  We analyze the phenomenology of a prolonged early epoch of matter domination
by an unstable but very long-lived massive particle. This new matter domination
era can help to relax some of the requirements on the primordial inflation. Its
main effect is the huge entropy production produced by the decays of such
particle that can dilute any possible unwanted relic, as the gravitino in
supersymmetric models, and thus relax the constraints on the inflationary
reheating temperature. Furthermore, a long period of matter domination reduces
the number of $e$-foldings after the horizon crossing by observable
perturbations and therefore the requirements on flatness of the inflationary
potential. A natural candidate for such heavy, long-lived particle already
present in the Standard Model of the electroweak interactions would be a heavy
right-handed neutrino. In this case, we show that its decays can also generate
the observed baryon asymmetry with right-handed neutrino masses well above the
bound from gravitino overproduction.
