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

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