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 $S\!M$.