Coherent phenomena at the last scattering in the CMB light

Decoupling of the baryon–photon fluid in the early universe is studied taking into account the highly coherent character of the acoustic oscillations in the plasma at the decoupling. An effective nonlinear Schrödinger equation for a macroscopic wave function that specifies the index of the coherent states is used for description of the coherent phenomena. Generation of a transitional acoustic turbulence preceding formation of large-scale condensate in the plasma and its influence on the cosmic microwave background (CMB) power spectrum has been studied. A scaling k−1k−1 law is derived for the CMB Doppler spectrum E(k)E(k) (angle-averaged) in the wavenumber space, for sufficiently large wavenumber k   and for the weak nonlinear initial conditions. Using the recent WMAP data it is shown that the so-called first acoustic peak represents a pre-condensate fraction of the spectrum E(k)E(k) at a rather advance stage of the condensate formation process.