Cosmic flexion, like cosmic shear, is a correlation function whose signal originates from the large-scale structure of the universe. Building on the observational success of cosmic shear, along with the unprecedented quality of large-scale cosmological datasets, the time is ripe to explore the practical constraints from cosmic flexion. Unlike cosmic shear, which has a broad window function for power, cosmic flexion is only measurable on small scales and therefore can uniquely place constraints on the small-scale matter power spectrum. Here, we present a full theoretical formalism for cosmic flexion, including both flexion-flexion and shear-flexion two-point correlations. We present forecasts for measuring cosmic flexion in the Dark Energy Survey (DES), a Stage III cosmological survey, and comment on the future prospects of measuring these cosmological flexion signals in the upcoming era of Stage IV experiments.

21 pages, 9 figures; accepted for publication in Phys.Rev.D; revisions to Section IV. A and Appendix A, as well as other minor changes from submitted version