. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 CHAPTER 1: INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 CHAPTER 2: ONE-DIMENSIONAL POWER SPECTRUM . . . . . . . . . . . . 17 2.1 Three-Dimensional Power Spectrum . . . . . . . . . . . . . . . . . . . . . 17 2.2 One-Dimensional Power Spectrum . . . . . . . . . . . . . . . . . . . . . . 19 2....

We study perturbations of the Drazin inverse of a closed linear operator A for the case when the perturbed operator has the same spectral projection as A. This theory subsumes results recently obtained by Wei and Wang, Rakočević and Wei, and Castro and Koliha. We give explicit error estimates for the perturbation of Drazin inverse, and error estimates involving higher powers of the operators.

We study the behaviour of the power spectrum (PS) in the case of fractal structures. We show that in this case the main observational features of the PS, the large scale flattening and the scaling of the amplitude with sample depth, are related to finite size effects, due to the fractal nature of galaxy distribution in the sample. Comparing with the recent results of the PS for the CfA2 we conc...

Gaussianity and statistical isotropy of the universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By de ning the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperat...

We modify the public PM code developed by Anatoly Klypin and Jon Holtzman to simulate cosmology with arbitrary initial power spectrum and equation of state of dark energy. With this tool in hand, we perform the following studies on the matter power spectrum. With an artificial sharp peak at k ∼ 0.2hMpc in the initial power spectrum, we find that the position of the peak is not shifted by nonlin...

Inflationary attractors predict the spectral index and tensor-to-scalar ratio to take specific values that are consistent with Planck. An example is the universal attractor for models with a generalised non-minimal coupling, leading to Starobinsky inflation. In this paper we demonstrate that it also predicts a specific relation between the amplitude of the power spectrum and the number of e-fol...

We reconstruct the shape of the primordial power spectrum from the latest cosmic microwave background data, including the new results from the Wilkinson Microwave Anisotropy Probe (WMAP), and large scale structure data from the two degree field galaxy redshift survey (2dFGRS). We tested four parameterizations taking into account the uncertainties in four cosmological parameters. First we parame...

The combination of Cosmic Microwave Background (CMB) anisotropy measurements and Large-Scale Structure observations has caused dissatisfaction with the standard Cold Dark Matter (sCDM) cosmogony, leading some to advocate a “tilt” of the primordial power spectrum away from scale-invariant (n = 1) to n = 0.8− 0.9. 1 Other CDM cosmogonies have not commonly been tilted but their agreement with the ...

Semi-analytic treatment of the power spectrum with the approximation of constant linear bias provides a way to compare cosmological models to a large amount of data, as Peacock & Dodds (1994, 1996; hereafter PD94 and PD96, respectively) have shown. By applying the appropriate corrections to the observational power spectrum it is possible to recover the underlying linear power spectrum for any g...

We provide a simple, unified approach to describing the impact of super-sample covariance on power spectrum estimation in a finite-volume survey. For a wide range of survey volumes, the sample variance that arises from modes that are larger than the survey dominates the covariance of power spectrum estimators for modes much smaller than the survey. The perturbative and deeply nonlinear versions...