  We prove that every $C^2$ conservative partially hyperbolic diffeomorphism of
a closed 3-manifold without periodic points is ergodic, which gives an
affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the
absence of periodic points. We also show that a partially hyperbolic
diffeomorphism of a closed 3-manifold $M$ with no periodic points is accessible
if the non-wandering set is all of $M$ and the fundamental group $\pi_1(M)$ is
not virtually solvable.
