Extensions of two-field mimetic gravity

Two-field mimetic gravity was recently realized by looking at the singular limit of the conformal transformation between the auxiliary metric and the physical metric with two scalar fields involved. In this paper, we reanalyze the singular conformal limit and find a more general solution for the conformal factor A, which greatly broadens the form of two-field mimetic constraint and thus extends the two-field mimetic gravity. We find the general setup still mimics the roles of dark matter at the cosmological background level. Moreover, we extend the action by introducing extra possible term for phenomenological interests. Surprisingly, some special cases are found to be equivalent to general relativity, k-essence theory and Galileon theory. Finally, we further extend the theory by allowing the expression of mimetic constraint to be arbitrary without imposed condition, and show that the dark matter-like behavior is unaffected even in this extension.