Vacuum creation of massive vector bosons and its application to a   conformal cosmological model
  In the simple model of a massive vector field in flat space-time, we derive a kinetic equation of non-Markovian type, describing the vacuum pair creation under the action of external fields of different nature. We use for this aim the non-perturbative methods of kinetic theory in combination with a new element when the transition of the instantaneous quasiparticle representation is realized within the oscillator (holomorphic) representation. We study in detail the process of vacuum creation of vector bosons generated by a time-dependent boson mass in accordance with a conformal-invariant scalar-tensor gravitational theory and its cosmological application. It is indicated that the choice of the equation of state (EoS) of the Universe allows to obtain a number density of the vector bosons that is sufficient to explain the observed number density of photons in the cosmic microwave background radiation. It is shown that the vector boson gas created from the vacuum is in a strong non-equilibrium state and corresponds to a cold dust-like EoS. 
D.B. Blaschke, A.V. Prozorkevich, S.A. Smolyansky