124311895
Evaluation of correlation functions in integrable quantum field theories
The aim of this thesis is to explore correlation functions in two dimensional quantum field theories in two distinct ways. In part I a new method for calculating the differential equations parametrising the correlation functions of twist fields associated with the U (1) symmetry of the Dirac model is presented. While developing this method a new family of descendent twist fields are identified and their form factors calculated. This provides a novel way of calculating the vacuum expectation values of the primary twist fields and is shown to be entirely consistent with known results. The method of calculating the correlation functions of twist fields provides a parametrisation of several other correlation functions for various quantum states. Since this method relies on the Ward identities found in a double copy model it is hoped to have wider applications in other free fermion models. Part II concerns the truncated conformal space approach which has been developed to approximate perturbed conformal field theories. In this part the theory underpinning the approach is discussed and a working algorithm is developed for both bulk and boundary perturbed minimal models. The energy levels, mass gaps and one point functions of various models are computed using the truncated conformal space approach and are shown to be in good agreement with previous calculations. A possible method for using this approach to approximate two point functions in perturbed conformal field theories is discussed.
119268926
More general correlation functions of twist fields from Ward identities in the massive Dirac theory
Following on from previous work we derive the nonlinear differential equations of more general correlators of U(1) twist fields in two-dimensional massive Dirac theory. Using the conserved charges of the double-copy model equations parametrizing the correlators of twist fields with arbitrary twist parameter are found. This method also gives a parametrization of the correlation functions of general, fermionic, descendent twist fields. The equations parametrizing correlators of primary twist fields are compared to those of the literature and evidence is presented to confirm that these equations represent the correct parametrization.
118050107
Extreme value statistics of smooth random Gaussian fields
We consider the Gumbel or extreme value statistics describing the distribution function p_G(x_max) of the maximum values of a random field x within patches of fixed size. We present, for smooth Gaussian random fields in two and three dimensions, an analytical estimate of p_G which is expected to hold in a regime where local maxima of the field are moderately high and weakly clustered. When the patch size becomes sufficiently large, the negative of the logarithm of the cumulative extreme value distribution is simply equal to the average of the Euler Characteristic of the field in the excursion x > x_max inside the patches. The Gumbel statistics therefore represents an interesting alternative probe of the genus as a test of non Gaussianity, e.g. in cosmic microwave background temperature maps or in three-dimensional galaxy catalogs. It can be approximated, except in the remote positive tail, by a negative Weibull type form, converging slowly to the expected Gumbel type form for infinitely large patch size. Convergence is facilitated when large scale correlations are weaker. We compare the analytic predictions to numerical experiments for the case of a scale-free Gaussian field in two dimensions, achieving impressive agreement between approximate theory and measurements. We also discuss the generalization of our formalism to non-Gaussian fields.
118684371
Primordial non-Gaussianity and extreme-value statistics of galaxy clusters
What is the size of the most massive object one expects to find in a survey of a given volume? In this paper, we present a solution to this problem using Extreme-Value Statistics, taking into account primordial non-Gaussianity and its effects on the abundance and the clustering of rare objects. We calculate the probability density function (pdf) of extreme-mass clusters in a survey volume, and show how primordial non-Gaussianity shifts the peak of this pdf. We also study the sensitivity of the extreme-value pdfs to changes in the mass functions, survey volume, redshift coverage and the normalization of the matter power spectrum, {\sigma}_8. For 'local' non-Gaussianity parametrized by f_NL, our correction for the extreme-value pdf due to the bias is important when f_NL > O(100), and becomes more significant for wider and deeper surveys. Applying our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find that its existence is consistent with f_NL = 0, although the conclusion is sensitive to the assumed values of the survey area and {\sigma}_8. We also discuss the convergence of the extreme-value distribution to one of the three possible asymptotic forms, and argue that the convergence is insensitive to the presence of non-Gaussianity.
16010721
Reionization and cosmic microwave anisotropies
The effects of reionization, occurring after standard recombination in cold dark matter-dominated models, on cosmic microwave background (CMB) anisotropies are investigated. Late-time reionization reduces the CMB anisotropies, in particular, on degree scales. It is found that constraints on cold dark matter-dominated models from the highest frequency channel of the 9-point South Pole data are significantly relaxed for models which are consistent with big bang nucleosynthesis if reionization is assumed to have occurred by redshift ∼20
15837031
Reconstruction of primordial density fields
The Monge–Ampere–Kantorovich (MAK) reconstruction is tested against cosmological N-body simulations. Using only the present mass distribution sampled with particles, and the assumption of homogeneity of the primordial distribution, MAK recovers for each particle the non-linear displacement field between its present position and its Lagrangian position on a primordial uniform grid. 
 
 
 
To test the method, we examine a standard Lambda cold dark matter (ΛCDM) N-body simulation with Gaussian initial conditions and six models with non-Gaussian initial conditions: a χ2 model, a model with primordial voids and four weakly non-Gaussian models. 
 
 
 
Our extensive analyses of the Gaussian simulation show that the level of accuracy of the reconstruction of the non-linear displacement field achieved by MAK is unprecedented, at scales as small as ∼3 h−1 Mpc. In particular, it captures in a non-trivial way the non-linear contribution from gravitational instability, well beyond the Zel'dovich approximation. This is also confirmed by our analyses of the non-Gaussian samples. 
 
 
 
Applying the spherical collapse model to the probability distribution function of the divergence of the displacement field, we also show that from a well-reconstructed displacement field, such as that given by MAK, it is possible to accurately disentangle dynamical contributions induced by gravitational clustering from possible initial non-Gaussianities, allowing one to efficiently test the non-Gaussian nature of the primordial fluctuations. 
 
 
 
In addition, we test successfully a simple application of MAK using the Zel'dovich approximation to recover in real space the present-day peculiar velocity field on scales of 8 h−1 Mpc. 
 
 
 
Although non-trivial observational issues yet remain to be addressed, our numerical investigations suggest that MAK reconstruction represents a very promising tool to be applied to three-dimensional Galaxy catalogues.
119293493
Direct gravitational imaging of intermediate mass black holes in extragalactic haloes
A galaxy halo may contain a large number of intermediate mass black holes (IMBHs) with masses in the range of 10^{2-6} solar mass. We propose to directly detect these IMBHs by observing multiply imaged QSO-galaxy or galaxy-galaxy strong lens systems in the submillimeter bands with high angular resolution. The silhouette of an IMBH in the lensing galaxy halo would appear as either a monopole-like or a dipole-like variation at the scale of the Einstein radius against the Einstein ring of the dust-emitting region surrounding the QSO. We use a particle tagging technique to dynamically populate a Milky Way-sized dark matter halo with black holes, and show that the surface mass density and number density of IMBHs have power-law dependences on the distance from the center of the host halo if smoothed on a scale of ~ 1 kpc. Most of the black holes orbiting close to the center are freely roaming as they have lost their dark matter hosts during infall due to tidal stripping. Next generation submillimeter telescopes with high angular resolution (< 0.3 mas) will be capable of directly mapping such off-nuclear freely roaming IMBHs with a mass of ~ 10^6 solar mass in a lensing galaxy that harbours a O(10^9) solar mass supermassive black hole in its nucleus.