Probing dynamical embeddings in a five-dimensional spacetime in light of DESI BAO

TL;DR

Nash gravity explores a geometrical extension of GR by embedding 4D spacetime into a 5D bulk with dynamical extrinsic curvature, introducing a scale-dependent effective gravity $G_{ m eff}(a)=G/[1-eta_0 a^{1-3w_0}]$ and an extrinsic-fluid component that modifies both background expansion and linear perturbations. The framework yields ghost-free scalar perturbations purely from geometry and is implemented in CLASS, then constrained with Planck 2018 CMB, DESI-DR2 BAO, and multiple SN Ia compilations. Results show Nash gravity provides a good fit and can modestly raise $H_0$ to about $69.3$ km s$^{-1}$ Mpc$^{-1}$ while suppressing $S_8$ to around $0.76$, with parameter degeneracies linking $w_0$, $eta_0$, and $H_0$; in several joint analyses the model is statistically competitive or preferred when including certain SN Ia data, though information criteria temper overall model preference. Overall, Nash gravity offers a physically motivated, statistically viable extension to ΛCDM that can alleviate both $H_0$ and $S_8$ tensions and motivates further tests of gravity beyond GR.

Abstract

We here investigate the observational viability of Nash gravity as an alternative to the standard $Λ$CDM cosmology. Based on Nash's embedding theorem, the model introduces orthogonal perturbations via variations in the extrinsic curvature, generating scalar-type metric perturbations directly from geometry, without the need to introduce additional fields. We confront the model with current observational data, including Cosmic Microwave Background (CMB) measurements from Planck, Baryon Acoustic Oscillations (BAO) from DESI DR2, and recent Type Ia supernova (SN Ia) compilations. Our analysis shows that Nash gravity provides a good fit to the data, yielding a slightly higher value for the Hubble constant, $H_0 = 69.32 \pm 0.72$ km/s/Mpc, compared to the $Λ$CDM model, thus offering a potential alleviation of the $H_0$ tension. Furthermore, the model naturally predicts a suppressed growth of structure, with $S_8 \approx 0.76$ across various joint analyses, potentially alleviating the so-called $S_8$ tension, assuming that this discrepancy is not solely due to systematic effects in other independent measurements. In some cases, Nash gravity achieves a better fit to the data than the $Λ$CDM paradigm at the $2σ$ level.

Figures (2)

• Figure 1: Marginalized posterior distributions and 68% and 95% CL contours for the parameters in the model. The results are shown for different combinations of datasets, as indicated in the legend.
• Figure 2: Left panel: Statistical reconstruction of the (rescaled) expansion rate of the universe, $H(z)/(1+z)$, at $2\sigma$ confidence levels for the $\Lambda$CDM and NASH models, based on the joint analysis of CMB+DESI-DR2, compared to DESI-DR2 measurements. Right panel: Comparison between the theoretical predictions of the $\Lambda$CDM and NASH models for the temperature anisotropy power spectrum. All cosmological parameters are fixed to their respective best-fit values obtained from the joint analysis of CMB + DESI-DR2 + DESY5 data. The error bars on the data points indicate $\pm 1\sigma$ uncertainties. The lower panel displays the relative deviation between the NASH and $\Lambda$CDM predictions.