The Light/Dark Universe: Light from Galaxies, Dark Matter and Dark Energy

236 Pages·2008·4.01 MB·English

by  James M. Overduin

THE
LIGHTDARK
UNIVERSE
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
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 Scientific
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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,
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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
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Preface
Why is the sky dark at night? If the Universe is in(cid:12)nite and uniformly
populatedwithluminousgalaxieswhichhaveexistedforever,thenthenight
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(cid:11)erent answers
to this question, which was dubbed \Olbers’ paradox"in 1952. It was not
reallyparadoxicalthen;nearlyallofthosewhonoticedthepuzzle(including
Olbers himself in 1823)wereperfectly content with their answers,whether
right or wrong. And it is neither paradoxical nor puzzling today: the
reasonsfor the darknessof the night sky arenow well understood. Yet the
problem runs so deep, and touches upon so many fundamental aspects of
cosmologyandmetaphysics,thatitcontinuestoholdaperennialfascination
for astronomers and the public alike. Perhaps most profoundly of all, the
darkness of the Universe at optical wavelengths is a clue to the (cid:12)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 (cid:12)lled up
with light. The fact that it has not tells us approximately how long they
havebeen shining. In fact, bymeasuringthe intensity of the nightskyand
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 darkthe skyshould be at night, using what astronomershave
learnedaboutstarsandgalaxiestogetherwiththedynamicsoftheUniverse
accordingtoEinstein’stheoryofgeneralrelativity. Theresultsagreeclosely
with what we see.
Such is the precisionof modern observationalcosmology,however, that
wecangofurtherthanthisandusetheexactlevelofintensityoftheextra-
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-
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vi The Light/DarkUniverse
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 propertiesare 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
thathavebeenproposedsofararenotcompletely dark. Rather,theydecay
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
theopportunitytostudynotonlyasapastimebutalsoasaprofession. We
are grateful for the input of numerous researchers, and for the hospitality
of several universities, notably Berkeley and Stanford. However, as we
emphasizeinthefollowing(mainlytechnical)account,anybody withaclear
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(cid:12)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
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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(cid:14)cient energy . . . . . . . . . . . . . . . . . . . . . . 20
1.13 Light-matter interconversion. . . . . . . . . . . . . . . . . 21
1.14 Cosmic expansion. . . . . . . . . . . . . . . . . . . . . . . 22
1.15 Olbers’ paradoxtoday . . . . . . . . . . . . . . . . . . . . 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 (cid:13)at models . . . . . . . . . . . . . . . . . . . . . . 39
2.6 Curved and multi-(cid:13)uid models . . . . . . . . . . . . . . . 41
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viii TheLight/Dark Universe
2.7 A bright sky at night? . . . . . . . . . . . . . . . . . . . . 44
3. The Spectrum of Cosmic BackgroundLight 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 Cosmologicalconcordance . . . . . . . . . . . . . . . . . . 88
4.7 The coincidental Universe . . . . . . . . . . . . . . . . . . 94
5. The Radio and MicrowaveBackgrounds 97
5.1 The cosmological\constant" . . . . . . . . . . . . . . . . 97
5.2 The scalar(cid:12)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 backgroundlight . . . . . . . . . . . 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 backgroundlight . . . . . . . . . . . . . . 127
7. The Ultraviolet Background 133
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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 backgroundlight . . . . . . . . . . . . 145
8. The X-ray and Gamma-rayBackgrounds 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 backgroundlight . . . . . . . . . . . . . . 169
9. The High-Energy Gamma-rayBackground 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