We review the measurements of dark energy enabled by observations of the Deep Drilling Fields and the optimization of survey design for cosmological measurements. This white paper is the result of efforts by the LSST DESC Observing Strategy Task Force (OSTF), which represents the entire collaboration, and aims to make recommendations on observing strategy for the DDFs that will benefit all cosmological analyses with LSST. It is accompanied by the DESC-WFD white paper (Lochner et al.). We argue for altering the nominal deep drilling plan to have $>6$ month seasons, interweaving $gri$ and $zy$ observations every 3 days with 2, 4, 8, 25, 4 visits in $grizy$, respectively. These recommendations are guided by metrics optimizing constraints on dark energy and mitigation of systematic uncertainties, including specific requirements on total number of visits after Y1 and Y10 for photometric redshifts (photo-$z$) and weak lensing systematics. We specify the precise locations for the previously-chosen LSST deep fields (ELAIS-S1, XMM-LSS, CDF-S, and COSMOS) and recommend Akari Deep Field South as the planned fifth deep field in order to synergize with Euclid and WFIRST. Our recommended DDF strategy uses $6.2%$ of the LSST survey time. We briefly discuss synergy with white papers from other collaborations, as well as additional mini-surveys and Target-of-Opportunity programs that lead to better measurements of dark energy.
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