Cosmographic degeneracy

We examine the dark energy and matter densities allowed by precision measurements of distances out to various redshifts, in the presence of spatial curvature and (near) arbitrary behavior of the dark energy equation of state. Degeneracies among the parameters permit a remarkably large variation in their values when using only distance measurements of the late-time universe and making no assumptions about the dark energy or curvature. Going beyond distance measurements to a lower limit on the growth of structure bounds the allowed region significantly but still leaves considerable freedom to match a flat Λ Cold Dark Matter model with dark energy very different from a cosmological constant. The combination of distances with Hubble parameter, gravitational lensing or other large-scale structure data is essential to determining the cosmological model robustly.