Tightening geometric and dynamical constraints on dark energy and
  gravity: galaxy clustering, intrinsic alignment and kinetic
  Sunyaev-Zel'dovich effect
  Conventionally, in galaxy surveys, cosmological constraints on the growth and
expansion history of the universe have been obtained from the measurements of
redshift-space distortions and baryon acoustic oscillations embedded in the
large-scale galaxy density field. In this paper, we study how well one can
improve the cosmological constraints from the combination of the galaxy density
field with velocity and tidal fields, which are observed via the kinetic
Sunyaev-Zel'dovich (kSZ) and galaxy intrinsic alignment (IA) effects,
respectively. For illustration, we consider the deep galaxy survey by Subaru
Prime Focus Spectrograph, whose survey footprint perfectly overlaps with the
imaging survey of the Hyper Suprime-Cam and the CMB-S4 experiment. We find that
adding the kSZ and IA effects significantly improves cosmological constraints,
particularly when we adopt the non-flat cold dark matter model which allows
both time variation of the dark energy equation-of-state and deviation of the
gravity law from general relativity. Under this model, we achieve $31\%$
improvement for the growth index $\gamma$ and $>35\%$ improvement for other
parameters except for the curvature parameter, compared to the case of the
conventional galaxy-clustering-only analysis. As another example, we also
consider the wide galaxy survey by the {\it Euclid} satellite, in which shapes
of galaxies are noisier but the survey volume is much larger. We demonstrate
that when the above model is adopted, the clustering analysis combined with kSZ
and IA from the deep survey can achieve tighter cosmological constraints than
the clustering-only analysis from the wide survey.
