Linear Nash-Greene fluctuations on the evolution of [Formula omitted] and [Formula omitted] tensions

• Published in: The European physical journal. C, Particles and fields Vol. 82; no. 5
• Main Authors: Capistrano, Abraão J. S, Cabral, Luís A, Marão, José A. P. F, Coimbra-Araújo, Carlos H
• Format: Journal Article
• Language: English
• Published: Springer 27.05.2022
• Subjects: Analysis; Cosmic background radiation; Force and energy; Markov processes; Monte Carlo method; Specific gravity; Telescope
• ISSN: 1434-6044
• DOI: 10.1140/epjc/s10052-022-10431-9

We present the perturbation equations in an embedded four space-time from the linear Nash-Greene fluctuations of background metric. In the context of a five-dimensional bulk, we show that the cosmological perturbations are only propagated by the gravitational tensorial field equation. In Newtonian conformal gauge, we study the matter density evolution in sub-horizon regime and on how such scale may be affected by the extrinsic curvature. We apply a joint likelihood analysis to the data by means of the Markov Chain Monte Carlo (MCMC) method for parameter estimation using a pack of recent datasets as the Pantheon Supernovae type Ia, the Baryon Acoustic Oscillations (BAO) from DR12 galaxy sample and Dark Energy Survey (DESY1). We discuss the tensions on the Hubble constant [Formula omitted] and the growth amplitude factor [Formula omitted] of the observations from Planck 2018 Cosmic Microwave Background (CMB) and the local measurements of [Formula omitted] with Hubble Space Telescope (HST) photometry and Gaia EDR3. As a result, we obtain an alleviation below [Formula omitted] in the contours ( [Formula omitted]- [Formula omitted]) at [Formula omitted] confidence level (CL) when compared with DESY1 data. On the other hand, the [Formula omitted] tension persists with [Formula omitted] at [Formula omitted] CL and [Formula omitted] at [Formula omitted] CL, aggravated with the inclusion of BAO data.