Curvature-Restored Gauge Invariance and Ultraviolet Naturalness
  It is shown that, $(a \Lambda^2 + b |H|^2)R$ in a spacetime of curvature $R$
is a natural ultraviolet $(U\!V)$ completion of $(a \Lambda^4 + b \Lambda^2
|H|^2)$ in the flat-spacetime Standard Model $(S\!M)$ with Higgs field $H$,
$U\!V$ scale $\Lambda$ and loop factors $a$, $b$. This curvature completion
rests on the fact that a $\Lambda$-mass gauge theory in flat spacetime turns,
on the cut-view $R = 4 \Lambda^2$, into a massless gauge theory in curved
spacetime. It provides a symmetry reason for curved spacetime, wherein gravity
and matter are both low-energy effective phenomena. Gravity arises correctly if
new physics exists with at least 63 more bosons than fermions, with no need to
interact with the $S\!M$ and with dark matter as a natural harbinger. It can
source various cosmological, astrophysical and collider phenomena depending on
its spectrum and couplings to the $S\!M$.
