D-branes, topological defects in string theory on which string endpoints ca
n live, may give new insight into the understanding of the cosmological evo
lution of the Universe at early epochs. We analyze the dynamics of D-branes
in curved backgrounds and discuss the parameter space of M-theory as a fun
ction of the coupling constant and of the curvature of the Universe. We sho
w that D-branes may be efficiently produced by gravitational effects. Furth
ermore, in curved space-times the transverse fluctuations of the D-branes d
evelop a tachyonic mode and when the fluctuations grow larger than the hori
zon the branes become tensionless and break up. This signals a transition t
o a new regime. We discuss the implications of our findings for the singula
rity problem present in string cosmology, suggesting the existence of a lim
iting value for the curvature which is in agreement with the value suggeste
d by the cosmological version of the holography principle. We also comment
on possible implications for the so-called brane world scenario, where the
Standard Model gauge and matter fields live inside some branes while gravit
ons live in the bulk, (C) 1999 Elsevier Science B.V. All rights reserved.