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

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.

10 pages, 8 figures, 3 tables

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