Jason Dossett

A new independent limit on the cosmological constant/dark energy from the relativistic bending of light by Galaxies and clusters of Galaxies

We derive new limits on the value of the cosmological constant, A, 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 A 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 A-contribution term appears in the deflection angle within the lens equation. We find that the contribution of the A-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 A. These limits constitute the best observational upper bound on A after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints.

Testing general relativity at cosmological scales: Implementation and parameter correlations

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 parametrized modified growth equations and their evolution. We implement known functional and binning approaches, and propose a new hybrid approach to evolve 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 Sachs-Wolfe-galaxy cross correlation module of Ho et al and a new weak-lensing likelihood module for the refined HST-COSMOS weak lensing tomography data. We obtain parameter constraints and correlation coefficients finding that modified gravity parameters are significantly correlated with \sigma_8 and mildly correlated with \Omega_m, for all evolution methods. The degeneracies between \sigma_8 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.

Constraints on growth index parameters from current and future observations

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.

More on lensing by a cosmological constant

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 A 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 A contribution was missed because of initial too stringent smallness assumptions. Namely, our method has been to insert a Kottler (Schwarzschild with A) 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 A bending continues throughout the vacuole. Thus, if one deliberately restricts ones search for A bending to the immediate neighbourhood of the lens, one will not find it. Lastly, we show that the A bending also follows from standard Weyl focusing, and so again, it cannot be a coordinate effect.

Figures of merit and constraints from testing General Relativity using the latest cosmological data sets including refined COSMOS 3D weak lensing

We use cosmological constraints from current data sets and a figure of merit (FoM) approach to probe any deviations from general relativity (GR) at cosmological scales. The FoM approach is used to study the constraining power of various combinations of data sets on modified gravity (MG) parameters. We use recently refined HST-COSMOS weak-lensing tomography data, ISW-galaxy cross correlations from 2MASS and SDSS LRG surveys, matter power spectrum from SDSS-DR7 (MPK), WMAP7 temperature and polarization spectra, BAO from 2DF and SDSS-DR7, and Union2 compilation of supernovae, in addition to other bounds from H_0 measurements and BBN. We use 3 parametrizations of MG parameters that enter the perturbed field equations. In order to allow for variations with redshift and scale, the first 2 parametrizations use recently suggested functional forms while the third is based on binning methods. Using the first parametrization, we find that CMB + ISW + WL provides the strongest constraints on MG parameters followed by CMB+WL or CMB+MPK+ISW. Using the second parametrization or binning methods, CMB+MPK+ISW consistently provides some of the strongest constraints. This shows that the constraints are parametrization dependent. We find that adding up current data sets does not improve consistently uncertainties on MG parameters due to tensions between best-fit MG parameters preferred by different data sets. Furthermore, some functional forms imposed by the parametrizations 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, we find in all cases that the values corresponding to GR are within the 95% confidence level contours for all data set combinations. (abridged)

Constraints and tensions in testing general relativity from Planck and CFHTLenS data including intrinsic alignment systematics

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 Sigma. 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 ACFHTLenS are sensitive to the MG parametrization used, and the correlations between ACFHTLenS and MG parameters are found to be weak to moderate. For all three MG parametrizations ACFHTLenS 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 scale-independent 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 Sigma. The analysis of the confidence contours and probability distributions suggest that the bimodality found follows that of the known tension in the sigma(8) parameter.

Spatial curvature and cosmological tests of general relativity

It is well-known that allowing for spatial curvature affects constraints on cosmological parameters such as the dark energy equation of state parameters. Here we study the effect of curvature on constraints on parameters used to test general relativity (GR) at cosmological scales, commonly known as modified growth (MG) parameters, as while current data taken in the context of the

Effects of dark energy perturbations on cosmological tests of general relativity

\Lambda

Contiguous redshift parameterizations of the growth index

CDM model points to a universe that is flat or very close to it, this constraint may not hold in modified theories of gravity. Using the latest cosmological data sets we find that MG parameters are correlated with the curvature parameter

Constraining models of f(R) gravity with Planck and WiggleZ power spectrum data

\Omega_k