  Spin-triplet superconductors are of extensive current interest because they
can host topological state and Majorana ferimons important for quantum
computation. The uranium based heavyfermion superconductor UTe$_2$ has been
argued as a spin-triplet superconductor similar to UGe$_2$, URhGe, and UCoGe,
where the superconducting phase is near (or coexists with) a ferromagnetic (FM)
instability and spin-triplet electron pairing is driven by FM spin
fluctuations. Here we use neutron scattering to show that although UTe$_2$
exhibits no static magnetic order down to 0.3 K, its magnetism is dominated by
incommensurate spin fluctuations near antiferromagnetic (AF) ordering wave
vector and extends to at least 2.6 meV. We are able to understand the dominant
incommensurate spin fluctuations of UTe$_2$ in terms of its electronic
structure calculated using a combined density functional and dynamic mean field
theory.
