Comparison of two theories of Type-IIa minimally modified gravity

We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theories. confirm that all acceptable solutions are always for theory. However, the inverse does not hold. find allows existence of exact General Relativity (GR) with or without presence matter fields a cosmological constant. determine conditions such GR-VCDM in terms trace extrinsic curvature on which define On other hand, theory, we same set GR (such as Schwarzschild Kerr spacetimes) is compatible timelike configurations field therefore cannot be considered solutions. Nonetheless, there could exist but close enough to also show intrinsic-VCDM solutions, i.e. differ from do belong model. finally cosmology mapping between possible, generic form potential. In particular, quadratic potential this well defined giving an effective redefinition Planck mass background both