Supersymmetric Models For Gauge Inflation

We present possible realizations of gauge inflation arising from a 5D ${\cal N}=1$ supersymmetric U(1) model, where the extra dimension is compactified on a circle. A one-loop inflaton effective 4D potential is generated, with the inflaton being a 'Wilson-line field'. It relies on a SUSY breaking. We first consider SUSY breaking to occur spontaneously within a 'no-scale' model by a non zero $F$-term of the radion superfield which transmits SUSY breaking into the 'visible' sector. As an alternative, we study $D$-term SUSY breaking originating directly from the 5D gauge supermultiplet. Together with the usual KK resummation method, we present a calculation with the world-line formalism. The latter allows one to get the resulting effective potential directly as a sum over all winding modes. For both presented scenarios, the generated effective potentials have suitable forms for realizing successful inflation, i.e. are flat enough and give the needed number of ${\rm e}$-foldings. In addition, there is a natural way to get strongly suppressed values for the potentials, which then could be associated with dark energy/quintessence.