# σ_{8} Tension. Is Gravity Getting Weaker at Low z? Observational Evidence and Theoretical Implications

Published in *Springer*, 2019

# Abstract

Dynamical observational probes of the growth of density perturbations indicate that gravity may be getting weaker at low redshifts z. This evidence is at about 2-3σ level and comes mainly from weak lensing data that measure the parameter and redshift space distortion data that measure the growth rate times the amplitude of the linear power spectrum parameter fσ_{8}(z). The measured fσ_{8}(z) appears to be lower than the prediction of General Relativity (GR) in the context of the standard ΛCDM model as defined by the Planck best fit parameter values. This is the well known fσ_{8} tension of ΛCDM, which constitutes one of the two main large scale challenges of the model along with the H_{0} tension. We review the observational evidence that leads to the fσ_{8} tension and discuss some theoretical implications. If this tension is not a systematic effect it may be an early hint of modified gravity with an evolving effective Newton’s constant G_{eff} and gravitational slip parameter η. We discuss such best fit parametrizations of G_{eff} and point out that they can not be reproduced by simple scalar-tensor and f(R) modified gravity theories because these theories generically predict stronger gravity than General Relativity (GR) at low z in the context of a ΛCDM background H(z). Finally, we show weak evidence for an evolving reduced absolute magnitude of the SnIa of the Pantheon dataset at low redshifts () which may also be explained by a reduced strength of gravity and may help resolve the H_{0} tension.

# Instructions

- Install the MGCAMB and MGCOSMOMC packages as it is decribed in the official repositories.
- Substitute the appropriate files with the corresponding ones inside the folders MGCAMB-eff_newt_const and MGCosmoMC-eff_newt_const
- Run on your terminal:
`make clean`

and`make`

which compile the MGCAMB and MGCOSMOMC packages. Wait until everything is finished. After that you are good to go!

# Cite

If you use any of the above codes or the figures in a published work please cite the following paper: *σ _{8} Tension. Is Gravity Getting Weaker at Low z? Observational Evidence and Theoretical Implications*

Lavrentios Kazantzidis, Leandros Perivolaropoulos

10.1007/978-3-030-83715-033, arxiv:1907.03176, as well as the appropriate papers described in the offficial MGCAMB and MGCOSMOMC repositories.

Any further questions/comments are welcome.

# Authors Lists

Lavrentios Kazantzidis - l.c.kazantzidis@gmail.com

Leandros Perivolaropoulos - leandros@uoi.gr