Sub-horizon modes and growth index in a linear scalar cosmological perturbations

Abstract

We test a four dimensional cosmological model embedded in a five dimensional bulk space by means of the dynamical Nash-Greene theorem. In a fluid approach, we apply a joint likelihood analysis to the data with the Markov Chain Monte Carlo (MCMC) method for cosmological parameter estimation. We use recent datasets as the “Gold 2018” growth-rate data, the Planck2018/$$\varLambda $$ Λ CDM data on the cosmic microwave background (CMB) anisotropies, the Baryon acoustic oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the data on the Hubble parameter H(z) with redshift ranging from $$0.01< z < 2.3$$ 0.01 < z < 2.3 . Performing the Information Criterion (IC) analysis, we find that the present model is in very good agreement with observations with a close statistical equivalence with wCDM cosmologies at 1-$$\sigma $$ σ level with a slightly larger growth profiles. By modifications of () code, we make a comparison between the models on their unlensed CMB TT temperature spectra. Moreover, the proposed model presents a low power spectrum by the reduction of the ISW effect at lower multipoles. We also find that the overall percentage relative difference of the growth index $$\varDelta \gamma (\%)$$ Δ γ ( % ) is up to 1.4$$\%$$ % as compared to wCDM pattern in sub-horizon scales.