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Authors:  Rota, Stefano 
Internal Tutor:  TREVES, ALDO 
Tutor:  GUZZO, LUIGI BEL, JULIEN GRANETT, BEN 
Title:  Estimating the galaxy power spectrum of the VIPERS galaxy distribution. 
Abstract:  The power spectrum is a statistic that describes the clustering of matter in Fourier space. The shape and amplitude of the power are directly predicted by theory and direct measurements of the power can constrain cosmological parameters.
The large size of recent surveys has opened new windows in the observation of secondary features of the galaxy power spectrum such as the Baryonic Acoustic Oscillations (BAO), which used as standard ruler can infer dark energy properties, and RedshiftSpace Distortions (RSD), which thanks to the anisotropic observed clustering in redshift space can discriminate between different theories of gravity.
In this thesis, we apply the power spectrum statistic to the VIMOS Public Extragalactic Redshift Survey (VIPERS) distribution of galaxies in order to study the underlying clustering of matter.
VIPERS is an ongoing spectroscopic survey, composed of two fields, W1 and W4, with the aim of mapping the spatial distribution of galaxies within a large volume of the z ∼ 1 Universe. The main properties of VIPERS are the high redshift range surveyed 0.4 < z < 1.2 and the high sampling rate at those redshifts.
Its main goal is the measurement of the anisotropy of the galaxy clustering in redshift space in order to constrain the growth rate of structure at a mean redshift hzi ∼ 0.8, never reached by other surveys.
Even the measure of the galaxy power spectrum at these redshifts is something new. Our goal is to estimate the clustering of matter in Fourier space constraining the cosmological quantities that mainly affect the power spectrum shape such as the matter density and the baryonic fraction. The approach used to estimate the galaxy power spectrum is quite classical and has been used in past surveys such as the Two Degree Field Galaxy Redshift Survey (2dFGRS).
We describe the power spectrum estimator using a novel simulation approach called “Γ”simulation, including the main properties of a real survey such as the conelike geometry and the density gradient function of the redshift.
The main factor that alters our power spectrum measurement is the window function, due to the limited size of the sample, which is not negligible even for a box geometry.
We show a method to correctly take into account the window function effects including it with a three dimensional convolution with the input model of the simulation.
To analyse the potential of the VIPERS sample for extracting cosmological information, we use a set of VIPERS mock catalogues drawn from the MultiDark simulation. We analyse all the selection function effects of the survey, such as the sampling strategy and the decreasing mean density, in our estimation and study their effect on the recovered power spectrum.
The VIPERS window function is problematic due to the small angular coverage, strongly suppressing the clustering in Fourier space at large scales and completely damping the BAO signal. We measure the window function of VIPERS which will be used to perform a three dimensional convolution with the theoretical model generated from the tested cosmology.
RSD also determine the observed clustering and, in the simplest case, their impact could be divided in two regimes. Small scale effects due to the high nonlinear velocity of galaxies inside virialised structures are corrected with a simple velocity dispersion model, an empirical prediction of the behaviour of the clustering in redshift space. Large scale effects due to the linear infall of galaxies in high density peaks, which increase the observed clustering of matter, are included with the Kaiser term dependent on the linear growth rate of matter. We include these two terms before applying the 3D convolution of the model with the window function.
Some tests are performed on VIPERS mock catalogues to recover the known cosmological information of the simulation with a chisquare technique and, in all cases, we were able to extract the input cosmology with lower systematics errors than statistical ones.
Finally we apply this approach to the data dividing the full survey into four subsamples, two redshift bins, 0.6 < z1 < 0.9 and 0.9 < z2 < 1.1, for each field. Despite the different window functions in each subsample due to small differences in volume and in geometry, the four measurements are consistent with each other. This is due to the fact that, at large scales, statistical fluctuations related to cosmic variance are much bigger with respect to small differences in the window. Even the overall amplitude is similar between the two redshift bins because the lower amplitude expected for the higher redshift power spectrum (because structures were less compact in the past) is compensated by the higher bias factor.
We compare the measured power spectrum from data with some theoretical models in order to extract the baryonic fraction and the amount of matter density in the Universe. The probability contours display evidence of a wellknown degeneracy previously observed in other surveys (such as 2dFGRS) between the two recovered parameters in the determination of the overall shape of the matter power spectrum. Increasing the matter density of the Universe in fact shifts the power spectrum toward higher modes enhancing the clustering at the scales sampled by VIPERS. In this case to compensate the increase of power, the good fit is given by models with high baryonic fraction necessary to suppress the power at those scales. Viceversa a lowM Universe does not need a high baryonic fraction. This degeneracy is broken combining the two redshift bins with a joint likelihood.
Finally, we provide an estimation of the matter density fixing all the other cosmological parameters to the best known values. We evaluate the matter density to be M = 0.272+0.027 −0.031 in perfect agreement with Planck (once we rescale the Hubble factor from the Hubble Space Telescope used for the estimation of M to be consistent with the Planck one) and with the matter density estimated from the VIPERS Public Data Release1 measurements of the clustering ratio. 
Keywords:  missing 
Subject MIUR :  FIS/05 ASTRONOMIA E ASTROFISICA 
Issue Date:  2014 
Language:  eng 
Doctoral course:  Astronomia e Astrofisica 
Academic cycle:  27 
Publisher:  Università degli Studi dell'Insubria 
Citation:  Rota, S.Estimating the galaxy power spectrum of the VIPERS galaxy distribution. (Doctoral Thesis, Università degli Studi dell'Insubria, 2014). 

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