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Inverse non-metricity in $f(Q)$ gravity: cosmology and observational constraints

Luís Atayde, Simão Marques Nunes, Noemi Frusciante

Abstract

We study a minimal modified gravity scenario in the symmetric teleparallel (non-metricity) formulation, focusing on an inverse non-metricity term with $f(Q)=Q+M^4 Q^{-1}$. The model does not introduce additional free parameters relative to $Λ$CDM, but modifies the late-time expansion and linear growth via an enhanced effective gravitational coupling. We identify key signatures: an enhanced matter power spectrum and CMB lensing, alongside a reduced late-time ISW effect and a shift in CMB peak positions. We confront the model with CMB data alone and in combination with BAO, RSD, SNIa, and DES large-scale structure data, considering both fixed minimal neutrino mass and varying $Σm_ν$. We find that the model typically prefers higher $H_0$ than $Λ$CDM, alleviating the $H_0$ tension, while its boosted growth tends to increase clustering amplitudes unless offset by larger neutrino masses when $Σm_ν$ is free. Overall, CMB-only data provide at most weak statistical support compared to $Λ$CDM, whereas late-time measurements impose tight restrictions that largely remove any improvement, positioning this model as a minimal yet strongly constrained alternative to dark energy.

Inverse non-metricity in $f(Q)$ gravity: cosmology and observational constraints

Abstract

We study a minimal modified gravity scenario in the symmetric teleparallel (non-metricity) formulation, focusing on an inverse non-metricity term with . The model does not introduce additional free parameters relative to CDM, but modifies the late-time expansion and linear growth via an enhanced effective gravitational coupling. We identify key signatures: an enhanced matter power spectrum and CMB lensing, alongside a reduced late-time ISW effect and a shift in CMB peak positions. We confront the model with CMB data alone and in combination with BAO, RSD, SNIa, and DES large-scale structure data, considering both fixed minimal neutrino mass and varying . We find that the model typically prefers higher than CDM, alleviating the tension, while its boosted growth tends to increase clustering amplitudes unless offset by larger neutrino masses when is free. Overall, CMB-only data provide at most weak statistical support compared to CDM, whereas late-time measurements impose tight restrictions that largely remove any improvement, positioning this model as a minimal yet strongly constrained alternative to dark energy.

Paper Structure

This paper contains 11 sections, 18 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. $f(Q)$-theory
  3. Background equations
  4. Linear cosmological scales
  5. The inverse non-metricity $f(Q)$ model
  6. Theoretical predictions
  7. Background evolution
  8. Effects on cosmological power spectra
  9. Data sets
  10. Cosmological constraints
  11. Conclusion

Figures (3)

  • Figure 1: Evolution of the density parameters for the inverse non-metricy $f(Q)$ model (dashed lines) and $\Lambda$CDM (solid lines) for comparison.
  • Figure 2: Top panel: CMB TT angular power spectra $D_{\ell}^{TT} = \ell(\ell+1)C_{\ell}^{TT}/(2\pi)$, middle panel: Lensing angular power spectra $D_{\ell}^{\phi \phi} = \ell^2(\ell+1)^2C_{\ell}^{\phi \phi}/(2\pi)$ and bottom panel: Matter power spectra $P(k)$ for the inverse non-metricity model and $\Lambda$CDM scenario and different values of $\Sigma m_{\nu}$. For each power spectra we present the percentage relative difference with respect to $\Lambda$CDM model.
  • Figure 3: Marginalised constraints of inverse non-metricity model and $\Lambda$CDM at 68% (darker) and 95% (lighter) C.L. on the $H_0$ and $\sigma_8^0$ obtained with the CMB data from Planck 2018 (PLK18, red), its combination with BAO, RSD and SNIa data (PBRS, green) and with DES-1Y data (PBRSD, blue).