[en] The cosmological realization of the spontaneous breaking of B-L, the difference of baryon and lepton number, can generate the initial conditions for the hot early universe. In particular, we show that entropy, dark matter and a matter-antimatter asymmetry can be produced in accordance with current observations. If B-L is broken at the grand unification scale, F-term hybrid inflation can be realized in the false vacuum of unbroken B-L. The phase transition at the end of inflation, governed by tachyonic preheating, spontaneously breaks the U(1)_B-L symmetry and sets the initial conditions for the following perturbative reheating phase. We provide a detailed, time-resolved picture of the reheating process. The competition of cosmic expansion and entropy production leads to an intermediate plateau of constant temperature, which controls both the generated lepton asymmetry and the dark matter abundance. This enables us to establish relations between the neutrino and superparticle mass spectrum, rendering this mechanism testable. Moreover, we calculate the entire gravitational wave spectrum for this setup. This yields a promising possibility to probe cosmological B - L breaking with forthcoming gravitational wave detectors such as eLISA, advanced LIGO and BBO/DECIGO. The largest contribution is obtained from cosmic strings which is, for typical parameter values, at least eight orders of magnitude higher then the contribution from inflation. Finally, we study the possibility of realizing hybrid inflation in a superconformal framework. We find that superconformal D-term inflation is an interesting possibility generically leading to a two-field inflation model, but in its simplest version disfavoured by the recently published Planck data.