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SUPERSYMMETRY AND COSMOLOGY

Jonathan L. Feng ∗

Department of Physics and Astronomy

University of California, Irvine, CA 92697

ABSTRACT

Cosmology now provides unambiguous, quantitative evidence for new

particle physics. I discuss the implications of cosmology for supersym-

metry and vice versa. Topics include: motivations for supersymmetry; su-

persymmetry breaking; dark energy; freeze out and WIMPs; neutralino

dark matter; cosmologically preferred regions of minimal supergravity;

direct and indirect detection of neutralinos; the DAMA and HEAT sig-

nals; inﬂation and reheating; gravitino dark matter; Big Bang nucleosyn-

thesis; and the cosmic microwave background. I conclude with specula-

tions about the prospects for a microscopic description of the dark universe,

stressing the necessity of diverse experiments on both sides of the particle

physics/cosmology interface.

c 2004 by Jonathan L. Feng.

Contents

1 Introduction

2 Supersymmetry Essentials 4

2.1 A New Spacetime Symmetry . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Supersymmetry and the Weak Scale . . . . . . . . . . . . . . . . . . . 5

2.3 The Neutral Supersymmetric Spectrum . . . . . . . . . . . . . . . . . . 7

2.4 R -Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5 Supersymmetry Breaking and Dark Energy . . . . . . . . . . . . . . . 9

2.6 Minimal Supergravity . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Neutralino Cosmology 15

3.1 Freeze Out and WIMPs . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Thermal Relic Density . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 Bulk Region . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.2 Focus Point Region . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.3 A Funnel Region . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.4 Co-annihilation Region . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 Indirect Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.1 Positrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.2 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4.3 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4 Gravitino Cosmology 34

4.1 Gravitino Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Thermal Relic Density . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3 Production during Reheating . . . . . . . . . . . . . . . . . . . . . . . 38

4.4 Production from Late Decays . . . . . . . . . . . . . . . . . . . . . . . 39

4.5 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.5.1 Energy Release . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5.2 Big Bang Nucleosynthesis . . . . . . . . . . . . . . . . . . . . 43

4.5.3 The Cosmic Microwave Background . . . . . . . . . . . . . . . 47

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5 Prospects 49

5.1 The Particle Physics/Cosmology Interface . . . . . . . . . . . . . . . . 49

5.2 The Role of Colliders . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6 Acknowledgments

References

1 Introduction

Not long ago, particle physicists could often be heard bemoaning the lack of unam-

biguous, quantitative evidence for physics beyond their standard model. Those days

are gone. Although the standard model of particle physics remains one of the great

triumphs of modern science, it now appears that it fails at even the most basic level —

providing a reasonably complete catalog of the building blocks of our universe.

Recent cosmological measurements have pinned down the amount of baryon, mat-

ter, and dark energy in the universe. 1, 2

In units of the critical density, these energy

densities are

B = 0.044±0.004

(1)

matter = 0.27±0.04

(2)

= 0.73±0.04 ,

(3)

implying a non-baryonic dark matter component with

0.094 < DM h 2 < 0.129 (95% CL) ,

(4)

where h≃0.71 is the normalized Hubble expansion rate. Both the central values and

uncertainties were nearly unthinkable even just a few years ago. These measurements

are clear and surprisingly precise evidence that the known particles make up only a

small fraction of the total energy density of the universe. Cosmology now provides

overwhelming evidence for new particle physics.

At the same time, the microscopic properties of dark matter and dark energy are

remarkably unconstrained by cosmological and astrophysical observations. Theoretical

insights from particle physics are therefore required, both to suggest candidates for dark

matter and dark energy and to identify experiments and observations that may conﬁrm

or exclude these speculations.

Weak-scale supersymmetry is at present the most well-motivated framework for

new particle physics. Its particle physics motivations are numerous and are reviewed in

Sec. 2. More than that, it naturally provides dark matter candidates with approximately

the right relic density. This fact provides a strong, fundamental, and completely inde-

pendent motivation for supersymmetric theories. For these reasons, the implications of

supersymmetry for cosmology, and vice versa, merit serious consideration.

Many topics lie at the interface of particle physics and cosmology, and supersym-

metry has something to say about nearly every one of them. Regrettably, spacetime

constraints preclude detailed discussion of many of these topics. Although the discus-

sion below will touch on a variety of subjects, it will focus on dark matter, where the

connections between supersymmetry and cosmology are concrete and rich, the above-

mentioned quantitative evidence is especially tantalizing, and the role of experiments

is clear and promising.

Weak-scale supersymmetry is brieﬂy reviewed in Sec. 2 with a focus on aspects

most relevant to astrophysics and cosmology. In Secs. 3 and 4 the possible roles of

neutralinos and gravitinos in the early universe are described. As will be seen, their

cosmological and astrophysical implications are very different; together they illustrate

the wealth of possibilities in supersymmetric cosmology. I conclude in Sec. 5 with

speculations about the future prospects for a microscopic understanding of the dark

universe.

2 Supersymmetry Essentials

2.1 A New Spacetime Symmetry

Supersymmetry is an extension of the known spacetime symmetries. 3 The spacetime

symmetries of rotations, boosts, and translations are generated by angular momentum

operators L i , boost operators K i , and momentum operators P µ , respectively. The L and

K generators form Lorentz symmetry, and all 10 generators together form Poincare

symmetry. Supersymmetry is the symmetry that results when these 10 generators are

further supplemented by fermionic operators Q . It emerges naturally in string theory

and, in a sense that may be made precise, 4 is the maximal possible extension of Poincare

symmetry.

If a symmetry exists in nature, acting on a physical state with any generator of

the symmetry gives another physical state. For example, acting on an electron with a

momentum operator produces another physical state, namely, an electron translated in

space or time. Spacetime symmetries leave the quantum numbers of the state invariant

— in this example, the initial and ﬁnal states have the same mass, electric charge, etc.

In an exactly supersymmetric world, then, acting on any physical state with the

supersymmetry generator Q produces another physical state. As with the other space-

time generators, Q does not change the mass, electric charge, and other quantum

numbers of the physical state. In contrast to the Poincare generators, however, a su-

persymmetric transformation changes bosons to fermions and vice versa. The basic

prediction of supersymmetry is, then, that for every known particle there is another

particle, its superpartner, with spin differing by

2.2 Supersymmetry and the Weak Scale

Once supersymmetry is broken, the mass scale for superpartners is unconstrained.

There is, however, a strong motivation for this scale to be the weak scale: the gauge

hierarchy problem. In the standard model of particle physics, the classical mass of the

Higgs boson (m h ) 0 receives quantum corrections. (See Fig. 1. ) Including quantum

corrections from standard model fermions f L and f R , one ﬁnds that the physical Higgs

2 .

One may show that no particle of the standard model is the superpartner of an-

other. Supersymmetry therefore predicts a plethora of superpartners, none of which

has been discovered. Mass degenerate superpartners cannot exist — they would have

been discovered long ago — and so supersymmetry cannot be an exact symmetry. The

only viable supersymmetric theories are therefore those with non-degenerate superpart-

ners. This may be achieved by introducing supersymmetry-breaking contributions to

superpartner masses to lift them beyond current search limits. At ﬁrst sight, this would

appear to be a drastic step that considerably detracts from the appeal of supersymmetry.

It turns out, however, that the main virtues of supersymmetry are preserved even if such

mass terms are introduced. In addition, the possibility of supersymmetric dark matter

emerges naturally and beautifully in theories with broken supersymmetry.

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