  We show that spontaneous breaking of the translational symmetry (SBTS) of
strongly interacting electron and phonon fields acknowledged in lightly doped
cuprates to interpret broad bands in their ARPES and optical conductivity
spectra influences the carrier distribution function as charge carrier momentum
is no longer certain. We develop appropriate distribution and use it to
calculate the carrier concentration in different states in essentially doped
systems with SBTS. This allows studying doping and temperature evolution of
ARPES spectra of such systems. We reveal that at increasing both temperature or
doping polarons concede dominance to bipolarons that results in a shift of the
broad band maximum to higher binding energy as it occurs in ARPES spectra of
cuprates. At further doping delocalized carriers appear and coexist with
bipolarons. We show that intimate property of systems with SBTS is partition of
the momentum space between autolocalized and delocalized carriers caused by
Pauli exclusion rule. We demonstrate that in ARPES spectra such partition
manifests itself as `vertical dispersion` or waterfalls universally observed in
all the cuprates at essential doping and in undoped parent compounds. Thus,
studying the carriers distribution in systems where electron-phonon interaction
breaks the translation symmetry leads simultaneously to both types of
waterfalls observed in significantly doped and undoped cuprates. The article
also represents the methods developed to calculate the band in ARPES spectrum
caused by bipolaron photodissociation and the bipolaron binding energy and
radius using coherent states for the phonon field characterization.
