Redshift drift provides a direct kinematic measurement of cosmic acceleration but it occurs with a characteristic time scale of a Hubble time. Thus redshift observations with a challenging precision of $10^{-9}$ require a 10 year time span to obtain
a signal-to-noise of 1. We discuss theoretical and experimental approaches to address this challenge, potentially requiring less observer time and having greater immunity to common systematics. On the theoretical side we explore allowing the universe, rather than the observer, to provide long time spans; speculative methods include radial baryon acoustic oscillations, cosmic pulsars, and strongly lensed quasars. On the experimental side, we explore beating down the redshift precision using differential interferometric techniques, including externally dispersed interferometers and spatial heterodyne spectroscopy. Low-redshift emission line galaxies are identified as having high cosmology leverage and systematics control, with an 8 hour exposure on a 10-meter telescope (1000 hours of exposure on a 40-meter telescope) potentially capable of measuring the redshift of a galaxy to a precision of $10^{-8}$ (few $times 10^{-10}$). Low-redshift redshift drift also has very strong complementarity with cosmic microwave background measurements, with the combination achieving a dark energy figure of merit of nearly 300 (1400) for 5% (1%) precision on drift.
Kim et al. (2013) [K13] introduced a new methodology for determining peak-brightness absolute magnitudes of type Ia supernovae from multi-band light curves. We examine the relation between their parameterization of light curves and Hubble residuals,
based on photometry synthesized from the Nearby Supernova Factory spectrophotometric time series, with global host-galaxy properties. The K13 Hubble residual step with host mass is $0.013pm 0.031$ mag for a supernova subsample with data coverage corresponding to the K13 training; at $ll 1sigma$, the step is not significant and lower than previous measurements. Relaxing the data coverage requirement the Hubble residual step with host mass is $0.045pm 0.026$ mag for the larger sample; a calculation using the modes of the distributions, less sensitive to outliers, yields a step of 0.019 mag. The analysis of this article uses K13 inferred luminosities, as distinguished from previous works that use magnitude corrections as a function of SALT2 color and stretch parameters: Steps at $>2sigma $ significance are found in SALT2 Hubble residuals in samples split by the values of their K13 $x(1)$ and $x(2)$ light-curve parameters. $x(1)$ affects the light-curve width and color around peak (similar to the $Delta m_{15}$ and stretch parameters), and $x(2)$ affects colors, the near-UV light-curve width, and the light-curve decline 20 to 30 days after peak brightness. The novel light-curve analysis, increased parameter set, and magnitude corrections of K13 may be capturing features of SN~Ia diversity arising from progenitor stellar evolution.
This document presents the results from the Distances subgroup of the Cosmic Frontier Community Planning Study (Snowmass 2013). We summarize the current state of the field as well as future prospects and challenges. In addition to the established pro
bes using Type IA supernovae and baryon acoustic oscillations, we also consider prospective methods based on clusters, active galactic nuclei, gravitational wave sirens and strong lensing time delays.
