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Inflationary cosmology explains the origin of primordial inhomogeneities of matter serving as initial conditions for the structure formation in the Universe. It predicts at the same time the primordial gravitational waves whose indirect detection announced BICEP2 experiment in March 2014. I will introduce the standard mechanism of generation of stochastic gravitational wave background and comment on methods and prospects of their direct detection in future gravitational wave interferometry in space.