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Geometric acceleration in $f(Q,C)$ theories

Mikel Artola, Ismael Ayuso, Ruth Lazkoz, Gonzalo Olmo, Vincenzo Salzano

TL;DR

This work investigates f(Q,C) gravity within Connection I to realize late-time acceleration purely from spacetime geometry, while maintaining second-order field equations. A generic ansatz f(Q,C) = Q + α C / g(Q) yields a geometric dark-energy source, and the authors analyze simple square-root and power-law deformations as well as a DGP-like damping deformation that regularizes the original DGP pathologies. They demonstrate a background-level mapping to f(Q) theories and perform a Bayesian observational test against BAO, CC, CMB, and SNeIa data, finding the DGP-like model to be competitive with ΛCDM and capable of fitting current cosmological observations with a modest preference in some parameter regions. The results highlight non-metricity and its boundary term as viable geometric drivers of cosmic acceleration, offering a promising extension to GR with testable predictions for the expansion history and dark-energy dynamics.

Abstract

The $f(Q,C)$ framework of gravity enables the depiction of an effective dark energy fluid that emerges from geometry itself, thus leading to modifications in the cosmological phenomenology of General Relativity. We pursue this approach to discover new and observationally supported (effective) evolving dark energy models. We propose a general $f(Q,C)$ formulation that cannot be simply split into separate functions of $Q$ and $C$, yet it still results in second-order field equations. By employing a particular type of connection, we derive guidelines for new cosmological models, including a variant of the DGP model that appears to be statistically favored over $Λ$CDM. Notably, we also demonstrate how to translate solutions within this $f(Q,C)$ framework to $f(Q)$ counterparts at the background level.

Geometric acceleration in $f(Q,C)$ theories

TL;DR

This work investigates f(Q,C) gravity within Connection I to realize late-time acceleration purely from spacetime geometry, while maintaining second-order field equations. A generic ansatz f(Q,C) = Q + α C / g(Q) yields a geometric dark-energy source, and the authors analyze simple square-root and power-law deformations as well as a DGP-like damping deformation that regularizes the original DGP pathologies. They demonstrate a background-level mapping to f(Q) theories and perform a Bayesian observational test against BAO, CC, CMB, and SNeIa data, finding the DGP-like model to be competitive with ΛCDM and capable of fitting current cosmological observations with a modest preference in some parameter regions. The results highlight non-metricity and its boundary term as viable geometric drivers of cosmic acceleration, offering a promising extension to GR with testable predictions for the expansion history and dark-energy dynamics.

Abstract

The framework of gravity enables the depiction of an effective dark energy fluid that emerges from geometry itself, thus leading to modifications in the cosmological phenomenology of General Relativity. We pursue this approach to discover new and observationally supported (effective) evolving dark energy models. We propose a general formulation that cannot be simply split into separate functions of and , yet it still results in second-order field equations. By employing a particular type of connection, we derive guidelines for new cosmological models, including a variant of the DGP model that appears to be statistically favored over CDM. Notably, we also demonstrate how to translate solutions within this framework to counterparts at the background level.

Paper Structure

This paper contains 18 sections, 20 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. f(Q,C) gravity
  3. Generic model setup
  4. Preliminary cases
  5. Simple square root case
  6. Power-law case
  7. DGP-like deformation
  8. High-curvature regime
  9. Low-curvature regime
  10. Brief summary
  11. Observational analysis
  12. Datasets
  13. BAO
  14. CC
  15. CMB
  16. ...and 3 more sections

Figures (1)

  • Figure 1: Effective equation of state parameter associated to the geometric corrections of the damped DGP model. The solid line represents the median at each value of the scale factor, whereas the shaded regions encompass the $68\%$ and $95\%$ confidence regions; the black dashed lines indicate the cosmological constant equation of state, $w_\Lambda = -1$.