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

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.

Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the EinsteinHilbert action. Several studies showed that these models can have late-time self-acceleration and could, in some cases, fit various observational constraints. In view of the infinite spectrum of invariants that could be built from curvature tensors, we propose here a method based on minimal sets of independent invariants as a possible route for a systematic approach to these models. We explore a connection made between theorems on bases in invariants theory in relativity and higher-order cosmological models. A dynamical system analysis is performed and some models with accelerating attractors are discussed. The asymptotic behavior of the models is also studied using analytical calculations.PACS numbers: 98.80.-k, 95.36.+x

We use cosmological constraints from current datasets and a figure of merit approach (FoM) in order to probe any deviations from general relativity at cosmological scales. The FoM approach is used to study and compare the constraining power of various combinations of datasets on the modified gravity (MG) parameters. We use the recently refined HST-COSMOS weak lensing tomography data, the ISW-galaxy cross correlations from 2MASS and SDSS LRG galaxy surveys, the matterpower spectrum from SDSS-DR7 (MPK), the WMAP7 temperature and polarization spectra, the BAO from 2DF and SDSS-DR7, and the Union2 compilation of type Ia supernovae, in addition to other bounds from Hubble parameter measurements and Big Bang Nucleosynthesis. We use three parameterizations of MG parameters that enter the perturbed field equations. In order to allow for variations of the parameters with the redshift and scale, the first two parameterizations use recently suggested functional forms while the third is based on binning methods. Using the first parameterization, we find that the CMB+ISW+WL combination provides the strongest constraints on the MG parameters followed by CMB+WL or CMB+MPK+ISW. Using the second parameterization or the binning methods, we find that the combination CMB+MPK+ISW consistently provides some of the strongest constraints. This shows that the constraints are parameterization dependent. We find that adding up current datasets does not improve consistently the uncertainties on MG parameters due to tensions between the best fit MG parameters preferred by different datasets. Furthermore, some functional forms imposed by the parameterizations can lead to an exacerbation of these tensions. Next, unlike some studies that used the CFHTLS lensing data, we do not find any deviation from GR using the refined HST-COSMOS data, confirming previous claims in those studies that their result may have been due to some systematic effect. Finally, for all the parameterizations and binning methods used, we find that the values corresponding to general relativity are within the 95% confidence level contours for all data set combinations.

We compare higher order gravity models to observational constraints from magnitude-redshift supernova data, distance to the last scattering surface of the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed systematic approach to higher order gravity models based on minimal sets of curvature invariants, and select models that pass some physical acceptability conditions (free of ghost instabilities, real and positive propagation speeds, and free of separatrices). Models that satisfy these physical and observational constraints are found in this analysis and do provide fits to the data that are very close to those of the LCDM concordance model. However, we find that the limitation of the models considered here comes from the presence of superluminal mode propagations for the constrained parameter space of the models.PACS numbers: 98.80.-k, 95.36.+x

We present a collection of new, open-source computational tools for numerically modeling recent large-scale observational data sets using modern cosmology theory. Specifically, these tools will allow both students and researchers to constrain the parameter values in competitive cosmological models, thereby discovering both the accelerated expansion of the universe and its composition (e.g., dark matter and dark energy). These programs have several features to help the non-cosmologist build an understanding of cosmological models and their relation to observational data: a built-in collection of several real observational data sets; sliders to vary the values of the parameters that define different cosmological models; real-time plotting of simulated data; and χ 2 calculations of the goodness of fit for each choice of parameters (theory) and observational data (experiment). The current list of built-in observations includes several recent supernovae Type Ia surveys, baryon acoustic oscillations, the cosmic microwave background radiation, gamma-ray bursts, and measurements of the Hubble parameter. In this article, we discuss specific results for testing cosmological models using these observational data. These programs can be found at http://www.compadre.org/osp/ items/detail.cfm?ID=12406.

We consider recently proposed higher order gravity models where the action is built from the Einstein-Hilbert action plus a function f (G) of the Gauss-Bonnet invariant. The models were previously shown to pass physical acceptability conditions as well as solar system tests. In this paper, we compare the models to combined data sets of supernovae, baryon acoustic oscillations, and constraints from the CMB surface of last scattering. We find that the models provide fits to the data that are close to those of the LCDM concordance model. The results provide a pool of higher order gravity models that pass these tests and need to be compared to constraints from large scale structure and full CMB analysis.