THE LIGHTDARK UNIVERSE This page intentionally left blank James M Overduin Stanford University, USA Paul S Wesson University of Waterloo, Canada THE LIGHTDARK UNIVERSE Light from Galaxies, Dark Matter and Dark Energy World Scientifc NE W J E R S E Y • L O N D O N • S I N G A P O R E • B E I J I N G • S H A N G H A I • H O N G K O N G • TA I P E I • C H E N N A I Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. THE LIGHT/DARK UNIVERSE Galactic Light, Dark Matter and Dark Energy Copyright © 2008 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-283-441-6 ISBN-10 981-283-441-9 Printed in Singapore. Alvin - The LightDark Universe.pmd 1 7/4/2008, 4:01 PM July 3, 2008 8:36 World Scienti�c Book - 9in x 6in ldu Preface Why is the sky dark at night? If the Universe is in�nite and uniformly populated with luminous galaxies which have existed forever, then the night sky should be ablaze with light. Obviously it is not|but why? Thinkers through the ages have come up with at least a dozen di�erent answers to this question, which was dubbed \Olbers’ paradox" in 1952. It was not really paradoxical then; nearly all of those who noticed the puzzle (including Olbers himself in 1823) were perfectly content with their answers, whether right or wrong. And it is neither paradoxical nor puzzling today: the reasons for the darkness of the night sky are now well understood. Yet the problem runs so deep, and touches upon so many fundamental aspects of cosmology and metaphysics, that it continues to hold a perennial fascination for astronomers and the public alike. Perhaps most profoundly of all, the darkness of the Universe at optical wavelengths is a clue to the �niteness in time of those sources of light that we call home: the stars and galaxies. They could not have existed forever, or the cosmos would have �lled up with light. The fact that it has not tells us approximately how long they have been shining. In fact, by measuring the intensity of the night sky and applying some simple physics, we can estimate the elapsed time since the big bang with a fair degree of accuracy. Alternatively, we can calculate exactly how dark the sky should be at night, using what astronomers have learned about stars and galaxies together with the dynamics of the Universe according to Einstein’s theory of general relativity. The results agree closely with what we see. Such is the precision of modern observational cosmology, however, that we can go further than this and use the exact level of intensity of the extra- galactic background light at all wavelengths (not just the optical) to look for hints as to what else may or may not be shining in the Universe. Cos- v July 3, 2008 8:36 World Scienti�c Book - 9in x 6in ldu vi The Light/Dark Universe mologists are now convinced that the Universe is dynamically dominated by two mysterious and apparently independent substances, known as dark matter and dark energy, whose energy density dwarfs that of conventional matter and radiation, and whose properties are inconsistent with anything in the existing standard model of particle physics. Very little is known about these new forms of matter-energy. However, most of the candidates that have been proposed so far are not completely dark. Rather, they decay into or otherwise interact with photons in characteristic ways that can be accurately modelled and compared with observational data. Experimental limits on the intensity of cosmic background radiation in the microwave, infrared, optical, ultraviolet, x-ray and gamma-ray bands rule out certain kinds of decaying dark energy, as well as dark matter in the form of light axions, neutrinos, unstable weakly-interacting massive particles (WIMPs) and objects like black holes. Thus does Olbers’ paradox gain new impor- tance as a window on the Universe, both seen and unseen. The topic of the dark night sky is one which we, as authors, have had the opportunity to study not only as a pastime but also as a profession. We are grateful for the input of numerous researchers, and for the hospitality of several universities, notably Berkeley and Stanford. However, as we emphasize in the following (mainly technical) account, anybody with a clear mind can make the connection between the fact that the night sky is still dark and the fact that the Universe is young. The naked eye con�rms the birth of the Universe in something like a big bang. The poet and writer Edgar Allan Poe guessed as much when he made the connection between darkness and age long before there were astrophysicists as such. We therefore dedicate this book to the thinking reader, who has looked at the glory of the night sky and wondered what does it mean? J.M. Overduin and P.S. Wesson July 3, 2008 8:36 World Scienti�c Book - 9in x 6in ldu Contents Preface v 1. The Enigma of the Dark Night Sky 1 1.1 Why is the sky dark at night? . . . . . . . . . . . . . . . . 1 1.2 \By reason of distance" . . . . . . . . . . . . . . . . . . . 4 1.3 Island Universe . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Non-uniform sources . . . . . . . . . . . . . . . . . . . . . 6 1.5 Tired light . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.7 Fractal Universe . . . . . . . . . . . . . . . . . . . . . . . 12 1.8 Finite age . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.9 Dark stars . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.10 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.11 Ether voids . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.12 Insu�cient energy . . . . . . . . . . . . . . . . . . . . . . 20 1.13 Light-matter interconversion . . . . . . . . . . . . . . . . . 21 1.14 Cosmic expansion . . . . . . . . . . . . . . . . . . . . . . . 22 1.15 Olbers’ paradox today . . . . . . . . . . . . . . . . . . . . 25 2. The Intensity of Cosmic Background Light 29 2.1 Bolometric intensity . . . . . . . . . . . . . . . . . . . . . 29 2.2 Time and redshift . . . . . . . . . . . . . . . . . . . . . . 32 2.3 Matter, energy and expansion . . . . . . . . . . . . . . . . 33 2.4 How important is expansion? . . . . . . . . . . . . . . . . 37 2.5 Simple �at models . . . . . . . . . . . . . . . . . . . . . . 39 2.6 Curved and multi-�uid models . . . . . . . . . . . . . . . 41 vii July 3, 2008 8:36 World Scienti�c Book - 9in x 6in ldu viii The Light/Dark Universe 2.7 A bright sky at night? . . . . . . . . . . . . . . . . . . . . 44 3. The Spectrum of Cosmic Background Light 49 3.1 Spectral intensity . . . . . . . . . . . . . . . . . . . . . . . 49 3.2 Luminosity density . . . . . . . . . . . . . . . . . . . . . . 52 3.3 The delta function . . . . . . . . . . . . . . . . . . . . . . 54 3.4 The normal distribution . . . . . . . . . . . . . . . . . . . 58 3.5 The thermal spectrum . . . . . . . . . . . . . . . . . . . . 59 3.6 The spectra of galaxies . . . . . . . . . . . . . . . . . . . . 62 3.7 The light of the night sky . . . . . . . . . . . . . . . . . . 65 3.8 R.I.P. Olbers’ paradox . . . . . . . . . . . . . . . . . . . . 69 4. Dark Cosmology 73 4.1 The four dark elements . . . . . . . . . . . . . . . . . . . 73 4.2 Baryons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3 Dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.4 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.5 Dark energy . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.6 Cosmological concordance . . . . . . . . . . . . . . . . . . 88 4.7 The coincidental Universe . . . . . . . . . . . . . . . . . . 94 5. The Radio and Microwave Backgrounds 97 5.1 The cosmological \constant" . . . . . . . . . . . . . . . . 97 5.2 The scalar �eld . . . . . . . . . . . . . . . . . . . . . . . . 98 5.3 Decaying dark energy . . . . . . . . . . . . . . . . . . . . 102 5.4 Energy density . . . . . . . . . . . . . . . . . . . . . . . . 105 5.5 Source luminosity . . . . . . . . . . . . . . . . . . . . . . . 108 5.6 Bolometric intensity . . . . . . . . . . . . . . . . . . . . . 113 5.7 Spectral energy distribution . . . . . . . . . . . . . . . . . 114 5.8 Dark energy and the background light . . . . . . . . . . . 115 6. The Infrared and Visible Backgrounds 119 6.1 Decaying axions . . . . . . . . . . . . . . . . . . . . . . . 119 6.2 Axion halos . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.3 Bolometric intensity . . . . . . . . . . . . . . . . . . . . . 125 6.4 Axions and the background light . . . . . . . . . . . . . . 127 7. The Ultraviolet Background 133 July 3, 2008 8:36 World Scienti�c Book - 9in x 6in ldu Contents ix 7.1 Decaying neutrinos . . . . . . . . . . . . . . . . . . . . . . 133 7.2 Neutrino halos . . . . . . . . . . . . . . . . . . . . . . . . 135 7.3 Halo luminosity . . . . . . . . . . . . . . . . . . . . . . . . 137 7.4 Free-streaming neutrinos . . . . . . . . . . . . . . . . . . . 140 7.5 Extinction by gas and dust . . . . . . . . . . . . . . . . . 141 7.6 Neutrinos and the background light . . . . . . . . . . . . 145 8. The X-ray and Gamma-ray Backgrounds 151 8.1 Weakly interacting massive particles . . . . . . . . . . . . 151 8.2 Pair annihilation . . . . . . . . . . . . . . . . . . . . . . . 154 8.3 One-loop decay . . . . . . . . . . . . . . . . . . . . . . . . 160 8.4 Tree-level decay . . . . . . . . . . . . . . . . . . . . . . . . 162 8.5 Gravitinos . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.6 WIMPs and the background light . . . . . . . . . . . . . . 169 9. The High-Energy Gamma-ray Background 175 9.1 Primordial black holes . . . . . . . . . . . . . . . . . . . . 175 9.2 Evolution and density . . . . . . . . . . . . . . . . . . . . 178 9.3 Spectral energy distribution . . . . . . . . . . . . . . . . . 181 9.4 Bolometric intensity . . . . . . . . . . . . . . . . . . . . . 184 9.5 Spectral intensity . . . . . . . . . . . . . . . . . . . . . . . 187 9.6 Higher dimensions . . . . . . . . . . . . . . . . . . . . . . 191 10. The Universe Seen Darkly 197 Bibliography 203 Index 217