Linear Nash-Greene fluctuations on the evolution of $$S_8$$ and $$H_0$$ tensions

Abstract

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 $$H_0$$ H 0 and the growth amplitude factor $$S_8$$ S 8 of the observations from Planck 2018 Cosmic Microwave Background (CMB) and the local measurements of $$H_0$$ H 0 with Hubble Space Telescope (HST) photometry and Gaia EDR3. As a result, we obtain an alleviation below $$\sim 1\sigma $$ ∼ 1 σ in the contours ($$S_8$$ S 8 -$$\varOmega _m$$ Ω m ) at $$68.4\%$$ 68.4 % confidence level (CL) when compared with DESY1 data. On the other hand, the $$H_0$$ H 0 tension persists with $$\sim 2.6\sigma $$ ∼ 2.6 σ at $$68.4\%$$ 68.4 % CL and $$1.95\sigma $$ 1.95 σ at $$95.7\%$$ 95.7 % CL, aggravated with the inclusion of BAO data.

Effective Potential for Quintessential Inflation Driven by Extrinsic Gravity

“…Detailed demonstrations of the fundamental field equations, from a bulk of five or in arbitrary dimensions, can be found in Refs. [26][27][28]31,40]. In this work, in search of constructing a viable physical model, we consider the extrinsic curvature as a main character of cosmic dynamics.…”

“…The semicolon sign in Equation ( 8) represents the ordinary covariant derivative with respect to the metric g µν and k α[β;γ] ≡ k αβ;γ − k αγ;β . The importance of Equations ( 7) and ( 8) is that they reflect the integrability conditions for the embedding explicitly relating the bulk and embedded space, and they are the starting point to obtain the induced field equations [26][27][28]31,40].…”

“…Such potential was also studied in the context of M-theory [63] and RSII scenarios [64]. Due to the strong constraints on PLI, based on Equation (40), our numerical study will take an effective quintessential dimensionless potential V(φ) e f f to generalize Equation ( 40), such as…”

“…In this paper, we make the first steps to answer this question in the context of a modification of gravity by extra dimensions. Apart from traditional models, such as the Arkani-Hamed-Dvali-Dimopoulos (ADD) model [21], the Randall-Sundrum model [22,23], and/or the Dvali-Gabadadze-Porrati model (DPG) [24], we explore the dynamical embedding of space-times as the main mathematical structure [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. In Encyclopaedia Inflationaris [41], the reader can find various types and classifications of inflationary models, such as supergravity brane inflation, supersymmetry (SUSY), and brane inflation models.…”

“…The paper is organized into sections. The second and third sections summarize the essentials of previously published results on the construction of the four-dimensional embedded model and cosmological applications [26][27][28]31,39,40]. The fourth section presents the fluid analogy necessary to make a comparison with phenomenological models.…”