in stark contrast to previous reports involving cervical cancer cell lines in which mir-143 was consistently down-regulated but mir-21 largely unaffected. We also identified, for the first time, that cytoplasmic expression of Programmed Cell Death Protein 4 PDCD4; a known target of mir-21) was significantly lower in women with invasive cervical carcinoma (ICC) in comparison to those with cervical intraepithelial neoplasia (2-3) or carcinoma in situ (CIN2-3/CIS), although there was no significant correlation between mir-21 and PDCD4 expression, despite previous studies identifying PDCD4 transcript as a known mir-21 target.Whilst microRNA biomarkers have a number of promising features, more studies on expression levels in histologically defined clinical specimens are required to investigate clinical relevance of discovery-based studies. Mir-21 may be of some utility in predictive screening, given that we observed a significant correlation between mir-21 expression level and worsening histological diagnosis of cervical cancer