Community access to deep (i ~ 25), highly-multiplexed optical and near-infrared multi-object spectroscopy (MOS) on 8-40m telescopes would greatly improve measurements of cosmological parameters from LSST. The largest gain would come from improvements to LSST photometric redshifts, which are employed directly or indirectly for every major LSST cosmological probe; deep spectroscopic datasets will enable reduced uncertainties in the redshifts of individual objects via optimized training. Such spectroscopy will also determine the relationship of galaxy SEDs to their environments, key observables for studies of galaxy evolution. The resulting data will also constrain the impact of blending on photo-z's. Focused spectroscopic campaigns can also improve weak lensing cosmology by constraining the intrinsic alignments between the orientations of galaxies. Galaxy cluster studies can be enhanced by measuring motions of galaxies in and around clusters and by testing photo-z performance in regions of high density. Photometric redshift and intrinsic alignment studies are best-suited to instruments on large-aperture telescopes with wider fields of view (e.g., Subaru/PFS, MSE, or GMT/MANIFEST) but cluster investigations can be pursued with smaller-field instruments (e.g., Gemini/GMOS, Keck/DEIMOS, or TMT/WFOS), so deep MOS work can be distributed amongst a variety of telescopes. However, community access to large amounts of nights for surveys will still be needed to accomplish this work. In two companion white papers we present gains from shallower, wide-area MOS and from single-target imaging and spectroscopy.

LSST will open new vistas for cosmology in the next decade, but it cannot reach its full potential without data from other telescopes. Cosmological constraints can be greatly enhanced using wide-field ($>20$ deg$^2$ total survey area), highly-multiplexed optical and near-infrared multi-object spectroscopy (MOS) on 4-15m telescopes. This could come in the form of suitably-designed large surveys and/or community access to add new targets to existing projects. First, photometric redshifts can be calibrated with high precision using cross-correlations of photometric samples against spectroscopic samples at $0 < z < 3$ that span thousands of sq. deg. Cross-correlations of faint LSST objects and lensing maps with these spectroscopic samples can also improve weak lensing cosmology by constraining intrinsic alignment systematics, and will also provide new tests of modified gravity theories. Large samples of LSST strong lens systems and supernovae can be studied most efficiently by piggybacking on spectroscopic surveys covering as much of the LSST extragalactic footprint as possible (up to $\sim20,000$ square degrees). Finally, redshifts can be measured efficiently for a high fraction of the supernovae in the LSST Deep Drilling Fields (DDFs) by targeting their hosts with wide-field spectrographs. Targeting distant galaxies, supernovae, and strong lens systems over wide areas in extended surveys with (e.g.) DESI or MSE in the northern portion of the LSST footprint or 4MOST in the south could realize many of these gains; DESI, 4MOST, Subaru/PFS, or MSE would all be well-suited for DDF surveys. The most efficient solution would be a new wide-field, highly-multiplexed spectroscopic instrument in the southern hemisphere with $>6$m aperture. In two companion white papers we present gains from deep, small-area MOS and from single-target imaging and spectroscopy.

The generation-defining Vera C. Rubin Observatory will make state-of-the-art measurements of both the static and transient universe through its Legacy Survey for Space and Time (LSST). With such capabilities, it is immensely challenging to optimize the LSST observing strategy across the survey's wide range of science drivers. Many aspects of the LSST observing strategy relevant to the LSST Dark Energy Science Collaboration, such as survey footprint definition, single-visit exposure time, and the cadence of repeat visits in different filters, are yet to be finalized. Here, we present metrics used to assess the impact of observing strategy on the cosmological probes considered most sensitive to survey design; these are large-scale structure, weak lensing, type Ia supernovae, kilonovae, and strong lens systems (as well as photometric redshifts, which enable many of these probes). We evaluate these metrics for over 100 different simulated potential survey designs. Our results show that multiple observing strategy decisions can profoundly impact cosmological constraints with LSST; these include adjusting the survey footprint, ensuring repeat nightly visits are taken in different filters, and enforcing regular cadence. We provide public code for our metrics, which makes them readily available for evaluating further modifications to the survey design. We conclude with a set of recommendations and highlight observing strategy factors that require further research.

Cosmology is one of the four science pillars of LSST, which promises to be transformative for our understanding of dark energy and dark matter. The LSST Dark Energy Science Collaboration (DESC) has been tasked with deriving constraints on cosmological parameters from LSST data. Each of the cosmological probes for LSST is heavily impacted by the choice of observing strategy. This white paper is written by the LSST DESC Observing Strategy Task Force (OSTF), which represents the entire collaboration, and aims to make recommendations on observing strategy that will benefit all cosmological analyses with LSST. It is accompanied by the DESC DDF (Deep Drilling Fields) white paper (Scolnic et al.). We use a variety of metrics to understand the effects of the observing strategy on measurements of weak lensing, large-scale structure, clusters, photometric redshifts, supernovae, strong lensing and kilonovae. In order to reduce systematic uncertainties, we conclude that the current baseline observing strategy needs to be significantly modified to result in the best possible cosmological constraints. We provide some key recommendations: moving the WFD (Wide-Fast-Deep) footprint to avoid regions of high extinction, taking visit pairs in different filters, changing the 2x15s snaps to a single exposure to improve efficiency, focusing on strategies that reduce long gaps (>15 days) between observations, and prioritizing spatial uniformity at several intervals during the 10-year survey.