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Line-of-sight effects in strong gravitational lensing have long been treated as a nuisance. However, it was recently proposed that the line-of-sight shear could be a cosmological observable in its own right, if it is not degenerate with lens model parameters. We firstly demonstrate that the line-of-sight shear can be accurately measured from a simple simulated strong lensing image with percent precision. We then extend our analysis to more complex simulated images and stress test the recovery of the line-of-sight shear when using deficient fitting models, finding that it escapes from degeneracies with lens model parameters, albeit at the expense of the precision. Lastly, we check the validity of the tidal approximation by simulating and fitting an image generated in the presence of many line-of-sight dark matter haloes, finding that an explicit violation of the tidal approximation does not necessarily prevent one from measuring the line-of-sight shear., 16 + 3 pages, 16 figures, matches version published in MNRAS (lens modelling and analysis results updated and improved, conclusions unchanged)

We analyse the clustering of matter on large scales in an extension of the concordance model that allows for spatial curvature. We develop a consistent approach to curvature and wide-angle effects on the galaxy 2-point correlation function in redshift space. In particular we derive the Alcock-Paczynski distortion of $f\sigma_{8}$, which differs significantly from empirical models in the literature. A key innovation is the use of the `Clustering Ratio', which probes clustering in a different way to redshift-space distortions, so that their combination delivers more powerful cosmological constraints. We use this combination to constrain cosmological parameters, without CMB information. In a curved Universe, we find that $\Omega_{{\rm m}, 0}=0.26\pm 0.04$ (68\% CL). When the clustering probes are combined with low-redshift background probes -- BAO and SNIa -- we obtain a CMB-independent constraint on curvature: $\Omega_{K,0} = 0.0041\,_{-0.0504}^{+0.0500}$. We find no Bayesian evidence that the flat concordance model can be rejected. In addition we show that the sound horizon at decoupling is $r_{\rm d} = 144.57 \pm 2.34 \; {\rm Mpc}$, in agreement with its measurement from CMB anisotropies. As a consequence, the late-time Universe is compatible with flat $\Lambda$CDM and a standard sound horizon, leading to a small value of $H_{0}$, {\em without} assuming any CMB information. Clustering Ratio measurements produce the only low-redshift clustering data set that is not in disagreement with the CMB, and combining the two data sets we obtain $\Omega_{K,0}= -0.023 \pm 0.010$., Comment: 40 pages; 13 figures; Version accepted by JCAP

Square Kilometre Array: et al., arXiv:1810.02680v3, The Square Kilometre Array (SKA) is a planned large radio interferometer designed to operate over a wide range of frequencies, and with an order of magnitude greater sensitivity and survey speed than any current radio telescope. The SKA will address many important topics in astronomy, ranging from planet formation to distant galaxies. However, in this work, we consider the perspective of the SKA as a facility for studying physics. We review four areas in which the SKA is expected to make major contributions to our understanding of fundamental physics: cosmic dawn and reionisation; gravity and gravitational radiation; cosmology and dark energy; and dark matter and astroparticle physics. These discussions demonstrate that the SKA will be a spectacular physics machine, which will provide many new breakthroughs and novel insights on matter, energy, and spacetime., A. Racanelli has received funding from the People Programme (Marie Curie Actions) of the European Union H2020 Programme under REA grant agreement number 706896 (COSMOFLAGS). Funding for this work was partially provided by the Spanish MINECO under MDM-2014-0369 of ICCUB (Unidad de Excelencia ‘Maria de Maeztu’).

While most strong-gravitational-lensing systems may be roughly modelled by a single massive object between the source and the observer, in the details all the structures near the light path contribute to the observed images. These additional contributions, known as line-of-sight effects, are non-negligible in practice. This article proposes a new theoretical framework to model the line-of-sight effects, together with very promising applications at the interface of weak and strong lensing. Our approach relies on the dominant-lens approximation, where one deflector is treated as the main lens while the others are treated as perturbations. The resulting framework is technically simpler to handle than the multi-plane lensing formalism, while allowing one to consistently model any sub-critical perturbation. In particular, it is not limited to the usual external-convergence and external-shear parameterisation. As a first application, we identify a specific notion of line-of-sight shear that is not degenerate with the ellipticity of the main lens, and which could thus be extracted from strong-lensing images. This result supports and improves the recent proposal that Einstein rings might be powerful probes of cosmic shear. As a second application, we investigate the distortions of strong-lensing critical curves under line-of-sight effects, and more particularly their correlations across the sky. We find that such correlations may be used to probe, not only the large-scale structure of the Universe, but also the dark-matter halo profiles of strong lenses. This last possibility would be a key asset to improve the accuracy of the measurement of the Hubble-Lema\^itre constant via time-delay cosmography., Comment: 39+14 pages, 15 figures. v2: discussion improved in sec. 3.2; figs. 4 and 15 updated. v3: minor typos corrected, matches published version; v4, v5: other typos corrected

When a luminous source is extended, its distortions by weak gravitational lensing are richer than a mere combination of magnification and shear. In a recent work, we proposed an elegant formalism based on complex analysis to describe and calculate such distortions. The present article further elaborates this finite-beam approach, and applies it to a realistic cosmological model. In particular, the cosmic correlations of image distortions beyond shear are predicted for the first time. These constitute new weak-lensing observables, sensitive to very-small-scale features of the distribution of matter in the Universe. While the major part of the analysis is performed in the approximation of circular sources, a general method for extending it to noncircular sources is presented and applied to the astrophysically relevant case of elliptic sources., 14+2 pages, 6 figures

The beyond-Horndeski gravity has recently been reformulated in the dark energy paradigm - which has been dubbed, Unified Dark Energy (UDE). The evolution equations for the given UDE appear to correspond to a non-conservative dark energy scenario, in which the total energy-momentum tensor is not conserved. We investigate both the background cosmology and, the large-scale imprint of the UDE by probing the angular power spectrum of galaxy number counts, on ultra-large scales; taking care to include the full relativistic corrections in the observed overdensity. The background evolution shows that only an effective mass smaller than the Planck mass is needed in the early universe in order for predictions in the given theory to match current observational constraints. We found that the effective mass-evolution-rate parameter, which drives the evolution of the UDE, acts to enhance the observed power spectrum and, hence, relativistic effects (on ultra-large scales) by enlarging the UDE sound horizon. Conversely, both the (beyond) Horndeski parameter and the kineticity act to diminish the observed power spectrum, by decreasing the UDE sound horizon. Our results show that, in a universe with UDE, a multi-tracer analysis will be needed to detect the relativistic effects in the large-scale structure. In the light of a multi-tracer analysis, the various relativistic effects hold the potential to distinguish different gravity models. Moreover, while the Doppler effect will remain significant at all epochs and, thus can not be ignored, the integrated Sachs-Wolfe, the time-delay and the potential (difference) effects, respectively, will only become significant at epochs near z=3 and beyond, and may be neglected at late epochs. In the same vein, the Doppler effect alone can serve as an effective cosmological probe for the large-scale structure or gravity models, in the angular power spectrum - at all z., Comment: 28 pages, 13 figures. Version accepted by JCAP

The standard theory of weak gravitational lensing relies on the approximation that light beams are infinitesimal. Our recent work showed that the finite size of sources, and the associated light beams, can cause nonperturbative corrections to the weak-lensing convergence and shear. This article thoroughly investigates these corrections in a realistic cosmological model. The continuous transition from infinitesimal to finite beams is understood, and reveals that the previous results overestimated finite-beam effects due to simplistic assumptions on the distribution of matter in the Universe. In a KiloDegree Survey-like setting, finite-beam corrections to the cosmic shear remain subpercent, while percent-level corrections are only reached on subarcmin scales. This article thus demonstrates the validity of the infinitesimal-beam approximation in the interpretation of current weak-lensing data., Comment: 14+2 pages, 10 figures

George Ellis and Julien Larena highlight the possibility that the universe could be curved and closed, and explore the theoretical importance of this possibility.

The galaxy bispectrum on scales around and above the equality scale receives contributions from relativistic effects. Some of these arise from lightcone deformation effects, which come from local and line-of-sight integrated contributions. Here we calculate the local contributions from the generated vector and tensor background which is formed as scalar modes couple and enter the horizon. We show that these modes are sub-dominant when compared with other relativistic contributions., 14 pages, 4 figures. v2 has minor changes, to appear in JCAP

We give an outline of an algorithm designed to reconstruct the background cosmological metric within the class of spherically symmetric dust universes that may include a cosmological constant. Luminosity and age data are used to derive constraints on the geometry of the universe up to a redshift of $z = 1.75$. It is shown that simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time Universe cannot be ruled out by these data alone., 6 pages, 2 figures, contribution to 14th Marcel Grossmann meeting

The standard theory of weak gravitational lensing relies on the infinitesimal light beam approximation. In this context, images are distorted by convergence and shear, the respective sources of which unphysically depend on the resolution of the distribution of matter---the so-called Ricci-Weyl problem. In this letter, we propose a strong-lensing-inspired formalism to describe the lensing of finite beams. We address the Ricci-Weyl problem by showing explicitly that convergence is caused by the matter enclosed by the beam, regardless of its distribution. Furthermore, shear turns out to be systematically enhanced by the finiteness of the beam. This implies, in particular, that the Kaiser-Squires relation between shear and convergence is violated, which could have profound consequences on the interpretation of weak lensing surveys., 6 pages, 2 figures, v2: matches published version, some typos corrected

We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \delta_{ij} + g(P^2) P_i P_j $ for any functions $f$. However, we restrict our study to the case of commuting $X$'s. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heisenberg algebra of operators and an aquadratic Hamiltonian, provided the boost sector of the symmetries is modified accordingly. The theory can also be mapped to a completely standard Quantum Mechanics with standard symmetries, but with momentum dependent position operators. Next, we investigate the Hilbert space representations of these algebraically equivalent models, and focus, specifically on whether they exhibit a minimal length. We carry the functional analysis of the various operators involved, and show that the appearance of a minimal length critically depends on the relationship between the generators of translations and the physical momenta. In particular, because this relationship is preserved by the algebraic mapping presented in this paper, when a minimal length is present in the standard GUP, it is also present in the corresponding Aquadratic Hamiltonian formulation, despite the perfectly standard algebra of this model. In general, a minimal length requires bounded generators of translations, i.e. a specific kind of quantization of space, and this depends on the precise shape of the function $f$ defined previously. This result provides an elegant and unambiguous classification of which universal quantum gravity corrections lead to the emergence of a minimal length., Comment: 21 pages, no figures. Results unchanged. Unnecessary Appendix B removed. Replaced to match final version published in General Relativity and Gravitation. Title shortened at the request of the referee

In order to understand how locally static configurations around gravitationally bound bodies can be embedded in an expanding universe, we investigate the solutions of general relativity describing a space-time whose spatial sections have the topology of a 3-sphere with two identical masses at the poles. We show that Israel junction conditions imply that two spherically symmetric static regions around the masses cannot be glued together. If one is interested in an exterior solution, this prevents the geometry around the masses to be of the Schwarzschild type and leads to the introduction of a cosmological constant. The study of the extension of the Kottler space-time shows that there exists a non-static solution consisting of two static regions surrounding the masses that match a Kantowski-Sachs expanding region on the cosmological horizon. The comparison with a Swiss-Cheese construction is also discussed., Comment: 15 pages, 5 figures. Replaced to match the published version

Vilkovisky has claimed to have solved the black hole backreaction problem and finds that black holes lose only ten percent of their mass to Hawking radiation before evaporation ceases. We examine the implications of this scenario for cold dark matter, assuming that primordial black holes are created during the reheating period after inflation. The mass spectrum is expected to be dominated by 10-gram black holes. Nucleosynthesis constraints and the requirement that the earth presently exist do not come close to ruling out such black holes as dark matter candidates. They also evade the demand that the photon density produced by evaporating primordial black holes does not exceed the present cosmic radiation background by a factor of about one thousand., As accepted by Astrophysics and Space Sciences. A few minor errors corrected over previous version, footnote added. 14 pages, 1 fig

In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case appearing as a special case of this larger framework. Then, depending on the rationality of the Kovalewski exponents, the different models, both in the vacuum and in presence of a barotropic matter fluid, are classified, and their integrability is discussed., Comment: 16 pages, no figure, accepted in CQG

Combined with other CMB experiments, the WMAP survey provides an accurate estimate of the baryon density of the Universe. In the framework of the standard Big Bang Nucleosynthesis (BBN), such a baryon density leads to predictions for the primordial abundances of $^{4}$He and D in good agreement with observations. However, it also leads to a significant discrepancy between the predicted and observed primordial abundance of $^{7}$Li. Such a discrepancy is often termed as 'the lithium problem'. In this paper, we analyze this problem in the framework of scalar-tensor theories of gravity. It is shown that an expansion of the Universe slightly slower than in General Relativity before BBN, but faster during BBN, solves the lithium problem and leads to $^4$He and D primordial abundances consistent with the observational constraints. This kind of behavior is obtained in numerous scalar-tensor models, both with and without a self-interaction potential for the scalar field. In models with a self-interacting scalar field, the convergence towards General Relativity is ensured without any condition, thanks to an attraction mechanism which starts to work during the radiation-dominated epoch.

We present a new algorithm that can reconstruct the full distributions of metric components within the class of spherically symmetric dust universes that may include a cosmological constant. The algorithm is capable of confronting this class of solutions with arbitrary data and opens a new observational window to determine the value of the cosmological constant. In this work we use luminosity and age data to constrain the geometry of the universe up to a redshift of $z = 1.75$. We show that, although current data are perfectly compatible with homogeneous models of the universe, simple radially inhomogeneous void models that are sometimes used as alternative explanations for the apparent acceleration of the late time universe cannot yet be ruled out. In doing so we reconstruct the density of cold dark matter out to $z = 1.75$ and derive constraints on the metric components when the universe was 10.5 Gyr old within a comoving volume of approximately 1 Gpc$^{3}$., 15 pages, 8 figures. Matches published version

We undertake a non-perturbative study of the evolution of the "gravitational entropy" proposed by Clifton, Ellis and Tavakol (CET) on local expanding cosmic CDM voids of $\sim 50-100$ Mpc size described as spherical under-dense regions with negative spatial curvature, whose dynamics is determined by Lemaitre-Tolman-Bondi (LTB) dust models asymptotic to three different types of FLRW background: $\Lambda$CDM, Einstein de Sitter and "open" FLRW with $\Lambda=0$ and negative spatial curvature. By assuming generic nearly spatially flat and linear initial conditions at the last scattering time, we examine analytically and numerically the CET entropy evolution into a fully non-linear regime in our present cosmic time and beyond. Both analytic and numerical analysis reveal that the late time CET entropy growth is determined by the amplitude of initial fluctuations of spatial curvature at the last scattering time. This entropy growth decays to zero in the late asymptotic time range for all voids, but at a faster rate in voids with $\Lambda$CDM and open FLRW backgrounds. However, only for voids in a $\Lambda$CDM background this suppression is sufficiently rapid for the CET entropy itself to reach a terminal equilibrium (or "saturation") value. The CET gravitational temperature vanishes asymptotically if $\Lambda=0$ and becomes asymptotically proportional to $\Lambda$ for voids in a $\Lambda$CDM background. In the linear regime of the LTB evolution our results coincide, qualitatively and quantitatively, with previous results based on linear perturbation theory., Comment: 24 pages, 6 figures. Replaced to match the published version

We show how two seemingly different theories with a scalar multiplicative coupling to electrodynamics are actually two equivalent parametrisations of the same theory: despite some differences in the interpretation of some phenemenological aspects of the parametrisations, they lead to the same physical observables. This is illustrated on the interpretation of observations of the Cosmic Microwave Background., 14 pages, matched published version

This paper proposes a systematic study of cosmological signatures of modifications of gravity via the presence of a scalar field with a multiplicative coupling to the electromagnetic Lagrangian. We show that, in this framework, variations of the fine structure constant, violations of the distance duality relation, evolution of the cosmic microwave background (CMB) temperature and CMB distortions are intimately and unequivocally linked. This enables one to put very stringent constraints on possible violations of the distance duality relation, on the evolution of the CMB temperature and on admissible CMB distortions using current constraints on the fine structure constant. Alternatively, this offers interesting possibilities to test a wide range of theories of gravity by analysing several datasets concurrently. We discuss results obtained using current data as well as some forecasts for future data sets such as those coming from EUCLID or the SKA., Comment: 14 pages, 4 figures, matched published version. Note: title changed upon suggestion of PRD editors

We present a regular cubic lattice solution to Einstein field equations that is exact at second order in a small parameter. We show that this solution is kinematically equivalent to the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution with the same averaged energy density. This allows us to discuss the fitting problem in that framework: are observables along the past lightcone of observers equivalent to those in the analogue FLRW model obtained by smoothing spatially the distribution of matter? We find a criterion on the compacity of the objects that must be satisfied in order for the answer to this question to be positive and given by perturbative arguments. If this criterion is not met, the answer to this question must be addressed fully non perturbatively along the past lightcone, even though the spacetime geometry can be described perturbatively.

We investigate the possibility of using Gaussian process regression to smooth data on the current past null-cone for use as the input to a relativistic integration scheme. The algorithm we present is designed to reconstruct the metric of spacetime within the class of spherically symmetric dust universes, with or without a cosmological constant. Assuming that gravity is well described by General Relativity, we demonstrate how the algorithm can be employed to test the Copernican principle based on currently available observations. It is shown that currently available data is not sufficient for a conclusive result. The intrinsic noise present in realistic data presents a challenge for our smoothing algorithm and we discuss some of its limitations as well as possible extensions to it. We conclude by demonstrating how a direct determination of the cosmological constant is possible using redshift drift data., 29 pages, 9 figures, published version

We consider generic Lemaitre-Tolman-Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non--local domain dependent manner for the two HB proposals. By looking at the fulfillment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to an FLRW background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a "gravitational entropy" may be a theoretically robust concept applicable to more general spacetimes., Version accepted for publication in Classical and Quantum Gravity. 39 pages, 6 figures

The Einstein Equivalence Principle is a fundamental principle of the theory of General Relativity. While this principle has been thoroughly tested with standard matter, the question of its validity in the Dark sector remains open. In this paper, we consider a general tensor-scalar theory that allows to test the equivalence principle in the Dark sector by introducing two different conformal couplings to standard matter and to Dark matter. We constrain these couplings by considering galactic observations of strong lensing and of velocity dispersion. Our analysis shows that, in the case of a violation of the Einstein Equivalence Principle, data favour violations through coupling strengths that are of opposite signs for ordinary and Dark matter. At the same time, our analysis does not show any significant deviations from General Relativity., Comment: 20 pages (+ 17 pages of appendix), 8 figures, version accepted for publication in JCAP

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.

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., 12 pages, 25 figures, references added, clarity improved, frame switching subtlety fixed, results unchanged, v3 minor typos fixed

Dark energy observations may be explained within general relativity using an inhomogeneous Hubble-scale depression in the matter density and accompanying curvature, which evolves naturally out of an Einstein-de Sitter (EdS) model. We present a simple parameterization of a void which can reproduce concordance model distances to arbitrary accuracy, but can parameterize away from this to give a smooth density profile everywhere. We show how the Hubble constant is not just a nuisance parameter in inhomogeneous models because it affects the shape of the distance-redshift relation. Independent Hubble-rate data from age estimates can in principle serve to break the degeneracy between concordance and void models, but the data is not yet able to achieve this. Using the latest Constitution supernova dataset we show that robust limits can be placed on the size of a void which is roughly independent of its shape. However, the sharpness of the profile at the origin cannot be well constrained due to supernova being dominated by peculiar velocities in the local Universe. We illustrate our results using some recently proposed diagnostics for the Friedmann models.

Working within the theory of modified Gauss‐Bonnet gravity, we show that FLRW‐like power‐law solutions only exist for a very special class of f(G) theories. Furthermore, we point out that any transition from decelerated to accelerated expansion must pass through G = 0, and no function f(G) that is differentiable at this point can admit both a decelerating power‐law solution and any accelerating solution. This strongly constrains the cosmological viability of f(G)gravity, since it may not be possible to obtain an expansion history of the universe which is compatible with observations. We compare to the case of f(R)‐gravity, and discuss possible caveats for the case of f(G)‐gravity.

We review some aspects of the backreaction problem. In a first part, using an averaging scheme generalized to arbitrary frames, we quantify the effect in the Poisson gauge of perturbation theory up to second order. The main result is the definition of a scale of homogeneity above which the backreaction effect becomes scale invariant. In a second part we present results about the structure of the effective lightcone in averaged cosmologies and show that a non‐trivial structure due to the backreaction may allow to test the relevance of the backreaction effect as a solution to the dark energy conundrum with future data.

In order to quantitatively test the ability of averaged inhomogeneous cosmologies to correctly describe observations of the large scale properties of the Universe, we introduce a smoothed template metric corresponding to a constant spatial curvature model at any time, but with an evolving curvature parameter. This metric is used to compute quantities along an approximate effective lightcone of the averaged model of the Universe. As opposed to the standard Friedmann model, we parameterize this template metric by exact scaling properties of an averaged inhomogeneous cosmology, and we also motivate this form of the metric by results on a geometrical smoothing of inhomogeneous cosmological hypersurfaces. We test our hypothesis for the template metric against supernova data and the position of the CMB peaks, and infer the goodness--of--fit and parameter uncertainties. We find that averaged inhomogeneous models can reproduce the observations without requiring an additional Dark Energy component (though a volume acceleration is still needed), and that current data do not disfavour our main assumption on the effective lightcone structure. We also show that the experimental uncertainties on the angular diameter distance and the Hubble parameter from Baryon Acoustic Oscillations measurements -- forseen in future surveys like the proposed EUCLID satellite project -- are sufficiently small to distinguish between a FLRW template geometry and the template geometry with consistently evolving curvature. (Abridged), Comment: 27 pages; new version with a corrected way to compute the redshifts; conclusions remain unchanged

This paper presents a general averaging procedure for a set of observers which are tilted with respect to the cosmological matter fluid. After giving the full set of equations describing the local dynamics, we define the averaging procedure and apply it to the scalar parts of Einstein's field equations. In addition to the standard backreaction, new terms appear that account for the effect of the peculiar velocity of the matter fluid as well as the possible effect of a shift in the coordinate system., Comment: 8 pages, no figure. Replaced to match the version published in Phys. Rev. D

We investigate the effect that the average backreaction of structure formation has on the dynamics of the cosmological expansion, within the concordance model. Our approach in the Poisson gauge is fully consistent up to second-order in a perturbative expansion about a flat Friedmann background, including a cosmological constant. We discuss the key length scales which are inherent in any averaging procedure of this kind. We identify an intrinsic homogeneity scale that arises from the averaging procedure, beyond which a residual offset remains in the expansion rate and deceleration parameter. In the case of the deceleration parameter, this can lead to a quite large increase in the value - more than 10% - and may therefore have important ramifications for dark energy measurements, even if the underlying nature of dark energy is a cosmological constant. We give the intrinsic variance that affects the value of the effective Hubble rate and deceleration parameter. These considerations serve to add extra intrinsic errors to our determination of the cosmological parameters, and, in particular, may render attempts to measure the Hubble constant to percent precision overly optimistic., Comment: 22 pages, 7 figures. v2 contains extra discussion and improvements; v3 is to appear in PRD

We show that within the class of f(R) gravity theories, FLRW power-law perfect fluid solutions only exist for R^n gravity. This significantly restricts the set of exact cosmological solutions which have similar properties to what is found in standard General Relativity., Comment: 4 pages, 2 figures

In the context of averaged cosmologies, the effective equations can be written in the form of "regional" Friedmannian equations with additional sources arising from the so-called backreaction of inhomogeneities. We propose a mean field description of this backreaction in terms of a regionally homogeneous scalar field: this provides a physical motivation to the phenomenological scalar fields generically called quintessence fields. We explicitly reconstruct the potential of the scalar field for a one-parameter family of scaling solutions to the backreaction problem, showing that it entails most of the standard scalar fields including e.g. standard and phantom quintessence scenarii., Comment: Prepared fro the proceedings of the 11th Marcel Grossmann meeting, Berlin, July 23-29 2006

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integrations of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes., Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published version

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., 36 pages and 6 Figures, matches published version in Class.Quant.Grav

The baryon density of our Universe, Ωbh2 = 0.0224±0.0009, as inferred from the WMAP first year of observations is used to predict the primordial abundances of light elements produced during Big Bang Nucleosynthesis (BBN). Such a baryon density, and a gravitation described by General Relativity, lead to predictions for the abundances of 4He and D in very good agreement with the observed ones; but they lead to a significant discrepancy between the calculated and the observed 7Li abundances. Supposing that the standard non gravitational sector is not modified, we consider scalar‐tensor theories of gravity, and study their impact on the 7Li abundance. It is shown that solving the lithium problem requires a non trivial behaviour of the expansion rate of the Universe at the epoch of BBN, in order not to violate the constraints from 4He and D. This kind of behaviour is obtained thanks to various models, both without and with self‐interaction for the scalar field.

The baryon density of our Universe, Ωbh2 = 0.0224 ± 0.0009, as inferred from the WMAP first year of observations is used to predict the primordial abundances of light elements produced during Big Bang Nucleosynthesis (BBN). Such a baryon density, and a gravitation described by General Relativity (GR), lead to predictions for the abundances of 4He and D in very good agreement with the observed ones; but they lead to a significant discrepancy between the calculated and the observed 7Li abundances. Supposing that the standard non gravitational sector is not modified, we consider scalar‐tensor theories of gravity, and study their impact on the 7Li abundance. It is shown that solving the lithium problem requires a non trivial behaviour of the expansion rate of the Universe at the epoch of BBN, in order not to violate the constraints from 4He and D.

We explore observables in a lattice Universe described by a recently found solution to Einstein field equations. This solution models a regular lattice of evenly distributed objects of equal masses. This inhomogeneous solution is perturbative, and, up to second order in a small parameter, it expands at a rate exactly equal to the one expected in a dust dominated Friedmann-Lemaître- Robertson-Walker (FLRW) model with the equivalent, smoothed energy density. Therefore, the kinematics of both cosmologies are identical up to the order of perturbation studied. Looking at the behaviour of the redshift and angular distance, we find a condition on the compactness of the objects at the centre of each cell under which corrections to the FLRW observables remain small, i.e. of order of a few percents at most. Nevertheless, we show that, if this condition is violated, i.e. if the objects are too compact, our perturbative scheme breaks down as far as the calculations of observables are concerned, even though the kinematics of the lattice remains identical to its FLRW counterpart (at the perturbative order considered). This may be an indication of an actual fitting problem, i.e. a situation in which the FLRW model obtained from lightcone observables does not correspond to the FLRW model obtained by smoothing the spatial distribution of matter. Fully non-perturbative treatments of the observables will be necessary to answer that question. © 2013 IOP Publishing Ltd.

Structure occurs over a vast range of scales in the universe. Our large-scale cosmological models are coarse-grained representations of what exists, which have much less structure than there really is. An important problem for cosmology is determining the influence the small-scale structure in the universe has on its large-scale dynamics and observations. Is there a significant, general relativistic, backreaction effect from averaging over structure? One issue is whether the process of smoothing over structure can contribute to an acceleration term and so alter the apparent value of the cosmological constant. If this is not the case, are there other aspects of concordance cosmology that are affected by backreaction effects? Despite much progress, this 'averaging problem' is still unanswered, but it cannot be ignored in an era of precision cosmology., Comment: 19 pages, 2 figures. Invited Key Issues Review to appear in Reports on Progress in Physics