  We study coarse-grained density fluctuations in the disordered phase of the
paradigmatic Vicsek-like models of self-propelled particles with alignment
interactions and random self-propulsion velocities. By numerically integrating
a fluctuation-response relation - the direct consequence of an additivity
property, we compute logarithm of the large-deviation probabilities of the
coarse-grained subsystem density, while the system is in the disordered fluid
phase with vanishing macroscopic velocity. The large-deviation probabilities,
computed within additivity, agree remarkably well with that obtained from
direct microscopic simulations of the models. Our results provide an evidence
of the existence of an equilibrium-like chemical potential, which governs the
coarse-grained density fluctuations in the Vicsek-like models. Moreover,
comparison of the particle-number fluctuations among several self-propelled
particle systems suggests a common mechanism through which the number
fluctuations arise in such systems.
