  The properties of a Bose gas of translation-invariant (TI) bipolarons
analogous to Cooper pairs are considered. As in the BCS theory, the description
of a TI-bipolaron gas is based on the electron-phonon interaction and Froehlich
Hamiltonian. As distinct from the BCS theory, when the correlation length
greatly exceeds the mean distance between the pairs, here we deal with the
opposite case when the correlation length is much less than the distance
between the pairs. We calculate the critical temperature of the transition of a
TI-bipolaron Bose-gas into the superconducting state, its energy, heat capacity
and heat of the transition. The results obtained are used to explain the
experiments on high-temperature superconductors. Possible ways of raising the
critical temperature of high-temperature superconductors are discussed.
