  We present a science forecast for the eBOSS survey, part of the SDSS-IV
project, which is a spectroscopic survey using multiple tracers of large-scale
structure, including luminous red galaxies (LRGs), emission line galaxies
(ELGs) and quasars (both as a direct probe of structure and through the
Ly-$\alpha$ forest). Focusing on discrete tracers, we forecast the expected
accuracy of the baryonic acoustic oscillation (BAO), the redshift-space
distortion (RSD) measurements, the $f_{\rm NL}$ parameter quantifying the
primordial non-Gaussianity, the dark energy and modified gravity parameters. We
also use the line-of-sight clustering in the Ly-$\alpha$ forest to constrain
the total neutrino mass. We find that eBOSS LRGs ($0.6<z<1.0$) (combined with
the BOSS LRGs at $z>0.6$), ELGs ($0.6<z<1.2$) and Clustering Quasars (CQs)
($0.6<z<2.2$) can achieve a precision of 1%, 2.2% and 1.6% precisions,
respectively, for spherically averaged BAO distance measurements. Using the
same samples, the constraint on $f\sigma_8$ is expected to be 2.5%, 3.3% and
2.8% respectively. For primordial non-Gaussianity, eBOSS alone can reach an
accuracy of $\sigma(f_{\rm NL})\sim10-15$, depending on the external
measurement of the galaxy bias and our ability to model large-scale systematic
errors. eBOSS can at most improve the dark energy Figure of Merit (FoM) by a
factor of $3$ for the Chevallier-Polarski-Linder (CPL) parametrisation, and can
well constrain three eigenmodes for the general equation-of-state parameter
(Abridged).
