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

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 $\Lambda$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 $\Sigma m_\nu$. We find that the model typically prefers higher $H_0$ than $\Lambda$CDM, alleviating the $H_0$ tension, while its boosted growth tends to increase clustering amplitudes unless offset by larger neutrino masses when $\Sigma m_\nu$ is free. Overall, CMB-only data provide at most weak statistical support compared to $\Lambda$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.