Pathological Character of Modifications to Coincident General Relativity: Cosmological Strong Coupling and Ghosts in $f\left(Q\right)$ Theories

The intrinsic presence of ghosts in the symmetric teleparallel framework is elucidated. We illustrate our general arguments in $f\left(Q\right)$ theories by studying perturbations in the three inequivalent spatially flat cosmologies. Two of these branches exhibit reduced linear spectra, signalling they are infinitely strongly coupled. For the remaining branch we unveil the presence of seven gravitational degrees of freedom and show that at least one of them is a ghost. Our results rule out $f\left(Q\right)$ cosmologies and clarify the number of propagating degrees of freedom in these theories.