  We study the spin correlations to probe time-reversal~(T) asymmetries in the
decays of $\Lambda_b \to \Lambda V ~(V=\phi, \rho^0, \omega, K^{*0})$. The
eigenstates of the T-odd operators are obtained along with definite angular
momenta. We obtain the T-odd spin correlations from the complex phases among
the helicity amplitudes. We give the angular distributions of $\Lambda_b \to
\Lambda(\to p \pi^-)V(\to PP')$ and show the corresponding spin correlations,
where $P^{(\prime)}$ are the pseudoscalar mesons. Due to the helicity
conservation of the $s$ quark in $\Lambda$, we deduce that the polarization
asymmetries of $\Lambda$ are close to $-1$. Since the decay of $\Lambda_b \to
\Lambda \phi$ in the standard model~(SM) is dictated by the single weak phase
from the product of CKM elements, $V_{tb}V_{ts}^*$, the true T and CP
asymmetries are suppressed, providing a clean background to test the SM and
search for new physics. In the factorization approach, as the helicity
amplitudes in the SM share the same complex phase, T-violating effects are
absent. Nonetheless, the experimental branching ratio of $Br(\Lambda_b \to
\Lambda \phi) = (5.18\pm 1.29 )\times 10^{-6}$ suggests that the
nonfactorizable effects or some new physics play an important role. By
parametrizing the nonfactorizable contributions with the effective color
number, we calculate the branching ratios and direct CP asymmetries. We also
explore the possible T-violating effects from new physics.
