Curvature-Restored Gauge Invariance and Ultraviolet Naturalness

It is shown that, $(a{\mathrm{\Lambda }}^2+b\mathrm{\mid }H{\mathrm{\mid }}^2)R$ in a spacetime of curvature $R$ is a natural ultraviolet $(U\text{\hspace{0.17em}⁣}V)$ completion of $(a \Lambda^4 + b \Lambda^2 |H|^2)$intheflat-spacetimeStandardModel$(S!M)$withHiggsfield$H$,$U!V$scale$\Lambda$andloopfactors$a$,$b$. This curvature completion rests on the fact that a $\mathrm{\Lambda }$-mass gauge theory in flat spacetime turns, on the cut-view $R=4{\mathrm{\Lambda }}^2$, 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 $S\text{\hspace{0.17em}⁣}M$ 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 $S\text{\hspace{0.17em}⁣}M$.