  A stochastic background of gravitational waves is expected to arise from a
superposition of a large number of unresolved gravitational-wave sources of
astrophysical and cosmological origin. It is expected to carry unique
signatures from the earliest epochs in the evolution of the universe,
inaccessible to the standard astrophysical observations. Direct measurements of
the amplitude of this background therefore are of fundamental importance for
understanding the evolution of the universe when it was younger than one
minute. Here we report direct limits on the amplitude of the stochastic
gravitational-wave background using the data from a two-year science run of the
Laser Interferometer Gravitational-wave Observatory (LIGO). Our result
constrains the energy density of the stochastic gravitational-wave background
normalized by the critical energy density of the universe, in the frequency
band around 100 Hz, to be less than 6.9 x 10^{-6} at 95% confidence. The data
rule out models of early universe evolution with relatively large
equation-of-state parameter, as well as cosmic (super)string models with
relatively small string tension that are favoured in some string theory models.
This search for the stochastic background improves upon the indirect limits
from the Big Bang Nucleosynthesis and cosmic microwave background at 100 Hz.
