### PhD Projects by Dr Jason McEwen

(Please see this page for more information)

### Weak Gravitational Lensing

Dr. Jason McEwen

We have recently entered an era of precision cosmology. The Big Bang cosmological model that describes our Universe explains many cosmological observations to exquisite accuracy, including the relic radiation of the Big Bang, the so-called cosmic microwave background (CMB). However, we remain ignorant of many of the components of this model. We know very little about dark matter and dark energy, which together constitute approximately 95% of the energy content of the Universe.Weak lensing is a powerful technique that can be used to uncover the secrets of dark energy. Weak lensing refers to the deflection of light due to the gravitational influence of intervening matter as it travels to us through the Universe. The lensing is weak in the sense that it is small and difficult to detect from a single background source, however its statistical impact can be studied.The goal of this project is to learn about dark energy through weak lensing. New analysis techniques will be developed to estimate the shear of galaxies due to weak lensing and to use this signal to constrain dark energy models. Novel 3D weak lensing techniques will also be developed. These new analysis techniques will build on recent developments in wavelet methods and compressive sensing, a revolutionary new development in the field of sampling theory. Data from current and forthcoming experiments will be used, such as the CFHTLenS and ESO KiDS surveys. The resulting analysis techniques are also expected to be used in the ESA Euclid mission, in which MSSL is playing a leading role.

### Cosmoinformatics

Dr Jason McEwen

Cosmological observations are inherently made on the celestial sphere, yielding data-sets defined on spherical manifolds, such as the sphere (e.g. surface of the Earth) and ball (e.g. interior of the Earth). For example, observations of the cosmic microwave background (CMB), the relic radiation of the Big Bang, are made on the sphere, while observations of the large-scale structure (LSS) of the Universe, such as clusters of galaxies, are made on the ball. However, signal processing techniques are typically restricted to Euclidean spaces.Signal processing techniques that live natively on spherical manifolds are thus required to analyse cosmological observations accurately. New signal representations, such as wavelets and learnt dictionaries, are required, in addition to new techniques for solving the inverse problems that typically arise in these settings. For example, denoising and deconvolution problems arise in a vast number of applications and, consequently, related algorithms have received considerable attention. However, many of these applications and algorithms have been restricted to Euclidean spaces, such as audio signals on the line and images on the plane, for example. Denoising and deconvolution algorithms for signals defined on the sphere, such as the CMB, have received relatively little attention.The goal of this project is to develop new signal representations on spherical manifolds and to apply these to solve inverse problems, such as denoising and deconvolution problems. The primary applications to be considered include the analysis of cosmological observations, such as the CMB. However, other domains of application, such as computer graphics, may also be considered.

### Machine learning and informatics techniques to detect cosmic strings

Dr. Jason McEwenÂ

Symmetry breaking phase transitions in the early Universe may have lead to the creation of topological defects. Cosmic strings are one particular type of defect, where axial or cylindrical symmetry is broken, leading to line-like discontinuities in the fabric of the Universe. Although we have not yet observed cosmic strings, we have observed string-like topological defects in other media, such as liquid crystals (see image). Note that cosmic strings are distinct to the fundamental superstrings of string theory. However recent developments in string theory suggest the existence of macroscopic superstrings, which could play a similar role to cosmic strings.Spacetime about a cosmic string is conical. Consequently, strings moving transverse to the line of sight induce line-like discontinuities in the cosmic microwave background (CMB), the relic radiation of the Big Bang. The detection of cosmic strings from CMB observations would open a new window into the physics of the early Universe.The goal of this project is to develop and apply methods to search for evidence of cosmic strings from observations of the CMB. In the absence of a detection, the allowable string tension (energy level) will be constrained. Novel techniques will be developed by combining ideas from Bayesian inference, machine learning and compressive sensing, a revolutionary new development in the field of sampling theory. Both Planck and WMAP observations of the CMB will be analysed.