Constraints on \(\sigma_8\) Degeneracies from Linear Nash-Greene Perturbations in Subhorizon Scale

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.