  The success of spectroscopy to characterise equilibrium fluids, for example
the heat capacity ratio, suggests a parallel approach for active fluids. Here,
we start from a hydrodynamic description of chiral active fluids composed of
spinning constituents and derive their low-frequency, long-wavelength response
functions using the Kadanoff-Martin formalism. We find that the presence of odd
(equivalently, Hall) viscosity leads to mixed density-vorticity response even
at linear order. Such response, prohibited in time-reversal-invariant fluids,
is a large-scale manifestation of the microscopic breaking of time-reversal
symmetry. Our work suggests possible experimental probes that can measure
anomalous transport coefficients in active fluids through dynamic light
scattering.
