  We consider a model for a one-dimensional quantum wire with Rashba spin-orbit
coupling and repulsive interactions, proximity coupled to a conventional s-wave
superconductor. Using a combination of Hartree-Fock and density matrix
renormalization group calculations, we show that for sufficiently strong
interactions in the wire, a time-reversal invariant topological superconducting
phase can be stabilized in the absence of an external magnetic field. This
phase supports two zero-energy Majorana bound states at each end, which are
protected by time-reversal symmetry. The mechanism for the formation of this
phase is a reversal of the sign of the effective pair potential in the wire,
due to the repulsive interactions. We calculate the differential conductance
into the wire and its dependence on an applied magnetic field using the
scattering-matrix formalism. The behavior of the zero-bias anomaly as a
function of the field direction can serve as a distinct experimental signature
of the topological phase.
