Illuminating dark energy with cosmic shear

TL;DR: In this article, a fiducial cosmic shear survey is used to determine the best-fit equation of state, which is assumed constant due to our poor understanding of its behavior (and since higher order parametrizations lead to unwieldy errors).

Abstract: One of the principal goals of modern cosmology is to constrain the properties of dark energy. At present, numerous surveys are aiming to determine the equation of state, which is assumed constant due to our poor understanding of its behavior (and since higher order parametrizations lead to unwieldy errors). This raises the question---how does our ``best-fit'' equation of state relate to the true function, which may vary with redshift. Saini et al. [Mon. Not. R. Astron. Soc. 343, 533 (2003).] have demonstrated that the value of $w$ attained by a supernova study is well described by a weighted integral over the true function. Adopting a similar approach, we calculate the corresponding ``weight function'' for a fiducial cosmic shear survey. We disentangle contributions from the angular diameter distance and the growth factor, finding that they partially cancel each other out. Consequentially, the sensitivity to $w$ at high redshift is enhanced beyond that of supernova studies, and is comparable, if not higher, than lensing of the cosmic microwave background. This illustrates the complementary nature of the different techniques. Furthermore, we find that results which would na\"{\i}vely be interpreted as inconsistent could arise from a time-dependent equation of state.