We derive new limits on the value of the cosmological constant, Λ, based on the Einstein bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. We use an amended lens equation in which the contribution of Λ to the Einstein deflection angle is taken into account and use observations of Einstein radii around several lens systems. We use in our calculations a Schwarzschild–de Sitter vacuole exactly matched into a Friedmann–Robertson–Walker background and show that a Λ‐contribution term appears in the deflection angle within the lens equation. We find that the contribution of the Λ‐term to the bending angle is larger than the second‐order term for many lens systems. Using these observations of bending angles, we derive new limits on the value of Λ. These limits constitute the best observational upper bound on Λ after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints.

The testing of general relativity at cosmological scales has become a possible and timely endeavor that is not only motivated by the pressing question of cosmic acceleration but also by the proposals of some extensions to general relativity that would manifest themselves at large scales of distance. We analyze here correlations between modified gravity growth parameters and some core cosmological parameters using the latest cosmological data sets including the refined Cosmic Evolution Survey 3D weak lensing. We provide the parametrized modified growth equations and their evolution. We implement known functional and binning approaches, and propose a new hybrid approach to evolve the modified gravity parameters in redshift (time) and scale. The hybrid parametrization combines a binned redshift dependence and a smooth evolution in scale avoiding a jump in the matter power spectrum. The formalism developed to test the consistency of current and future data with general relativity is implemented in a package that we make publicly available and call ISiTGR (Integrated Software in Testing General Relativity), an integrated set of modified modules for the publicly available packages CosmoMC and CAMB, including a modified version of the integrated SachsWolfe-galaxy cross correlation module of Ho et al and a new weak-lensing likelihood module for the refined Hubble Space Telescope Cosmic Evolution Survey weak gravitational lensing tomography data. We obtain parameter constraints and correlation coefficients finding that modified gravity parameters are significantly correlated with σ8 and mildly correlated with Ωm, for all evolution methods. The degeneracies between σ8 and modified gravity parameters are found to be substantial for the functional form and also for some specific bins in the hybrid and binned methods indicating that these degeneracies will need to be taken into consideration when using future high precision data.PACS numbers: 95.36.+x,98.80.Es,98.62.Sb

In order to explain cosmic acceleration without invoking "dark" physics, we consider f (R) modified gravity models, which replace the standard Einstein-Hilbert action in General Relativity with a higher derivative theory. We use data from the WiggleZ Dark Energy survey to probe the formation of structure on large scales which can place tight constraints on these models. We combine the large-scale structure data with measurements of the cosmic microwave background from the Planck surveyor. After parameterizing the modification of the action using the Compton wavelength parameter B 0 , we constrain this parameter using ISiTGR, assuming an initial non-informative log prior probability distribution of this cross-over scale. We find that the addition of the WiggleZ power spectrum provides the tightest constraints to date on B 0 by an order of magnitude, giving log 10 (B 0 ) < −4.07 at 95% confidence limit. Finally, we test whether the effect of adding the lensing amplitude A Lens and the sum of the neutrino mass m ν is able to reconcile current tensions present in these parameters, but find f (R) gravity an inadequate explanation.

The question of whether or not the cosmological constant affects the bending of light around a concentrated mass has been the subject of some recent papers. We present here a simple, specific and transparent example where bending clearly takes place, and where it is clearly neither a coordinate effect nor an aberration effect. We then show that in some recent works using perturbation theory the contribution was missed because of initial too stringent smallness assumptions. Namely, our method has been to insert a Kottler (Schwarzschild with ) vacuole into a Friedmann universe, and to calculate the total bending within the vacuole. We assume that no more bending occurs outside. It is important to observe that while the mass contribution to the bending takes place mainly quite near the lens, the bending continues throughout the vacuole. Thus, if one deliberately restricts one's search for bending to the immediate neighbourhood of the lens, one will not find it. Lastly, we show that the bending also follows from standard Weyl focusing, and so again, it cannot be a coordinate effect.

We use current and future simulated data of the growth rate of large scale structure in combination with data from supernova, BAO, and CMB surface measurements, in order to put constraints on the growth index parameters. We use a recently proposed parameterization of the growth index that interpolates between a constant value at high redshifts and a form that accounts for redshift dependencies at small redshifts. We also suggest here another exponential parameterization with a similar behaviour. The redshift dependent parametrizations provide a sub-percent precision level to the numerical growth function, for the full redshift range. Using these redshift parameterizations or a constant growth index, we find that current available data from galaxy redshift distortions and Lyman-alpha forests is unable to put significant constraints on any of the growth parameters. For example both ΛCDM and flat DGP are allowed by current growth data. We use an MCMC analysis to study constraints from future growth data, and simulate pessimistic and moderate scenarios for the uncertainties. In both scenarios, the redshift parameterizations discussed are able to provide significant constraints and rule out models when incorrectly assumed in the analysis. The values taken by the constant part of the parameterizations as well as the redshift slopes are all found to significantly rule out an incorrect background. We also find that, for our pessimistic scenario, an assumed constant growth index over the full redshift range is unable to rule out incorrect models in all cases. This is due to the fact that the slope acts as a second discriminator at smaller redshifts and therefore provide a significant test to identify the underlying gravity theory.

We present constraints on testing general relativity (GR) at cosmological scales using recent data sets and assess the impact of galaxy intrinsic alignment in the CFHTLenS lensing data on those constraints. We consider data from Planck temperature anisotropies, the galaxy power spectrum from the WiggleZ survey, weak-lensing tomography shear-shear cross-correlations from the CFHTLenS survey, integrated Sachs Wolfe-galaxy cross-correlations, and baryon acoustic oscillation data. We use three different parametrizations of modified gravity (MG), one that is binned in redshift and scale, a parametrization that evolves monotonically in scale but is binned in redshift, and a functional parametrization that evolves only in redshift. We present the results in terms of the MG parameters Q and Σ. We employ an intrinsic alignment model with an amplitude A CFHTLenS that is included in the parameter analysis. We find an improvement in the constraints on the MG parameters corresponding to a 40-53% increase on the figure of merit compared to previous studies, and GR is found consistent with the data at the 95% confidence level. The bounds found on A CFHTLenS are sensitive to the MG parametrization used, and the correlations between A CFHTLenS and MG parameters are found to be weak to moderate. For all three MG parametrizations A CFHTLenS is found to be consistent with zero when the whole lensing sample is used; however, when using the optimized early-type galaxy sample a significantly nonzero A CFHTLenS is found for GR and the scaleindependent MG parametrization. We find that the tensions observed in previous studies persist, and there is an indication that cosmic microwave background (CMB) data and lensing data prefer different values for MG parameters, particularly for the parameter Σ. The analysis of the confidence contours and probability distributions suggest that the bimodality found follows that of the known tension in the σ 8 parameter.

We present measurements of both scale-and time-dependent deviations from the standard gravitational field equations. These late-time modifications are introduced separately for relativistic and non-relativistic particles, by way of the parameters G matter (k, z) and G light (k, z) using two bins in both scale and time, with transition wavenumber 0.01 Mpc −1 and redshift 1. We emphasize the use of two dynamical probes to constrain this set of parameters, galaxy power spectrum multipoles and the direct peculiar velocity power spectrum, which probe fluctuations on different scales. The multipole measurements are derived from the WiggleZ and BOSS Data Release 11 CMASS galaxy redshift surveys and the velocity power spectrum is measured from the velocity sub-sample of the 6-degree Field Galaxy Survey. We combine with additional cosmological probes including baryon acoustic oscillations, Type Ia SNe, the cosmic microwave background (CMB), lensing of the CMB, and the temperaturegalaxy cross-correlation. Using a Markov Chain Monte Carlo likelihood analysis, we find the inferred best-fit parameter values of G matter (k, z) and G light (k, z) to be consistent with the standard model at the 95% confidence level. Furthermore, accounting for the Alcock-Paczynski effect, we perform joint fits for the expansion history and growth index gamma; we measure γ = 0.665 ± 0.0669 (68% C.L) for a fixed expansion history, and γ = 0.73 +0.08 −0.10 (68% C.L) when the expansion history is allowed to deviate from ΛCDM. With a fixed expansion history the inferred value is consistent with GR at the 95% C.L; alternatively, a 2σ tension is observed when the expansion history is not fixed, this tension is worsened by the combination of growth and SNe data.

The growth rate of matter perturbations can be used to distinguish between different gravity theories and to distinguish between dark energy and modified gravity at cosmological scales as an explanation to the observed cosmic acceleration. We suggest here parameterizations of the growth index as functions of the redshift. The first one is given by $\gamma(a)=\tilde\gamma(a) \frac{1}{1+(a_{_{ttc}}/a)}+\gamma_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$ that interpolates between a low/intermediate redshift parameterization $\tilde\gamma(a)=\gamma_{_{late}}(a)= \gamma_0 + (1-a) \gamma_a$ and a high redshift $\gamma_{_{early}}$ constant value. For example, our interpolated form $\gamma(a)$ can be used when including the CMB to the rest of the data while the form $\gamma_{_{late}}(a)$ can be used otherwise. It is found that the parameterizations proposed achieve a fit that is better than 0.004% for the growth rate in a $\Lambda$CDM model, better than 0.014% for Quintessence-Cold-Dark-Matter (QCDM) models, and better than 0.04% for the flat Dvali-Gabadadze-Porrati (DGP) model (with $\Omega_m^0=0.27$) for the entire redshift range up to $z_{_{CMB}}$. We find that the growth index parameters $(\gamma_0,\gamma_a)$ take distinctive values for dark energy models and modified gravity models, e.g. $(0.5655,-0.02718)$ for the $\Lambda$CDM model and $(0.6418,0.06261)$ for the flat DGP model. This provides a means for future observational data to distinguish between the models.Comment: 7 pages, 6 figures, matches PRD accepted versio