  We analyze, analytically and numerically, a periodically driven Rashba
nanowire proximity coupled to an $s$-wave superconductor using bosonization and
renormalization group analysis in the regime of strong electron-electron
interactions. Due to the repulsive interactions, the superconducting gap is
suppressed, whereas the Floquet Zeeman gap is enhanced, resulting in a higher
effective value of $g$-factor compared to the non-interacting case. The flow
equations for different coupling constants, velocities, and Luttinger-liquid
parameters explicitly establish that even for small initial values of the
Floquet Zeeman gap compared to the superconducting proximity gap, the
interactions drive the system into the topological phase and the interband
interaction term helps to achieve larger regions of the topological phase in
parameter space.
