Beyond the Cosmological Constant: Breaking the Geometric Degeneracy of $ f(Q) $ cosmology via Redshift-Space Distortions

TL;DR

This paper analyzes Hybrid $f(Q)$ cosmological models with late-time modifications, showing how growth data can break background degeneracies and provide testable signatures in large-scale structure.

Contribution

It introduces a physically bounded Hybrid $f(Q)$ model that breaks geometric degeneracy with $\\Lambda$CDM via perturbation effects, and demonstrates its testability with growth data.

Findings

Hybrid $f(Q)$ model is degenerate with $\Lambda$CDM at background level.

Perturbations induce a late-time suppression of $G_{eff}$, breaking degeneracy.

Growth data favors the Hybrid model moderately, with testable large-scale structure signatures.

Abstract

We present a rigorous theoretical and observational analysis of the Hybrid $ f(Q) $ class of models by including the late-time modifying $ 1/Q $ term. After deriving strict viability conditions from the analytical expansion history, we show that preserving early-universe structure formation dictates that the linear coupling be exactly unity. This fixes the background of the Hybrid model into a geometric degeneracy with $ \Lambda $CDM which is confirmed explicitly through MCMC analysis with the latest background-only probes. The physical novelty of this model is manifest in the perturbation sector, where the geometric coupling breaks the background degeneracy and induces a late-time suppression of the effective gravitational constant $ G_{eff} < G_N $. Consequently, the inclusion of RSD data reveals an amplitude compensation mechanism, by which the matching of the signature $ f\sigma_8 $ of the data causes the clustering amplitude $ \sigma_8 $ to inflate under weaker gravity. Statistical model comparison through AIC/DIC demonstrates that incorporating growth data yields a moderate to weak preference for the Hybrid model keeping the background cosmology intact. This provides a physically bounded alternative to $ \Lambda $CDM with a falsifiable signature in the large scale structure, directly testable by the next generation of galaxy surveys.