Secondary Signals in Cosmology By Zhen Pan B.S. (University of Science and Technology of China) 2010 M.S. (University of Science and Technology of China) 2013 Dissertation Submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Office of Graduate Studies of the University of California Davis Approved: Chair Lloyd Knox Andreas Albrecht Christopher Fassnacht Committee in Charge 2018 -i- � � � � ProQuest Number:10823014 � � � � All rights reserved � INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. � In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. � � � � � ProQuest 10823014 � Published by ProQuest LLC ( 2018). Copyright of the Dissertation is held by the Author. � � All rights reserved. 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To the Best of Times. -ii- Contents List of Figures . vi List of Tables . .................. xi Abstract . ................... xii Acknowledgments . xiii 1 Introduction 1 1.1 History of Thermal Big Bang: background . 2 1.1.1 Inflation and Reheating . 2 1.1.2 Annihilation, Recombination and Reionization . 3 1.1.3 Dark Energy . ............. 4 1.2 History of Big Bang: perturbation . 5 1.2.1 Initial Conditions . ........... 6 1.2.2 Baryon Acoustic Oscillation and CMB . 7 1.2.3 Dark Matter Collapse and Matter Power Spectrum . 7 1.3 Overview of My Research . ........... 8 2 Dependence of the Cosmic Microwave Background Lensing Power Spec- trum on the Matter Density 11 2.1 Introduction . 11 2.2 The spectrum below� = 1000 andω m .................... 12 2.3 Introduction to the lensing power spectrum . 13 2.4 The dependence of lensing power spectrum on matter density . 16 2.4.1 Qualitative Analysis . 16 2.4.2 Quantitative Analysis . 18 2.5 Discussion . .................. 20 3 Constraints on Neutrino Mass from Cosmic Microwave Background and Large Scale Structure 22 3.1 Introduction . 22 -iii- 3.2 Signatures of non-zero neutrino mass . 23 3.3 Influence of massive neutrinos on galaxy survey observables . 25 3.4 Influence of massive neutrinos on the CMB lensing power spectrum . 28 3.4.1 Introduction to the lensing power spectrum . 28 3.4.2 Influence of massive neutrinos on the lensing power spectrum: results 30 3.5 Forecast of constraints on the total neutrino mass from different data sets 33 3.5.1 CMB-S4 and DESI BAO . 33 3.5.2 Beyond DESI BAO . 34 3.6 Conclusion . 36 4 Cosmic Microwave Background Acoustic Peak Locations 38 4.1 Introduction . 38 4.2 Baseline Model . 40 4.2.1 Before Recombination . 40 4.2.2 After Recombination . 42 4.3 Evolution of phase shifts in the photon perturbations . 44 4.3.1 Decoupling:φ dcp .................... 45 4.3.2 Transient:φ gr,γ .................... 46 4.3.3 Neutrinos:φ gr,ν .................... 46 4.4 Phase shifts in photon perturbations at the LSS . 47 4.5 Projection . .................. 49 4.5.1 A Rigorous Treatment of Projection . 50 4.5.2 Corrections to the Baseline Model . 51 4.6 Comparison of predicted and measured peak locations . 57 4.7 Conclusions . 59 4.8 Appendix . .................. 60 4.8.1φ dcp .................... 60 4.8.2φ gr,γ .................... 62 4.8.3φ gr,ν .................... 63 -iv- 5 Searching for Signatures of Dark Matter-Dark Radiation Interaction in Observations of Large-scale Structure 65 5.1 Introduction . 65 5.2 Canonical DM-DRF Interaction Model . 67 5.2.1 LSS . .................. 68 5.2.2 CMB . 70 5.3 Parameter constraints from LSS data . 73 5.3.1 Previous Analyses . 73 5.3.2 Anaysis with SZ data: the impact of the mass bias parameter . 75 5.3.3 Analysis with only CMB Lensing and DES data . 77 5.4 Lyman-α forest data . 78 5.5 Generalized dm-drf models . 80 5.6 Summary . .................. 82 -v- List of Figures 2.1 The lensing power spectrum calculated from CAMB (solid line), calculated with Limber approximation (dashed line) and calculated with Limber ap- proximation and settingg(a) = 1 (dash-dotted line). 15 2.2 Factors in the integrand of the lensing power spectrum for large� = 800 (upper panel) and small� = 20 (lower panel). 17 2.3 The dependence of the lensing power spectrum on the matter density, �4Cφφ (ω )n. The solid line is the numerical result from CAMB, the � ∼ m dashed line is the result of the analytic scaling law derived in the text (n=0.75(m + 1) + 0.58) and the dash-dotted line is the result of the Limber approximation settingg(a)=1.................... 19 2.4 The contribution of each multipole of the CMB lensing power spectrum, φφ TT C� to the lensing of the CMB temperature power spectrum,C L , as- suming ourfiducial cosmology (WMAP9 best-fitΛCDM model), for two values ofL near acoustic peaks (1455 and 2075), and two values near troughs (1300 and 2245). 20 3.1 The dependence of expansion rateH(z) and comoving angular diameter 2 distanceD A(z) onM ν, where we minimize theχ (Θ,Mν) by adjusting the 6ΛCDM parametersΘ when increasingM ν from 0 to 50, 100, 200 meV. 26 3.2 The dependence of structure growth rate onM ν, where we minimize the 2 χ (Θ,Mν) by adjusting the 6ΛCDM parametersΘ when increasingM ν from 0 to 20 meV. 26 3.3 The lensing power spectrum calculated from CLASS (solid line), calculated with Limber approximation (dashed line) and calculated with Limber ap- proximation and settingg(a) = 1 (dashed-dotted line). 30 -vi- 3.4 The dependence of the lensing power spectrum on total neutrino mass, (Cφφ C φφ )/Cφφ =R (M /eV). The black line is the numerical result � − �,fid �,fid � × ν from CLASS, the red line is the result of Limber approximation setting χ = 1.4 10 4 Mpc, the blue line is the result of Limber approximation � × withg(a) = 1, the magenta line is the result of Limber approximationfixing bothω m andg(a), and green line is the result of Limber approximation withA s, ns,ω m,ω b andg(a)fixed. 31 3.5 Forecasted 1σ and 2σ constraints in theM ω plane, where the CMB-S4 ν − m experiment results in aσ(M ν) = 38 meV constraint, the combination of CMB-S4 and DESI BAO yield aσ(M ν) = 15 meV constraint. and adding measurements of the structure growth rate by DESI RSD further improves the constraint toσ(M ν) = 9 meV. 34 3.6 Same as Fig. 3.1, but with suppressed errorbars ofD A(z) andH(z) coming from CMB-S4 and a cosmic-variance-limited BAO experiment. 35 3.7 The uncertainties in relative distances from CMB-S4 + DESI BAO. Note that the uncertainties is multiplied by a factor of 104 in the plot. 36 4.1 Comparison of the spectra of thefiducial cosmology (solid curves) and the peak locations predicted by the baseline model (vertical dashed lines). 44 4.2 The intervalsΔ(kr s) of neighboring peak-trough of [Θ0 +Φ](k,η) for mode 1 k=0.5 Mpc − . Dots are numerical results of peak-trough intervals. Solid line is the analytic result of high-order correction to the tight coupling approximationφ dcp. Dashed line is the result of corrections from both late-time high-order correctionφ dcp and early-time gravitational driving φgr,γ sourced by photon perturbations. 45 4.3 Phase shifts of sources induced by 3.046 neutrinos and measured at the LSS. 47 4.4 The phase shifts of [Θ0 +Φ] (left panel) and ofΠ (right panel) induced by different physical effects measured at the LSS. 48 -vii- 4.5 Illustration of the projection from three to two dimensions. The round circle is the LSS, the vertical solid(dashed) lines are the peaks(troughs) of mode �k atη �. The wiggling curve around the LSS is a Legendre polynomial P (µ) with�=k(η η ), whereµ= kˆ ˆγ, is the cosine of the angle � 0 − � · subtended by the wavevector �k and the direction of observation ˆγ. In the µ = 0 direction, the peak-trough separation of the �k mode matches that ofP �m (µ) �m=k(η0 η�) (shown). In theµ = 1 direction, the peak-trough | − � separation of the k mode matches that ofP �m (µ) �m k(η0 η�) (not shown). 51 | � − 4.6 The comparison between the asymmetric visibility functiong(η) and two Gaussian functions both withσ = 20 Mpc, peaking atη � = 281 Mpc and ¯η = 293 Mpc, respectively, where ¯η is the mean decoupling time defined by ¯η= g(η)ηdη/ g(η)dη. ................... 55 TT 4.7 The contribution� to� the unlensedD � from each component: dominant monopole, subdominant dipole and early ISW, and negligible polarization and late ISW. 56 5.1 Upper Panel: the evolution of dark matter over-densityδ dm suppression for differentk modes. Middle Panel: the “self-similar” behavior of the over-density suppression, where we displace the suppression of modesk= 1 1 0.3 Mpc− andk=1.0 Mpc − by 0.05 and 0.096 respectively. Lower Panel: the dm-drf interaction induced matter power spectrum suppression today, where the dashed line is an analyticfit in the form of Equation (5.5). 71 -viii- 5.2 Comparison of TT and EE spectra of the three models listed in Table 5.1, where in the upper panel we plot the TT spectra with damping effect largely removed by multiplying a factorK = exp 2 (�/1267) 1.18 , in the � { × } lower panel we plot the EE spectra, and in the two inset plots, we normalize the spectra amplitudes to allow one to see the impact of the very small shift in peak locations induced by free-streaming species as done in [1].