f(Q) gravity is an extension of the symmetric teleparallel equivalent to general relativity (STEGR). This work shows that based on the scalar-nonmetricity formulation, a scalar mode in f(Q) gravity has a negative kinetic energy. This conclusion holds regardless of the coincident gauge frequently used in STEGR and f(Q) gravity. To study the scalar mode, we further consider the covariant f(Q) gravity as a special class in higher-order scalar tensor (HOST) theory and rewrite the four scalar fields, which play a role of the Stueckelberg fields associated with the diffeomorphism, by vector fields. ...
