GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run

The second Gravitational-Wave Transient Catalog reported on 39 compact binary coalescences observed by the Advanced LIGO and Advanced Virgo detectors between 1 April 2019 15:00 UTC and 1 October 2019 15:00 UTC. We present GWTC-2.1, which reports on a deeper list of candidate events observed over the same period. We analyze the final version of the strain data over this period with improved calibration and better subtraction of excess noise, which has been publicly released. We employ three matched-filter search pipelines for candidate identification, and estimate the astrophysical probability for each candidate event. While GWTC-2 used a false alarm rate threshold of 2 per year, we include in GWTC-2.1, 1201 candidates that pass a false alarm rate threshold of 2 per day. We calculate the source properties of a subset of 44 high-significance candidates that have an astrophysical probability greater than 0.5. Of these candidates, 36 have been reported in GWTC-2. If the 8 additional high-significance candidates presented here are astrophysical, the mass range of events that are unambiguously identified as binary black holes (both objects $\geq 3M_\odot$) is increased compared to GWTC-2, with total masses from $\sim 14 M_\odot$ for GW190924_021846 to $\sim 182 M_\odot$ for GW190426_190642. The primary components of two new candidate events (GW190403_051519 and GW190426_190642) fall in the mass gap predicted by pair instability supernova theory. We also expand the population of binaries with significantly asymmetric mass ratios reported in GWTC-2 by an additional two events (the mass ratio is less than $0.65$ and $0.44$ at $90\%$ probability for GW190403_051519 and GW190917_114630 respectively), and find that 2 of the 8 new events have effective inspiral spins $\chi_\mathrm{eff}>0$ (at $90\%$ credibility), while no binary is consistent with $\chi_\mathrm{eff}<0$ at the same significance.