<figure><img src="image_15.png" /><figcaption>Figure 13. The suppression of power at small angular scales due to free-streaming of massive neutrinos. A normal hierarchy for neutrino masses is assumed.</figcaption></figure>

Planck Collaboration et al. (2015b), these combined probes produce an upper limit $\sum m_\nu < 0.23$ eV (95% confidence) when assuming zero curvature. With eBOSS, we can provide comparable constraints if one combines information derived from the shape of the broadband power spectrum (for neutrino masses) with the distance measurements derived from BAO. Estimates from the clustering of BOSS galaxies have already shown the potential in spectroscopic surveys to constrain the neutrino mass (e.g., Zhao et al. 2013; Beutler et al. 2014a).

The projections in Table 10 include an estimated precision on the neutrino mass that is highly degenerate with the modified gravity parameters. If one were to assume a flat, $\Lambda$CDM cosmology described by GR on cosmological scales, we predict a 95% upper limit $\sum m_\nu < 0.104$ eV when combining the results from the BOSS, eBOSS, and CMB. The reported constraint assumes that that measurements of large-scale modes can be made with the eBOSS galaxies and quasars at all scales larger than $k_{max} = 0.1$ h Mpc$^{-1}$. If one were to assume measurements of large-scale modes with wavelengths up to $k_{max} = 0.2$ h Mpc$^{-1}$, the projections for the 95% upper limit improve to $\sum m_\nu < 0.072$ eV. The statistical power of eBOSS can potentially provide an upper limit on neutrino masses comparable to the minimum allowed mass in an inverted hierarchy.

An alternative way to constrain neutrino masses with optical spectroscopy is to use the information from the 1D flux power spectrum of $\text{Ly}\alpha$ forest. Measurements of the 1D flux power spectrum using BOSS quasars (Palanque-Delabrouille et al. 2013b) yield the tightest constraints to date using any cosmological tracer. When combining the BOSS measurement with CMB and BAO measurements, the sum of the neutrino masses is constrained with a 95% upper limit $\sum m_\nu < 0.15$ eV (Palanque-Delabrouille et al. 2015b), improved to $\sum m_\nu < 0.12$ eV (Palanque-Delabrouille et al. 2015a). We do not include projections for new constraints from 1D power on the neutrino mass from eBOSS. The deeper spectra obtained by reobserving $1.2 \text{ deg}^{-2}$ known quasars and the discovery of $1.2 \text{ deg}^{-2}$ new quasars at $z > 3$ should allow tighter constraints

on the redshift evolution of the 1D flux power spectrum, and thus tighter constraints on the neutrino mass.

### 7.3.4. Inflation

Inflation is the best candidate that we have for a theory that simultaneously established the initial conditions for structure formation while producing a homogeneous, nearly flat universe. Inflation can explain small super-horizon fluctuations which are nearly Gaussian and scale-independent. A review of inflation and the potential of upcoming cosmology programs to improve inflationary models is found in Abazajian et al. (2015a).

The eBOSS survey volume provides sensitivity to the standard inflationary parameters such as the spectral index of primordial matter fluctuations ($n_s$), defined according to $P(k) = k^{n_s}$. Most inflationary models predict a value of $n_s$ slightly less than one. One possible departure from standard inflationary scenarios is expected to appear as small deviations from Gaussian fluctuations in the initial density field. This signature of non-Gaussianity in the primordial fluctuations could also be visible in the large-scale structure maps from eBOSS.

A form of potential non-Gaussianity that arises naturally in many inflationary models (Wands 2010) is the “local” form, with a gravitational potential described by

$$ \phi = \phi_g + f_{\text{NL}} (\phi_g^2 - \langle \phi_g^2 \rangle), \quad (7) $$

where $\phi_g$ is an auxiliary Gaussian field. In the limit of $f_{\text{NL}} = 0$, one recovers the Gaussian case. It has been shown (Dalal et al. 2008) that such non-Gaussianity will generate a deviation from the standard prediction in which galaxies are a linear tracer of the underlying dark matter field on large scales. This correction scales inversely as the square of the wavenumber in the matter power spectrum, and it thus becomes important on the larges scales—precisely in the limit where nonlinearities in the dark-matter fluctuations are negligible.

We find that primordial non-Gaussianities of the local form can be constrained to a precision $\sigma_{f_{\text{NL}}} = 12$ (68% confidence) by the combination of eBOSS LRG, ELG, and quasars. This measurement will be independent of the current Planck bispectrum limits of $f_{\text{NL}} = 0.8 \pm 5$. (68% confidence) (Planck 2015 results. XXVII; Planck Collaboration et al. 2015a). While we do not have forecasts for constraints arising from measurements of the galaxy bispectrum, we expect these to significantly tighten the constraints from eBOSS, provided systematic effects can be brought under control (e.g., Ross et al. 2013a). In fact, the first analysis of the BOSS galaxy bispectrum (Gil-Marín et al. 2015a) and cosmological interpretation (Gil-Marín et al. 2015b) were completed in 2014.

## 8. CONCLUSION

As described throughout this paper, the eBOSS survey design has been thoroughly evaluated and should meet a high-level goal of precise clustering measurements using four distinct tracers over four different redshift intervals. A sample of $52 \text{ deg}^{-2}$ targets will be observed and will produce more than $35 \text{ deg}^{-2}$ LRGs with confident spectroscopic redshifts between $0.6 < z < 1.0$. When combined with the $z > 0.6$ tail of the BOSS CMASS sample, this LRG sample has the statistical power to constrain the matter power spectrum at
BAO scales for better than a 1% distance measurement. Similarly, a uniform sample of quasar candidates selected at a density of $115 \text{ deg}^{-2}$ can be efficiently identified. Roughly 30 targets $\text{deg}^{-2}$ have confident spectroscopic classification from SDSS-I, -II, or -III, revealing quasars at a density $13 \text{ deg}^{-2}$ between $0.9 < z < 2.2$. New observations will produce an average of $56 \text{ deg}^{-2}$ new quasars at $0.9 < z < 2.2$. The final sample should be sufficient for a 1.8% BAO distance measurement. The range of redshifts covered by the LRG and quasar program is only sparsely sampled by supernova surveys, but it covers the crucial epoch of transition from decelerating cosmic expansion to accelerating expansion. As with BOSS, the area covered by the LRG and quasar clustering samples approaches the limits accessible by ground-based telescopes: we will observe one-third of the extra-Galactic sky.

eBOSS will use a deeper sample of Ly$\alpha$ forest observations to improve the BOSS BAO distance measurements by a factor of 1.44 and will introduce a new sample of highly biased ELG targets. Several potential ELG programs have been identified that can provide BAO measurements at 2% precision. The final ELG program will be decided when the imaging data sets are better understood and when uniformity of the target selection is fully assessed. Beyond BAO, the clustering in LRG, ELG, quasars, and the Ly$\alpha$ forest provide broadband power spectra to further explore the cosmological model, particularly in the realm of modified gravity and neutrino mass estimates. The primary analysis effort within the eBOSS collaboration will be to mitigate systematic errors due to the non-uniformities in the target selection and improve modeling of the observed power spectrum at small scales to capitalize on this statistical power.

The cosmological projections presented in Section 7.3 assume a standard cosmological model. Because of the overlap in redshift range between the ELG sample and the LRG and quasar samples, the eBOSS data also enable techniques such as those introduced in McDonald & Seljak (2009) and Seljak (2009) to combine multiple tracers and reduce the effects of sample variance. Projections for $f_{\text{NL}}$ and RSD from eBOSS following the multi-tracer technique are found in the work by Zhao et al. (2015). Zhao et al. (2015) also present Fisher forecasts for the dark energy equation of state and modified gravity based on a principal component analysis parameterization.

eBOSS will provide unique spectroscopic information that will complement imaging cosmological surveys such as DES. Most imaging probes of dark energy rely on photometric redshift estimates which must be calibrated to extremely high accuracy to avoid degradation in dark energy inference. This calibration is typically done using spectroscopically calibrated redshifts of objects spanning the photometric properties of the sample of interest. However, existing spectroscopic surveys are inherently limited by the difficulty of securing redshifts for faint, high redshift galaxies. Spectroscopy from eBOSS offers an alternative approach to photometric redshift calibration through cross-correlation techniques (Newman 2008; Ménard et al. 2013). The observed degree of correlation between a well-measured spectroscopic sample and a photometrically selected sample provides information on the fraction of the imaging sample at that redshift. The possibility of cross-correlation as a tool to calibrate photometric redshifts for DES was the primary reason that the 500 deg$^2$ eboss2 region was tiled in the first year (see Figure 3).

Improvements in the automated data reduction pipeline are underway to ensure that we meet the redshift efficiencies required to meet the assumed cosmological precision. The introduction of new spectral templates that cover a more limited parameter space should significantly improve the ability of the pipeline to differentiate the best fit redshift from contaminating interlopers. When complete, the classifications will produce the largest sample of $z > 0.6$ LRGs to date, a high-redshift ELG sample exceeding that of the WiggleZ Dark Energy Survey (Drinkwater et al. 2010; Blake et al. 2011a), a sample of quasars exceeding that of all previous observations combined, and an enhanced sample of Ly$\alpha$ forest spectra. These new samples will allow studies of galaxy evolution and quasar astrophysics well beyond the cosmological studies that drove the survey design.

Several studies of galaxy evolution and quasar astrophysics have already begun with the early release of the SEQUELS sample in DR12 and the first eBOSS data taken in Fall 2014. At the redshifts of the LRG and quasar samples, many absorption lines are accessible in the eBOSS spectra. Measurements of quasar absorption features in the vicinity of BOSS spectroscopic galaxies revealed the Mg II distribution surrounding LRGs at redshifts as low as $z = 0.5$ (Zhu et al. 2014). Composite spectra constructed from Ly$\alpha$ forest absorbers shed light on circumgalactic regions and the intergalactic medium (Pieri et al. 2014). These studies will be extended to higher redshift with the eBOSS data. Studies of the correlations in the Ly$\alpha$ forest with other systems are underway following early studies in BOSS (e.g., Font-Ribera et al. 2012), while others have shown the potential of eBOSS to offer new probes of large-scale structure and BAO (e.g., Pieri 2014). The composite spectrum of ELGs from limited pilot observations already shows rich spectral features such as resonant absorption and non-resonant emission. The first science result from the eBOSS program resulted from studies of this composite ELG spectrum (Zhu et al. 2015). These features are rare in other spectroscopic samples; eBOSS will allow systematic investigation of these features to explore the effect of gas processes on galaxy evolution. The overlap in spectroscopic area covered by eBOSS and wide-field far-infrared imaging from the Herschel Space Telescope (Pilbratt et al. 2010) will enable an exploration of the far-IR luminosity function of the quasar host galaxies. Finally, the quasar sample will greatly exceed all prior work both in total numbers and in the coverage of luminosity–redshift phase space. The sample can be used to enhance BOSS constraints on the luminosity function (e.g., McGreer et al. 2013; Ross et al. 2013b), provide halo occupation statistics that can be used to constrain the duty cycle of quasars as a function of halo mass and quasar luminosity, and to explore the redshift and luminosity evolution of quasars. When complete, the eBOSS spectroscopic sample will results in a diverse range of findings both for cosmology and for galaxy and quasar science.

K.D. acknowledges support from the U.S. Department of Energy under Grant DE-SC000995. J.P.K. and T.D. acknowledge support from the ERC advanced grant LIDA. W.J.P. acknowledges support from the UK STFC through the consolidated grant ST/K0090X/1, and from the European Research Council through grant Darksurvey. This paper includes targets derived from the images of the *Wide-Field Infrared Survey Explorer*, which is a joint project of the
University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

This paper represents an effort by both the SDSS-III and SDSS-IV collaborations. Funding for SDSS-III was provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatory of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

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