A search for an N=2 inflaton potential

We consider equation image supergravity theories that have the same spectrum as the R + R2 supergravity, as predicted from the off-shell counting of degrees of freedom. These theories describe standard equation image supergravity coupled to one or two long massive vector multiplets. The central charge is not gauged in these models and they have a Minkowski vacuum with equation image unbroken supersymmetry. The gauge symmetry, being non-compact, is always broken. α-deformed inflaton potentials are obtained, in the case of a single massive vector multiplet, with α = 1/3 and 2/3. The α = 1 potential (i.e. the Starobinsky potential) is also obtained, but only at the prize of having a single massive vector and a residual unbroken gauge symmetry. The inflaton corresponds to one of the Cartan fields of the non-compact quaternionic-Kähler cosets.