On Low Hubble Expansion Rate from Planck Data Anomalies

From the linear perturbations of Nash–Greene fluctuations of a background metric, we obtain profiles of Hubble function evolution $H\left(z\right)$ and $f{\sigma }_8\left(z\right)$ measurements as compared with the $\mathrm{\Lambda }$CDM results at intermediate redshifts $0.1<z<1$. For parameter estimation, we use joint data from Planck Cosmic Microwave Background (CMB) likelihoods of CMB temperature and polarization angular power spectra, Barionic Acoustic Oscillations (BAO) and local measurements of Hubble constant $H_0$ from the Hubble Space Telescope (HST). We analyze the stability of the effective Newtonian constant $G_{eff}$ and its agreement with Big Bang Nucleosynthesis (BBN) constraints. We show that our results are highly compatible with the $\mathrm{\Lambda }$CDM paradigm, rather extending the perspective for further studies on redshift-space galaxy clustering data. Moreover, we obtain the CMB TT angular spectra with the Integrated Sachs–Wolfe (ISW) effect, which is weakened on low-l scales. The resulting linear matter power spectrum $P\left(k\right)$ profile is also compatible with $\mathrm{\Lambda }$CDM results but somewhat degenerate with an early dark energy (DE) contribution. Finally, posing a dilemma to the solution of Hubble tension, our results indicate a low Hubble expansion rate suggesting possible anomalies in Planck data in consonance with the recent South Pole Telescope (SPT-3G) data.