Working Paper Article Version 3 This version is not peer-reviewed

# Constraints on $\sigma_8$ Degeneracies from Linear Nash-Greene Perturbations in Subhorizon Scale

Version 1 : Received: 7 May 2019 / Approved: 8 May 2019 / Online: 8 May 2019 (11:39:29 CEST)
Version 2 : Received: 22 August 2019 / Approved: 22 August 2019 / Online: 22 August 2019 (10:27:49 CEST)
Version 3 : Received: 19 June 2020 / Approved: 19 June 2020 / Online: 19 June 2020 (08:38:18 CEST)

How to cite: Capistrano, A. Constraints on $\sigma_8$ Degeneracies from Linear Nash-Greene Perturbations in Subhorizon Scale. Preprints 2019, 2019050097 Capistrano, A. Constraints on $\sigma_8$ Degeneracies from Linear Nash-Greene Perturbations in Subhorizon Scale. Preprints 2019, 2019050097

## Abstract

Using a joint statistical analysis, we test a four-dimensional FLWR model embedded in a five-dimensional bulk based on the Nash-Greene embedding theorem. Performing a Markov Chain Monte Carlo (MCMC) modelling, we combine observational data sets as those of the recent Gold 2018'' growth data, the best-fit Planck2018/$\Lambda$CDM parameters on the Cosmic Microwave Background (CMB), the Baryon Acoustic Oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the Hubble parameter data with redshift ranging from $0.01 < z < 2.3$ to impose restrictions on the model. From linear Nash-Green fluctuations of the metric, we obtain the related perturbed equations in longitudinal Newtonian gauge to obtain the evolution of growth matter. We show that a mild alleviation is obtained from the $\sigma$ tension between the growth amplitude factor and the matter content $(\sigma_8$-$\Omega_m)$ of the observations from CMB and Large Scale Structure (LSS) probes with degeneracies on the parameters. We also apply the Om(z) diagnosis to distinguish the model from $\Lambda$CDM. The Akaike Information Criterion (AIC) is used and we find a relative statistical consistence of the present model with both $\Lambda$CDM and $w$CDM models up to 1$\%$ of percentage difference at early times.

## Keywords

modified Friedman equations; modified gravity; dark energy

## Subject

PHYSICAL SCIENCES, Astronomy & Astrophysics

Comment 1
Commenter: Abraao Capistrano
Commenter's Conflict of Interests: Author
Comment: New calculations and results, corrected typos and inaccuracies.
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