  We present new measurements of the clustering of stellar mass-complete
samples of $\sim40,000$ SDSS galaxies at $z\sim0.03$ as a joint function of
stellar mass and specific star formation rate (sSFR). Our results confirm what
Coil et al. (2017) find at $z\sim0.7$: galaxy clustering is a stronger function
of sSFR at fixed stellar mass than of stellar mass at fixed sSFR. We also find
that galaxies above the star-forming main sequence (SFMS) with higher sSFR are
less clustered than galaxies below the SFMS with lower sSFR, at a given stellar
mass. A similar trend is present for quiescent galaxies. This confirms that
main sequence scatter, and scatter within the quiescent sequence, is physically
connected to the large-scale cosmic density field. We compare the resulting
galaxy bias versus sSFR, and relative bias versus sSFR ratio, for different
galaxy samples across ${0<z<1.2}$ to mock galaxy catalogs based on the
empirical galaxy evolution model of Behroozi et al. (2019). This model fits
PRIMUS and DEEP2 clustering data well at intermediate redshift, but agreement
with SDSS is not as strong. We show that increasing the correlation between
galaxy SFR and halo accretion rate at $z\sim0$ in the model substantially
improves agreement with SDSS data. Mock catalogs suggest that central galaxies
contribute substantially to the dependence of clustering on sSFR at a given
stellar mass and that the signal is not simply an effect of satellite galaxy
fraction differences with sSFR. Our results are highly constraining for galaxy
evolution models and show that the stellar-to-halo mass relation (SHMR) depends
on sSFR.
