  XENONnT is a dark matter direct detection experiment, utilizing 5.9 t of
instrumented liquid xenon, located at the INFN Laboratori Nazionali del Gran
Sasso. In this work, we predict the experimental background and project the
sensitivity of XENONnT to the detection of weakly interacting massive particles
(WIMPs). The expected average differential background rate in the energy region
of interest, corresponding to (1, 13) keV and (4, 50) keV for electronic and
nuclear recoils, amounts to $12.3 \pm 0.6$ (keV t y)$^{-1}$ and $(2.2\pm
0.5)\times 10^{-3}$ (keV t y)$^{-1}$, respectively, in a 4 t fiducial mass. We
compute unified confidence intervals using the profile construction method, in
order to ensure proper coverage. With the exposure goal of 20 t$\,$y, the
expected sensitivity to spin-independent WIMP-nucleon interactions reaches a
cross-section of $1.4\times10^{-48}$ cm$^2$ for a 50 GeV/c$^2$ mass WIMP at 90%
confidence level, more than one order of magnitude beyond the current best
limit, set by XENON1T. In addition, we show that for a 50 GeV/c$^2$ WIMP with
cross-sections above $2.6\times10^{-48}$ cm$^2$ ($5.0\times10^{-48}$ cm$^2$)
the median XENONnT discovery significance exceeds 3$\sigma$ (5$\sigma$). The
expected sensitivity to the spin-dependent WIMP coupling to neutrons (protons)
reaches $2.2\times10^{-43}$ cm$^2$ ($6.0\times10^{-42}$ cm$^2$).
