Four-dimensional N=1 F[R] supergravity

We propose a supersymmetric generalization of f[R] gravity, calling it F[R] supergravity. We adopt the so-called unimodular supergravity (UMSG). We first give an explicitly invariant Lagrangian Linv≡LSG+LH in dimensions 2⩽D∀⩽11, where LH is linear in the D-form field strength H=dC, while LSG is the ordinary supergravity Lagrangian. We then establish the total Lagrangian Ltot≡eF[e−1Linv]+LC, with the constraint term LC for the UMSG formulation. As an explicit example, we study N=1 supergravity in four dimensions (4D). We show that the solutions to the field equations for conventional LSG satisfy the field equation of the new system with Ltot. Since the function F[e−1Linv] is an arbitrary (non)polynomial function of e−1Linv, there can be many other solutions, including those for non-supersymmetric f[R] gravity.