the homogeneous and isotropic state that describe the system below the onset of collective motion. Since our theory differs significantly from the previous work [@Stenhammar2017], we present its derivation in detail. We appreciate, however, that some readers might only be interested in the results of our theory without feeling the need to go through the rather technical Section \[section:theory\]. We, therefore, present our results in a stand-alone Section \[section:results\], which can be read without Section \[section:theory\]. There, we calculate the temporal and spatial correlation functions, fluid velocity variance, energy spectra, and the enhanced diffusivity of tracer particles. We conclude in Section \[section:discussion\], while Appendices contain additional derivations for technically oriented readers.

Kinetic theory of strongly interacting suspensions {#section:theory}
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Microscopic model {#subsection:microscopic}
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We consider a collection of $N$ microswimmers contained in a volume $V$ at a finite number density $n=N/V$. The microswimmers are suspended in a Newtonian fluid with the viscosity $\mu$. Each microswimmer is described by its instantaneous position ${\bm x}_i$ and orientation ${\bm p}_i$, that we collectively denote by ${\bm z}_i = \left( {\bm x}_i, {\bm p}_i\right)$, where $i=1\dots N$ enumerates the particles. Within our model, the dynamics of the suspension is governed by the following equations 