Modifying Growth Research Articles

Testing deviations from GR at cosmological scales including dynamical dark energy, massive neutrinos, functional or binned parametrizations, and spatial curvature

We introduce a new version of the Integrated Software in Testing General Relativity (ISiTGR) which is a patch to the software CAMB and CosmoMC. ISiTGR is intended to test deviations from GR at cosmological scales using cosmological data sets. While doing so, it allows for various extensions to the standard flat $\Lambda$CDM model. In this new release, we have support for the following: 1) dynamical dark energy parametrizations with a constant or time-dependent equation of state; 2) a consistent implementation of anisotropic shear to model massive neutrinos throughout the full formalism; 3) multiple commonly-used parametrizations of modified growth (MG) parameters; 4) functional, binned and hybrid time- and scale-dependencies for all MG parameters; 5) spatially flat or curved backgrounds. ISiTGR is designed to allow cosmological analyses to take full advantage of ongoing and future surveys to test simultaneously or separately various extensions to the standard model. We describe here the formalism and its implementation in the CMB code, the Integrated Sachs-Wolfe (ISW) effect, and the 3x2 point statistics. Next, we apply ISiTGR to current data sets from Planck-2018, Planck-2015, Dark Energy Survey YR1 release, Baryonic Acoustic Oscillations (BAO), Redshift Space Distortions (BAO/RSD) from the BOSS Data Release 12, the 6DF Galaxy Survey and the SDSS Data Release 7 Main Galaxy Sample, and Supernova from the Pantheon compilation, joint SNLS/SDSS data analysis and the Hubble Space Telescope. We derive constraints on MG parameters for various combinations of the five features above and find that GR is consistent with current data sets in all cases. The code is made publicly available at \url{https://github.com/mishakb/ISiTGR}.

Effects of dark energy perturbations on cosmological tests of general relativity

Cosmological tests to distinguish between dark energy (DE) and modifications to gravity are a promising route to obtain clues on the origin of cosmic acceleration. We study here the robustness of these tests to the presence of DE density, velocity, and anisotropic stress perturbations. We find that the dispersion in the growth index parameter remains small enough to distinguish between extreme cases of DE models and some commonly used modified gravity models. The sign of the slope parameter for a redshift-dependent growth index was found to be inconsistent as an additional test in extreme cases of DE models with perturbations. Next, we studied the effect of DE perturbations on the modified growth (MG) parameters that enter the perturbed Einstein equations. We find that while the dark energy perturbations affect the MG parameters, the deviations remain smaller than those due to modified gravity models. Additionally, the deviations due to DE perturbations with a nonzero effective sound speed occur at scale ranges that are completely different than those due to some modified gravity models such as the $f(R)$ models. In the case of modified gravity models with zero anisotropic stress at late times, the simultaneous determination of the effective dark energy equation of state and the MG parameters can provide the distinction between these models and DE. The growth index test was found to be the most robust to these perturbations. The scale dependence of the MG parameters in some cases of modified gravity constitutes a clear-cut discriminant regardless of any DE perturbations. In summary, we find that the currently proposed cosmological tests to distinguish between DE and modified gravity are robust to DE perturbations even for extreme cases. This is certainly the case even for DE models with equations of state of DE that fall well outside of current cosmological constraints.

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 $\Lambda$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 $\Omega_k$ and the constraints on the MG parameters are weakened compared to when $\Omega_k$ is not included in the parameter analysis. We next use various future simulated data sets, including cosmic microwave background, weak lensing, and Integrated Sachs-Wolfe-galaxy cross-correlations, where the fiducial model is spatially curved but we assume a flat model when fitting the MG parameters. We find the assumption of a spatially flat model on a spatially curved universe does indeed cause an artificial shift in the constraints on the MG parameters, in some cases even producing an apparent deviation from GR in the MG parameter space. For our simulated data, tension with GR begins to manifest itself for fiducial models with $\abs{\Omega_k} \geq 0.02$ and apparent deviations appear for $\abs{\Omega_k} \geq 0.05$. We find that for negatively curved models the apparent deviation is more significant. The manifestation of this apparent deviation from GR due to the assumption of spatial flatness above leads one to conclude that, when using future high-precision data to perform these tests, spatial curvature must be included in the parameter analysis along with the other core cosmological parameters and the MG parameters.