Probes of the Early Universe by Max Erik Tegmark B.A., Stockholm School of Economics, 1989 B.A., Royal Institute of Technology, Stockholm, 1990 M.A., University of California at Berkeley, 1992 A dissertation submitted in satisfaction of the final requirement for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California at Berkeley Committee in charge: Professor Joseph Silk, Chair Professor Bernard Sadoulet Professor Hyron Spinrad April 1994 The dissertation of Max Tegmark is approved: Chair Date Date Date University of California at Berkeley April 1994 Probes of the Early Universe °c 1994 by Max Tegmark Abstract Probes of the Early Universe by Max Erik Tegmark Doctor of Philosophy in Physics University of California at Berkeley Professor Joseph Silk, Chair One of the main challenges in cosmology is to quantify how small density fluctuations at the recombination epoch z ¼ 103 evolved into the galaxies and the large-scale structure we observe in the universe today. This thesis discusses ways of probing the intermediate epoch, focusing on the thermal history. The main emphasis is on the role played by non- linear feedback, where a small fraction of matter forming luminous objects can inject enough energy into the inter-galactic medium (IGM) to radically alter subsequent events. The main conclusions are: ² Early structures corresponding to rare Gaussian peaks in a cold dark matter (CDM) model can photoionize the IGM early enough to appreciably smooth out fluctuations in the cosmic microwave background radiation (CBR), provided that these early struc- 8 tures are quite small, no more massive than about 10 M¯. ² Typical parameter values predict that reionization occurs around z = 50, thereby reducing fluctuations on degree scales while leaving the larger angular scales probed by COBE relatively unaffected. ² For non-standard CDM incorporating mixed dark matter, vacuum density, a tilted primordial power spectrum or decaying ¿ neutrinos, early reionization is not likely to play a significant role. ² For CDM models with Ω < 1 and Λ = 0, the extent of this suppression is quite insensitive to Ω0, as opposing effects partially cancel. ² It is still not certain that the universe underwent a neutral phase, despite the new COBE FIRAS limit y < 2:5£10¡5 on Compton y-distortions of the cosmic microwave background. ² The observed absence of a Gunn-Peterson trough in the spectra of high-redshift quasars can be explained without photoionization, in in a scenario in which supernova-driven winds from early galaxies reionize the IGM by z = 5. vii ² It is possible to place constraints on cosmological models that are independent of the shape of the primordial power spectrum — the only assumption being that the random fields are Gaussian. As an example of an application, the recent measurement of bulk flows of galaxies by Lauer and Postman is shown to be inconsistent with the CBR experiment SP91 at a 95% confidence level regardless of the shape of the power spectrum. Prof. Irwin Shapiro Date viii To Richard Feynman, 1918-1988, who was the reason I decided to switch to physics ix Contents List of Figures . xiv List of Tables . xv List of Abbreviations . xvi Preface . xvii Acknowledgements . xviii ...and More Acknowledgements . xix 1 Introduction 1 1.1 Cosmology towards a New Millennium . 1 1.2 Reheating . 3 1.3 A Sneak Preview . 4 2 A Cosmology Primer 9 2.1 Where to Read More . 9 2.2 So what is cosmology all about? . 10 2.3 Bare Bones General Relativity and the FRW Metric . 13 2.3.1 General Relativity . 13 2.3.2 The raw equations . 13 2.3.3 The FRW metric . 14 2.3.4 Interpreting the FRW coordinates . 14 2.3.5 Curvature . 15 2.3.6 Redshift . 15 2.3.7 The Friedmann equation . 16 2.3.8 Some handy formulas for getting by in curved space . 18 2.4 Perturbing the Universe . 21 2.4.1 Linear perturbation theory . 21 2.4.2 Random fields . 23 2.4.3 The Press-Schechter recipe . 25 2.4.4 CDM and BDM . 27 2.5 The Microwave Background . 32 2.5.1 The thermal history of the universe . 32 2.5.2 CBR fluctuations . 34 2.5.3 Spectral distortions . 35 2.5.4 Spatial distortions . 36 2.5.5 How reionization suppresses fluctuations . 40 2.6 Cosmological Chemistry . 46 2.6.1 Evolution of the IGM . 46 2.6.2 Nucleosynthesis . 46 2.7 Astronomy Jargon . 47 2.8 An Abstract for Non-Cosmologists . 49 x 3 Early Reionization and CBR Fluctuations 59 3.1 Introduction . 59 3.2 The Mass Fraction in Galaxies . 61 3.3 Efficiency Parameters . 63 3.4 Scattering History . 65 3.5 Discussion . 66 4 Reionization in an Open Universe 79 4.1 Introduction . 79 4.2 The Boost Factor . 80 4.3 The Power Spectrum Shift . 81 4.4 The Optical Depth . 82 4.5 The Angular Scale . 82 4.6 Cosmological Consequences . 83 4.7 Discussion . 85 5 Did the Universe Recombine? 93 5.1 Introduction . 93 5.2 The Compton y-Parameter . 94 5.3 IGM Evolution in the Strong UV Flux Limit . 95 5.3.1 The ionization fraction . 95 5.3.2 The spectral parameter T ¤ ........................ 96 5.3.3 The thermal evolution . 97 5.4 Conclusions . 99 6 Late Reionization by Supernova-Driven Winds 105 6.1 Introduction . 105 6.2 The Explosion Model . 106 6.2.1 The expanding shell . 107 6.2.2 The interior plasma . 107 6.2.3 Solutions to the equations . 109 6.3 Cosmological Consequences . 111 6.3.1 IGM porosity . 111 6.3.2 IGM enrichment . 114 6.3.3 IGM temperature . 114 6.3.4 IGM ionization and the Gunn-Peterson effect . 115 6.3.5 Other spectral constraints . 116 6.4 Discussion . 117 7 Power Spectrum Independent Constraints 127 7.1 Introduction . 127 7.2 Consistency Tests for Cosmological Models . 129 7.2.1 Choosing a goodness-of-fit parameter . 130 7.2.2 Its probability distribution . 130 7.2.3 The consistency probability . 131 7.2.4 Ruling out whole classes of models . 131 7.3 Cold Dark Matter Confronts SP91, COBE and Lauer-Postman . 132 7.4 Allowing Arbitrary Power Spectra . 135 7.4.1 The optimization problem . 137 7.4.2 A useful inequality . 139 7.4.3 Including noise and cosmic variance . 140 7.4.4 Power spectrum independent constraints on LP, SP91 and COBE . 141 xi 7.5 Discussion . 141 A The Efficiency Parameter fion 147 A.1 Intergalactic Str¨omgrenSpheres . 147 A.2 The Expansion of Str¨omgrenRegions . 150 B Comparing Goodness-of-fit Parameters 153 B.1 Both ´l and ´p can be “fooled”... 153 B.2 ...but they usually give similar results. 154 C Window Functions 157 References 159 xii List of Figures 1.1 Limits on the Compton y-parameter. 7 2.1 Our backward light cone. 50 2.2 Evolution of a top hat overdensity. 51 2.3 Assorted power spectra. 52 2.4 Assorted angular windows functions. 53 2.5 Assorted angular power spectra. 54 2.6 Monte Carlo photons, top view. 55 2.7 Monte Carlo photons, side view. ..