  The details of the minimal cosmological standard model (MCSM) proposed in
Ref.~\cite{Barenboim:2024akt} are discussed. The model is based on the
scale-symmetry and the global Peccei-Quinn(PQ) symmetry with a key assumption
that the latter is broken only in the gravity sector in a scale-invariant
manner. We show that the model provides a quite simple unified framework for
the unknown history of the universe from inflation to the epoch of big-bang
nucleosynthesis, simultaneously addressing key puzzles of high energy theory
and cosmology: (i) the origin of scales, (ii) primordial inflation, (iii)
matter-antimatter asymmetry, (iv) tiny neutrino masses, (v) dark matter, and
(vi) the strong CP-problem. Scale symmetry can be exact, and the Planck scale
is dynamically generated. The presence of Gauss-Bonnet term may safely retain
dangerous non-perturbative symmetry-breaking effects negligible, allowing a
large-field trans-Planckian inflation along the PQ-field. Iso-curvature
perturbations of axi-majorons are suppressed. A sizable amount of PQ-number
asymmetry is generated at the end of inflation, and conserved afterwards.
Domain wall problem is absent due to the non-restoration of the symmetry and
the non-zero PQ-number asymmetry. Baryogenesis can be realized by either the
transfer of the PQ-number asymmetry through the seesaw sector, or by resonant
leptogenesis. Dark matter is purely cold axi-majorons from the mis-alignment
contribution with the symmetry-breaking scale of $\mathcal{O}(10^{12}) {\rm
GeV}$. Hot axi-majorons from the decay of the inflaton become a natural source
for a sizable amount of dark radiation. Inflationary gravitational waves have
information about the masse parameters of the lightest left-handed and
right-handed neutrinos, thanks to the presence of an early matter-domination
era driven by the long-lived lightest right-handed neutrino species.
