  The inflation-free solution of problems of the modern cosmology (horizon,
cosmic initial data, Planck era, arrow of time, singularity,homogeneity, and so
on) is considered in the conformal-invariant unified theory given in the space
with geometry of similarity where we can measure only the conformal-invariant
ratio of all quantities. Conformal General Relativity is defined as the
$SU_c(3)\times SU(2)\times U(1)$-Standard Model where the dimensional parameter
in the Higgs potential is replaced by a dilaton scalar field described by the
negative Penrose-Chernikov-Tagirov action. Spontaneous SU(2) symmetry breaking
is made on the level of the conformal-invariant angle of the dilaton-Higgs
mixing, and it allows us to keep the structure of Einstein's theory with the
equivalence principle. We show that the lowest order of the linearized
equations of motion solves the problems mentioned above and describes the Cold
Universe Scenario with the constant temperature T and z-history of all masses
with respect to an observable conformal time. A new fact is the intensive
cosmic creation of $W,Z$-vector bosons due to their mass singularity. In the
rigid state, this effect is determined by the integral of motion $(m_w^2H_{\rm
hubble})^{1/3}=2.7 K k_B$ that coincides with the CMB temperature and has the
meaning of the primordial Hubble parameter. The created bosons are enough to
consider their decay as an origin of the CMB radiation and all observational
matter with the observational element abundances and the baryon asymmetry.
Recent Supernova data on the relation between the luminosity distance and
redshift (including the point $z=1.7$) do not contradict the dominance of the
rigid state of the dark matter in the Conformal Cosmology.
