Precision Dark Energy Measurements using Gravitational Lensing 

Royal Society Funded PhD, 4 years 

Supervisor: Dr. Thomas Kitching

Weak gravitational lensing (known as ‘weak lensing’) is the effect whereby light from distant galaxies is slightly perturbed along the line of sight by intervening dark matter structures. By measuring these distortions we can simultaneously measure the expansion history of the Universe, and the growth of structure over time. These aspects of the Universe depend on the properties of dark energy in different ways, making weak lensing a particularly sensitive probe of this phenomenon. The problem of dark energy can scarcely be exaggerated, its energy density accounts for approximately 70% of the total Universal energy budget, and the possible theoretical explanations require either a change to general relativity, an additional force or field, or multiverses to exist. During my fellowship to date I have developed the state-of-the-art in weak lensing analysis. This is the first and only fully three-dimensional analysis of gravitational lensing data (Kitching et al., 2014, MNRAS, 442, 1326). However there are several assumptions that enter the cosmic shear statistic that have not been included in data analyses to date, but could be critical for next generation experiments. These are technical approximations that are made at the mathematical level in order to make calculations easier to compute and to simplify analyses. In now particular order these are:

• The Limber Approximation. This makes the assumption that a spherical-Bessel transform of a 3D field (i.e. the cosmic shear field) can be instead represented as a spherical-Delta function expansion (Kaiser, 1998; ISBN: 2-8 6332-241-9; LoVerde & Afshordi, 2008, PRD, 78, 12). For current surveys this is expected to be a small effect, but for Euclid and LSST this assumption must be relaxed. Only Kitching et al. (2014, MNRAS, 442, 1326) have applied a non-Limber approximated statistic to data.

• Reduced Shear. When measuring weak lensing from data a non-linear combination of the ellipticity (the quantity of interest) and convergence (an overall scaling of an object) is measured. This leads to third order corrections to the cosmic shear power spectrum (Shapiro, 2009 AJ, 696, 775; Krause & Hirata, 2010, A&A, 523, 28), that can affect Euclid-like surveys. Such effects have not been accounted for in any current analysis, and can have up to a 10% effect on the amplitude of the cosmic shear power spectrum at scales of l~1000 (scales of ~10 Mpc).  

• Unequal-time Power Spectra. The standard cosmic shear power spectrum assumes that correlations in the matter density field δ(k, t) at different times can be approximated by a single time-slice i.e. <δ(k, t1)δ(k, t2)>~P(k,t1) or <δ(k, t1)δ(k, t2)>~[P(k,t2)P(k,t1)]1/2. This is known as the equal-time ansatz. In Kitching & Heavens (2016, PRD, 95, 063522) it was shown that for cosmic shear surveys like Euclid this approximation may need to be relaxed such that equal-time power spectra are replaced by unequal-time power spectra that include the correlations between multiple time slices <δ(k, t1) δ(k, t2)>=P(k,t1, t2).

Each of these effects needs to be accounted for, however there are also dependencies between the effects. For example the calculations of Krause & Hirata (2010, 2010, A&A, 523, 28) for the reduced shear effect assume the Limber approximation, and the equal-time ansatz. A full treatment of all these effects is missing and is critical in order to understand the impact they may have on Euclid. This PhD will address these concerns.