  Ground-based gravitational-wave detectors like Cosmic Explorer can be tuned
to improve their sensitivity at high or low frequencies by tuning the response
of the signal extraction cavity. Enhanced sensitivity above 2 kHz enables
measurements of the post-merger gravitational-wave spectrum from binary neutron
star mergers, which depends critically on the unknown equation of state of hot,
ultra-dense matter. Improved sensitivity below 500 Hz favors precision tests of
extreme gravity with black hole ringdown signals and improves the detection
prospects while facilitating an improved measurement of source properties for
compact binary inspirals at cosmological distances. At intermediate
frequencies, a more sensitive detector can better measure the tidal properties
of neutron stars. We present and characterize the performance of tuned Cosmic
Explorer configurations that are designed to optimize detections across
different astrophysical source populations. These tuning options give Cosmic
Explorer the flexibility to target a diverse set of science goals with the same
detector infrastructure. We find that a 40 km Cosmic Explorer detector
outperforms a 20 km in all key science goals other than access to post-merger
physics. This suggests that Cosmic Explorer should include at least one 40 km
facility.
