Tension of the EG statistic and redshift space distortion data with the Planck - ΛCDM model and implications for weakening gravity

Abstract

The EG statistic is a powerful probe for detecting deviations from GR by combining weak lensing (WL), real-space clustering and redshift space distortion (RSD) measurements thus probing both the lensing and the growth effective Newton constants (GL and G ef f ). We construct an up to date compilation of EG statistic data including both redshift and scale dependence (EG(R, z)). We combine this EG data compilation with an up to date compilation of f σ8 data from RSD observations to identify the current level of tension between the Planck/ΛCDM standard model based on general relativity and a general model independent redshift evolution parametrization of GL and G ef f . Each f σ8 datapoint considered has been published separately in the context of independent analyses of distinct galaxy samples. However, there are correlations among the datapoints considered due to overlap of the analyzed galaxy samples. Due to these correlations the derived levels of tension of the best fit parameters with Planck/ΛCDM are somewhat overestimated but this is the price to pay for maximizing the information encoded in the compilation considered. We find that the level of tension increases from about 3.5σ for the f σ8 data compilation alone to about 6σ when the EG data are also included in the analysis. The direction of the tension is the same as implied by the f σ8 RSD growth data alone (lower Ωm and/or weaker effective Newton constant at low redshifts for both the lensing and the growth effective Newton constants (GL and G ef f )). These results further amplify the hints for weakening modified gravity discussed in other recent analyses [1][2][3][4].

Cosmological framework for renormalization group extended gravity at the action level

“…We did this with the modified gravity parametrizations evaluated in the previous subsections, which lead to bounds, but no explicit links towards solving some of the current CDM anomalies. Although it is beyond the purpose of this work to do a complete cosmological analysis, we consider here f σ 8 data, which have shown discrepancies at low redshift (z 2) (e.g., [60][61][62]) with the CDM parameters as inferred from the Planck collaboration [55].…”

“…With respect to the scale factor a and using the physical time Hubble parameter H , Eq. (96) can be written as [62] (see also [63,64])…”

“…(97) numerically, it is important to know the initial conditions. Considering standard CDM background, at z ∼ 10 3 the universe is dominated by dust, hence using initial conditions at this z from the dust-only solution (77) should work as a good approximation in the CDM context (i.e., ν = 0, see e.g., [62]). In order to better evaluate the impact of such approximation to the model under consideration (ν = 0), we also consider imposing initial conditions and using Eq.…”

“…The mode proportional to C 1 will eventually dominate over the one proportional to C 2 , hence we only consider the C 1 mode (which, apart from the case ν −1, it is an increasing mode, while C 2 is the coefficient of a decreasing mode). Neglecting the decreasing mode is commonly done (e.g., [62]) since it simplifies considerably the issue of initial conditions while the approximation is a very good one: indeed, at z ∼ 100 one is deep in the matter dominated phase, thus providing sufficient time for the decreasing mode to be negligible.…”

The growth factor parametrization versus numerical solutions in flat and non-flat dark energy models

“…Later, this parametrization was reintroduced into the paradigm of the accelerated expansion of the Universe by Wang and Steinhartd [17], and this idea was expanded by Linder [18][19][20], among others. Recently, this approach has been widely used to discriminate between modifying gravity models versus dark energy models, see references [21][22][23][24][25][26][27].…”