  We construct a new effective field theory approach to the equation of state
(EoS), dubbed pseudo-confomal model "PCM," for nuclear and compact star matter
entirely in terms of effective hadron degrees of freedom. The possible
transition at $n\sim (2-4) n_0$ (where $n_0$ is the normal nuclear matter
density) from hadron degrees of freedom to strongly-coupled quark degrees of
freedom, giving rise to a soft-to-hard changeover in the EoS that can
accommodate the massive stars observed, is effectuated by the topology change
at $n_{1/2}\gsim 2n_0$ from skyrmions to half-skyrmions without involving local
order-parameter fields. The mechanism exploits possible emergence of hidden
scale and local symmetries of QCD at high density, leading to a precocious
"pseudo-conformal" sound velocity $v_s^2=1/3$ (in unit of $c=1$) for $n\gsim
3n_0$. The resulting prediction signals a drastic departure from standard
nuclear many-body theory in the density regime involved in the massive stars.
We suggest that the tidal deformability implemented in gravitational waves
coming from coalescing neutron stars in LIGO/Virgo-type observations could pin
down the location of the topology change density $n_{1/2}$.
