All Off-Shell R² Invariants in Five Dimensional N=2 Supergravity

We construct supersymmetric completions of various curvature squared terms in five dimensional supergravity with eight supercharges. Adopting the dilaton Weyl multiplet, we obtain the minimal off-shell supersymmetric Ricci scalar squared as well as all vector multiplets coupled curvature squared invariants. Since the minimal off-shell supersymmetric Riemann tensor squared and Gauss-Bonnet combination in the dilaton Weyl multiplet have been obtained before, both the minimal off-shell and the vector multiplets coupled curvature squared invariants in the dilation Weyl multiplet are complete. We also constructed an off-shell Ricci scalar squared invariant utilizing the standard Weyl multiplet. The supersymmetric Ricci scalar squared in the standard Weyl multiplet is coupled to n number of vector multiplets by construction, and it deforms the very special geometry. We found that in the supersymmetric AdS_5 vacuum, the very special geometry defined on the moduli space is modified in a simple way. Finally, we study the magnetic string and electric black hole solutions in the presence of supersymmetric Ricci scalar squared.