Constraints on sigma _8 and degeneracies from linear Nash-Greene perturbations in subhorizon scale

Abstract

Using a joint statistical analysis, we test a four-dimensional FLRW 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 growth data, the best-fit Planck2018/varLambda CDM parameters on the Cosmic Microwave Background (CMB), the Baryon Acoustic Oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the Hubble parameter data. From linear Nash-Greene fluctuations of the metric, we show the related perturbed equations in longitudinal Newtonian gauge to obtain the evolution of growth matter. A mild alleviation may be obtained from the degeneracies on the model parameter analyzing the sigma tension between the growth amplitude factor and the matter content in the plane (sigma _8-varOmega _m) on the observations from CMB and Large Scale Structure (LSS) probes. The Akaike Information Criterion (AIC) is also applied and we find a relative statistical consistence of the present model with both varLambda CDM and wCDM models lower than 1% of percentage difference at early times on the evolution of the Hubble function H(z). We also apply the Om(z) diagnosis to distinguish the present model from varLambda CDM and wCDM models.