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Einstein-Cartan cosmology and the S8 problem

Davor Palle

TL;DR

The paper addresses the $S_{8}$ tension by adopting Einstein-Cartan cosmology with torsion generated by spin densities in a noncontractible space, avoiding inflaton-related solutions. It derives gauge-invariant linear perturbation equations for a Weyssenhoff fluid and compares EC to LCDM by computing the evolution of $\\sigma_{8}(z)$, finding that EC yields larger clustering amplitudes at high redshift. The key result is that $\\sigma_{8}(z)$ grows more rapidly in EC, driven by torsion and higher early mass density, with minimal sensitivity to the acceleration parameter $\\lambda$. These findings motivate further N-body simulations of EC dynamics and predict observable signatures such as distinct redshift-drift histories, offering a torsion-based mechanism to mitigate the $S_{8}$ tension.

Abstract

The measurements of cluster abundances, gravitational lensings, redshift space distortions and peculiar velocities at lower redshifts point out to much smaller sigma_8 than its value deduced from the measurements of the CMB fluctuations assuming the standard LCDM cosmology. High redshift measurements of ALMA and JWST imply even more striking problems for LCDM. We examine and compare the sigma_8 redshift dependence calculated within the gauge invariant formalism. Because the CMB fluctuations comprise a cosmological data from the recombination era to the present, the S_8 problem of the LCDM cosmology is not a surprise from the standpoint of the Einstein-Cartan cosmology because it predicts much larger mass density and sigma_8(z) than the LCDM model at high redshifts.

Einstein-Cartan cosmology and the S8 problem

TL;DR

The paper addresses the tension by adopting Einstein-Cartan cosmology with torsion generated by spin densities in a noncontractible space, avoiding inflaton-related solutions. It derives gauge-invariant linear perturbation equations for a Weyssenhoff fluid and compares EC to LCDM by computing the evolution of , finding that EC yields larger clustering amplitudes at high redshift. The key result is that grows more rapidly in EC, driven by torsion and higher early mass density, with minimal sensitivity to the acceleration parameter . These findings motivate further N-body simulations of EC dynamics and predict observable signatures such as distinct redshift-drift histories, offering a torsion-based mechanism to mitigate the tension.

Abstract

The measurements of cluster abundances, gravitational lensings, redshift space distortions and peculiar velocities at lower redshifts point out to much smaller sigma_8 than its value deduced from the measurements of the CMB fluctuations assuming the standard LCDM cosmology. High redshift measurements of ALMA and JWST imply even more striking problems for LCDM. We examine and compare the sigma_8 redshift dependence calculated within the gauge invariant formalism. Because the CMB fluctuations comprise a cosmological data from the recombination era to the present, the S_8 problem of the LCDM cosmology is not a surprise from the standpoint of the Einstein-Cartan cosmology because it predicts much larger mass density and sigma_8(z) than the LCDM model at high redshifts.

Paper Structure

This paper contains 4 sections, 35 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction and motivation
  2. Resume of the theoretical setup in Minkowski and Riemann-Cartan spacetimes
  3. Derivation of perturbation equations
  4. Results and discussion

Figures (5)

  • Figure 1: Model of torsion $\bar{Q}$(z) used in numerical evaluations.
  • Figure 2: Age of the Universe for the EC (solid line) and LCDM (dotted line) models.
  • Figure 3: Redshift drifts for the EC (solid line) and LCDM (dotted line) models in the unit $100 km s^{-1} Mpc^{-1}$.
  • Figure 4: $\sigma_{8}(z)/\sigma_{8}(z=0)$ for the EC (solid line) and LCDM (dotted line) models.
  • Figure 5: $\lambda$(y) for initial $\lambda(R=10^{-8})=10^{-2}$.