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\begin{document}

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\fancyhead[L]{ \rm Facilitating Cosmology Measurements from LSST}
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%{\bf General guidelines for April 18th: we should produce brief "white papers" describing the science in greater detail and
%		quantifying the capabilities needed. Similar to a rough draft of an NOAO observing proposal.
%		It has the same elements of compelling science, technical description and quantitative
%		statement of resource needs. But does not have to be very polished.}

\begin{centering}
{\huge{\bf{{Facilitating Cosmology Measurements from LSST}}}}


{\it{\bf Executive Summary:}}
\end{centering}
%
%{\it One paragraph summarizing (1) the main science goals, (2) needed capabilities (top level detailed specifications such as resolution, wavelength coverage, FOV, multiplex), (3) estimate of demand to meet science goals (e.g., number of nights, fiber hours), and (4) priorities for each capability (3-tier: critical, very important, important). The chapter should be $\sim$10 pages. }

Almost all LSST studies of cosmology can be enhanced by the addition of spectroscopic information.   The most critical needs, as they affect essentially all cosmological probes (but particularly weak lensing, large-scale structure, and galaxy cluster studies), are training of photometric redshifts (i.e., obtaining spectroscopic samples to refine photo-$z$ algorithms) and photo-$z$ calibration (i.e., characterizing the actual biases and errors of photo-$z$ algorithms).  The former will require a wide-field ($>20$ arcmin, with $>1$ degree preferred), highly-multiplexed ($>2000\times$), medium-resolution ($R>4000$ in the red), broad-wavelength coverage (0.4--1.0$\mu$m minimum, 0.3--1.5$\mu$m preferred) multi-object spectrograph on an 8m-class telescope.  A minimum of 1.1 years of observing time would be necessary for this campaign (assuming a Subaru/PFS-like instrument; other planned spectrographs for 4-8m telescopes would take longer). Calibration of photometric redshifts via cross-correlation techniques will require overlap of a DESI-like galaxy and quasar survey with the LSST footprint, which is already planned to occur.  A number of cosmological probes can utilize such a spectrograph (or, in some cases, instruments with smaller fields of view but otherwise similar capabilities) to mitigate potential systematics in cosmological measurements or to provide new constraints on modified gravity theories; these activities will provide very important contributions to cosmological studies taken as a whole.

For efforts to constrain cosmology using strong gravitational lensing, adaptive optics imaging and IFU spectroscopy on 8-30m telescopes will be critical (and hence very important for cosmology taken as a whole).  Instrumental requirements include a resolution of $\sim 0.1$ arcsec FWHM, field of view of 4 arcsec diameter, and (for spectroscopy) $R \sim 4000 - 5000$ over a wavelength range of 1.0-2.2$\mu$m.   Total time requirements are roughly 30 hours for imaging and 100 hours for spectroscopy (split between 8-10m telescopes and GSMTs according to brightness) to cover a sample of 100 particularly high-quality strong lens systems.

Supernova cosmology will be critically dependent upon spectroscopy of thousands of active supernovae to investigate supernova physics and constrain the properties of supernovae which are not associated with a visible host galaxy.  Additionally, spectroscopic redshift measurements for hosts of supernovae whose spectra were not obtained when they were active can greatly enhance the size of the samples used for constraining cosmology, providing very important contributions to supernova cosmology.  Direct supernova spectroscopy will require broad wavelength coverage (0.3--1.0$\mu$m minimum, $\sim$ 0.3 -- 2.5~$\mu$m preferred), modest resolution ($R>\sim 100$), high efficiency single-object spectrographs on 4m, 8-10m, and GSMT telescopes, with total time requirements over the life of LSST of 300-900 telescope-nights (split roughly 20\%/60\%/20\% between 4m, 8-10m, and GSMT telescopes).  Supernova host spectroscopy is most efficiently conducted with very large field, highly-multiplexed spectrographs similar to those required for photometric redshift training and calibration. Redshifts can be obtained for the majority of supernovae in the 10-20 LSST ``deep drilling'' high-cadence fields with $\sim 15-30$ nights of observations per year on a DESI-like spectrograph on a 4m telescope.

\section{Introduction}

A key driver for LSST is to explain the accelerating expansion of the Universe.  The primary possibilities are that there is a new, unknown component which dominates the energy density in the Universe today (commonly labeled ``dark energy''), or else that Einstein's theory of General Relativity (GR) fails to provide an accurate description of the action of gravity on large scales (a class of models generally referred to as ``modified gravity'' theories).  Many of the planned cosmological measurements from LSST can also be used to constrain neutrino masses and dark matter properties.  {\bf By strengthening LSST cosmological constraints and mitigating potential systematics, the work described in this chapter will help LSST to address a key objective identified in the {\it New Worlds, New Horizons} report, studying the Physics of the Universe.}

The constraining power of almost all LSST probes of cosmology (as well as other extragalactic work with LSST) will be greatly strengthened by the addition of spectroscopic redshift measurements for training photometric redshift algorithms.  Obtaining such samples requires spectrographs that maximize multiplexing, areal coverage, wavelength range, resolution, and telescope aperture, as described below.  Studies of cosmology using strong gravitational lensing also requires adaptive optics IFU observations of the highest-priority lens systems in order to obtain precision source positions and tighten constraints; instruments currently available on 8-10m telescopes or planned for ELTs are well-suited for this work.


%%Almost all LSST probes of cosmology will be greatly strengthened by the addition of spectroscopic redshift measurements for large samples of galaxies.
%Spectroscopic samples to train photometric redshift algorithms will improve constraints from almost all LSST extragalactic studies, including cosmology.
%%;. spectroscopy obtained with the same instruments can be important for investigating the effects of intrinsic alignments between galaxies on the observed weak lensing signal or for improving the use of galaxy clusters as a cosmological probe, amongst other applications.
%This work will benefit from spectrographs that maximize multiplexing, areal coverage, wavelength range, resolution, and telescope aperture, as described below.  {\bf By strengthening LSST cosmological constraints and mitigating potential systematics, this spectroscopy will help LSST to address a key objective identified in the {\it New Worlds, New Horizons} report, studying the Physics of the Universe.}
%
%Larger, wider-area samples of bright galaxies and QSOs with redshifts, such as those provided by DESI, can be used to accurately calibrate the results of photometric redshift algorithms via cross-correlation measurements; the same samples can contribute to cross-correlation studies of intrinsic alignments and LSST large-scale structure.  We will focus on the training and calibration of photometric redshift algorithms in this section; however, a broad swath of dark energy science would benefit from the same capabilities, and we highlight a few examples at the end of the section.
%


\section{Science Case 1: Multi-Object Spectroscopy for Training and Calibrating Photometric Redshifts}

%A) Photo-z training and calibration (including in cluster regime, spectroscopy of blends identified in space-based imaging)
%		- JN, AvdL, WD, SS, MD
\input{photoz_short}

%B) Weak lensing: Intrinsic alignment studies, exquisite-seeing data for morphology templates, etc.
% RM, WD

%C) Strong lensing: time delay and compound lens cosmography, high resolution imaging and spatially resolved spectroscopy to elevate weach of ~100 lenses to a 4-5% distance probe
%      - PM, TT, EL, with input from the DESC SL WG
\section{Science Case 2: AO Imaging and/or IFU Spectroscopy for Strong Lensing Cosmography}

\input{sl_short}

\section{Science Case 3: Wide Field and Single-Object Spectroscopy for Supernova Cosmology}

\input{sn_short}

%D) LSS: BAO (including cross-correlation enhancements), redshift-space distortions on cluster or large scales, QSO absorber power spectra \& BAO
% EG, EJ, WD, JN

%E) Science-driven needs for other resources: software, computing and data management resources, access to archival data, etc.
% AB, CS, EG, WD, BW

%\chapter{Science Case 3: Computing, Statistical, and Data Processing Needs}

%\input{datacomp}

%F) Development of statistical techniques; e.g. for utilizing photo-z pdf information/samples for, e.g. clustering measurements.  Developing techniques for probabilistic inference over redshift distributions
% CS, EG, JN, WD, BW, EJ

%\input{stats}

%\section{Dark matter in galaxy clusters}

%\input{dm_short}
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