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Obtaining the Best Cosmological Information from CMB, CMB Lensing and Galaxy Information

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Obtaining the Best Cosmological Information from CMB, CMB Lensing and Galaxy Information Obtaining the best cosmological information from CMB, CMB lensing and galaxy information. Larissa Santos P.H.D thesis in Astronomy Supervisors: Amedeo Balbi and Paolo Cabella Rome 2012 Contents 1 Prologue 1 2 Introduction: The standard cosmology 3 2.1 The ΛCDM model: an overview . .3 2.2 The expanding universe . .4 2.2.1 The Friedmann Robertson-Walker metric . .4 2.2.2 Cosmological distances . .5 2.3 The discovery of CMB . .6 2.4 Temperature anisotropies . .7 2.4.1 Primary temperature anisotropies . .8 2.4.2 Secondary temperature anisotropies . .9 2.5 CMB temperature angular power spectrum . 10 2.6 Cosmological parameters . 12 2.7 Polarization . 13 2.8 The matter power spectrum . 16 2.9 The ΛCDM model + primordial isocurvature fluctuations . 17 2.10 The CDM model + massive neutrinos + time evolving dark en- ergy equation of state . 19 2.11 The script of the present thesis . 20 I Asymmetries in the angular distribution of the CMB 22 3 The WMAP satellite and used dataset 23 3.1 Internal linear combination maps . 24 3.2 The WMAP masks . 25 4 The quadrant asymmetry 28 4.1 Mehod: The two-point angular correlation function . 29 4.2 Results . 30 4.2.1 The cold spot . 38 i 4.3 Discussion . 38 4.4 Conclusions . 41 II Constraining cosmological parameters 43 5 The Planck satellite 44 6 The SDSS galaxy survey 46 7 Mixed models (adiabatic + isocurvature initial fluctuations) 48 7.1 Isocurvature notation . 48 7.2 Methodology . 49 7.2.1 Information from CMB . 49 7.2.2 Information from galaxy survey . 52 7.3 Results . 53 7.4 Discussion and conclusions . 57 8 Euclid survey 66 9 SCM with massive neutrinos and a time evolving dark energy equation of state. 68 9.1 Methodology . 68 9.1.1 Information from CMB . 68 9.1.2 Information from galaxy survey . 71 9.2 Fiducial models . 74 9.3 Preliminary results . 75 9.4 Discussion and conclusions . 80 ii List of Figures 2.1 The CMB blackbody spectrum. .7 2.2 Angular power spectrum obtained by the Wilkinson microwave anisotropy probe (WMAP). 11 2.3 Sensitivity of the temperature angular power spectrum to four different cosmological parameters. 14 2.4 The 7-year temperature-polarization cross correlation power spec- trum (TE) and the EE power spectrum. 15 2.5 The matter power spectrum for different experiments datasets in z =0. ................................. 17 2.6 Comparison of the temperature angular power spectrum for a purely adiabatic and purely isocurvature models. 18 3.1 The WMAP satellite leaving Earth/Moon orbit for L2 . 24 3.2 WMAP temperature maps for the 7 years data release in 2011 are seen in the left column. The right column displays the difference between the 7 year maps and the previous maps from the 5 years WMAP data release. 26 3.3 ILC 7 year map produced by the WMAP team. 27 4.1 TPCF curves computed for the WILC7 map using the WMAP KQ85 mask, smoothed for illustration purposes.The NWQ (top) and the NEQ (bottom) appear as solid red lines. The shadow part depicts the standard deviation intervals for 1000 simulated maps produced with the ΛCDM spectrum. 31 4.2 Same as Figure 4.1, but now with the SWQ at the top and the SEQ at the bottom. 32 4.3 Same as Figure 4.1, but now using the WMAP KQ85 mask + jbj < 10◦ Galactic cut in the temperature WMAP7 data. From top to bottom, the curves refer to the NWQ and the NEQ, re- spectively................................ 33 iii 4.4 Same as Figure 4.3. From top to bottom, the curves refer to the SWQ and the SEQ, respectively. 34 4.5 Same as Figures 4.1-4.4, but now using jbj < 10◦ Galactic cut, again in the temperature WILC7 map. From top to bottom the curves refer to the NWQ and the NEQ, respectively. 35 4.6 Same as Figure 4.5 for the SWQ (top) and the SEQ (bottom). 36 4.7 Top: Comparison between the SEQ quadrant for the TPCF using the KQ85 mask + these circular masks centered on the cold spot can be seen with a radius of 5 degrees (red line), 10 degrees (yellow line) and 15 degrees (green line). The black line refers to the function without masking the Cold Spot. Bottom: TPCF for the WMAP7 map using KQ85 + circular masks centered on the specified angles with a radius of 15 degrees each. The red dashed-dot curve refers to the Cold Spot region. 39 4.8 Comparison between NWQ (top-lef), NEQ (top-right), SWQ (bottom- left) and SEQ (bottom-right) for the TPCF using the KQ85 mask (solid blue line) and the KQ85y7 (solid red line). 40 5.1 Planck satellite . 44 6.1 SDSS survey telescope . 46 6.2 Large scale structure in the Northern equatorial slice of SDSS main galaxy redshift sample. 47 7.1 Fisher contours for ΛCDM model plus a contribution of initial isocurvature fluctuation with fiducials amplitude of α = 0:06, correlation phase of β = 0 and scalar spectral index of niso = 2:7 for the axion scenario. The red and blue contours represent 95.4% and 68% C.L., respectively, for the unlesed CMB + SDSS (dashed lines) and for the lensed CMB + SDSS (solid lines)(see Table 9.3). 61 7.2 Fisher contours for ΛCDM model plus a contribution of initial isocurvature fluctuation with fiducials amplitude of α = 0:06, correlation phase of β = 0 and scalar spectral index of niso = 0:982 for the axion scenario. The red and blue contours represent 95.4% and 68% C.L. respectively for the unlesed CMB + SDSS (dashed lines) and for the lensed CMB + SDSS (solid lines) (see Table 9.5). 62 iv 7.3 Fisher contours for ΛCDM model plus a contribution of initial isocurvature fluctuation with fiducials amplitude of α = 0:003, correlation phase of β = −1 and scalar spectral index of niso = 0:984 for the curvaton scenario. The red and blue contours rep- resent 95.4% and 68% C.L. respectively for the unlesed CMB + SDSS (dashed lines) and for the lensed CMB + SDSS (solid lines). In this case we consider β fixed (see Table 7.7). 63 7.4 CMB power spectra derivatives in respect to the isocurvature parameters α (purple) and β(red). The dashed darker lines are related to the unlensed power spectra's derivative and the solid lighter ones are related to the lensed power spectra's derivative for the axion scenario of α = 0:06, β = 0. On the left column the scalar spectral index is niso = 2:7 and on the right column the scalar spectral index is niso = 0:982 . 64 7.5 The same as Figure 7.4 but now the scalar spectral index is niso = 0:982.................................. 65 8.1 An Euclid satellite illustration . 66 9.1 Fisher contours for our model 1. The red and blue contours represent 95.4% and 68% C.L. respectively for the unlesed CMB (dashed lines) and for Euclid galaxy survey (solid lines). 77 9.2 Fisher contours for our model 2. The red and blue contours represent 95.4% and 68% C.L. respectively for the unlesed CMB (dashed lines) and for Euclid galaxy survey (solid lines). 78 9.3 Fisher contours for our model 3. The red and blue contours represent 95.4% and 68% C.L. respectively for the unlesed CMB (dashed lines) and for Euclid galaxy survey (solid lines). 79 v List of Tables 2.1 Six-parameters ΛCDM fit (Larson et al. , 2011) . 13 4.1 Calculated probabilities of finding the same asymmetries as in WMAP data in the MC simulations using the WMAP KQ85 mask and considering the ΛCDM model. 37 4.2 Calculated probabilities of finding the same asymmetries as in WMAP data in the MC simulations using the WMAP KQ85 mask + jbj < 10◦ Galactic cut and considering the ΛCDM model. 37 4.3 Calculated probabilities of finding the same asymmetries as in WMAP data in the MC simulations using the jbj < 10◦ Galactic cut and considering the ΛCDM model. 37 4.4 Sigma ratios for the simulated CMB maps considering the ΛCDM model and the three Galactic cuts. 38 4.5 Calculated probabilities of finding the same asymmetries as in WMAP data in the MC simulations using the WMAP KQ85 mask and considering the MΛCDM model. 41 7.1 Planck specifications . 50 7.2 Marginalized errors for ΛCDM model plus a contribution of initial isocurvature fluctuation with fiducials amplitude of α = 0:06, correlation phase of β = 0 and scalar spectral index of niso = 2:7. 54 7.3 The same as Table 9.3, but in this case β = 0 will be kept fixed. 55 7.4 Marginalized errors for ΛCDM model plus a contribution of initial isocurvature fluctuation with fiducials amplitude of α = 0:06, correlation phase of β = 0 and scalar spectral index of niso = nad = 0:982. 56 7.5 The same as Table 9.5, but in this case β = 0 will be kept fixed. 57 7.6 Marginalized errors for ΛCDM model plus a contribution of initial isocurvature fluctuation with fiducials amplitude of α = 0:003, correlation phase of β = −1 and scalar spectral index of niso = 0:984. 58 vi 7.7 The same as Table 9.4, but in this case β = −1 will be kept fixed. 59 9.1 Values of kmax, the galaxy bias and the galaxy density for each redshift bin. 74 9.2 Fiducial models . 75 9.3 Marginalized errors for ΛCDM model with three massive neutri- nos with identical mass (mν = 0.310 eV) .
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