Cosmological Tensions as Consistency Conditions for f(Q) Gravity

Abstract

Cosmology has entered a precision era in which discrepancies between independent datasets, most notably the $H_0$ and $S_8$ tensions, have become robust and statistically significant. These tensions are no longer isolated anomalies but increasingly appear as global consistency constraints on the underlying cosmological model, defining what we will refer to here as a \emph{consistency triangle} of background expansion ($H_0$), structure-growth amplitude ($S_8$), and the redshift-dependence of growth - summarised by the growth index $\gamma$, or equivalently the shape of $f\sigma_8(z)$. The third vertex is non-trivial because in modified-gravity scenarios with a redshift-dependent effective gravitational coupling, growth amplitude and growth shape evolve independently, breaking the rigid coupling characteristic of $\Lambda$CDM. In this work, we use $f(Q)$ gravity as a test case for this emerging paradigm. By drawing on a focused set of recent Bayesian and dynamical-system analyses of the three best-studied functional families - power-law, exponential, and logarithmic - we show that while $f(Q)$ models can alleviate individual tensions, the requirement of simultaneous consistency across $H_0$, $S_8$ and the growth index severely restricts the viable parameter space. A bulk-viscous extension is then briefly examined as a representative illustration of how additional matter-sector freedom is constrained by the same consistency requirement. Our reading of the current literature supports the view that cosmological tensions should be interpreted as global consistency conditions, and that viable extensions of $\Lambda$CDM must satisfy this multi-probe constraint \cite{CosmoVerse,DiValentino2025Corfu}. Within this framework, only a restricted subset of $f(Q)$ models remains competitive.