DARK MATTER

Jun.-Prof. Susanne Westhoff Winter term 2019/20 — Heidelberg University

Lecture 5: The kind of dark matter

The kind of dark matter

2

electrically neutral

Observations Properties

does not emit lightis abundant today stableis needed for structure formation cold

The kind of dark matter

3

electrically neutraldoes not emit lightis abundant today stableis needed for structure formation cold

What are its mass, spin, interactions?Does it interact with itself?When was it formed?Is there an entire dark sector?

Questions

Observations Properties

How warm can dark matter be?

4

Hot dark matter is relativistic.Cold dark matter is non-relativistic.

Characteristic scale:

�FS ⇡ 1Mpc

✓keV

m�

◆✓T�

T�

◆

�⇢ > 0

�⇢ < 0

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⇢0average density

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Before radiation-matter equality:

free-streaming length

Structures grow during matter domination.

Free-streaming length of neutrinos

5[Y. Mambrini, Histories of Particles in the Dark Universe]

10−8 10−6 10−4 0.01 1

0.01

0.1

1

10

100a

(1

00

eV

)

nr

a

(1 k

eV)

EQa

νm = 1 eV

νm = 10 eV

νm = 100 eV

νm = 1 keV

(Mpc)FS

λ

a(t)

nr

Figure 2.32: Free streaming distance (in Mpc) as function of the scaling parameter a(t) for di↵erent masses

of neutrino (from 1 eV to 1 keV)

2.9 The CMB

2.9.1 Generalities

2.9.2 Accoustic oscilations

2.9.3 WMAP/PLANCK results

2.10 Baryogenesis, leptogenesis

2.11 The Sunyaev-Zeldovich e↵ect

2.12 Reheating

2.12.1 Generalities and first approach

We discussed in the section 2.6.6 the general process of thermalization of a dark bath heatedby the standard model plasma. In this section we will concentrate on the processes happeningbefore this epoch: the thermalization of the standard model bath in itself. In other words,we will describe how a bath of standard model particles produced by the decay of an inflaton(see section 2.13). The spectrum of the particles in the plasma at the production can be flator monochromatic, but the equilibrium is then established in two phases: kinetic equilibriumfirst where the scattering (elastic or inelastic) or annihilation 2 ! 2 processes redistribute the

110

�FS[M

pc]

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Structure formation with dark matter

6

hot warm cold

early universe

today

[ICT, University of Zurich]

10Mpc

The matter power spectrum⇠(r) ⌘ h�⇢(x) �⇢(x+ r)i = V

2⇡2

ZP (k)

sin(kr)

krk2dkDensity fluctuations:

Given the profusion of recent measurements of H(z)and P (k, z), it is striking that there is a fairly simplemodel that currently seems to fit everything (Fig. 2 andFig. 4). In this so-called concordance model [18,19,50,51],the cosmic matter budget consists of about 5% ordi-nary matter (baryons), 30% cold dark matter, 0.1% hotdark matter (neutrinos) and 65% dark energy based onCMB and LSS observations, in good agreement withLyαF [18,52,53], lensing [54–60] and SN Ia [27,28]. Theseed fluctuations created in the early universe are consis-tent with the inflation prediction of a simple power lawP (k, z) ∝ kn early on, with n = 0.9± 0.1 [18,19]. Galaxyformation appears to have heated and reionized the uni-verse not too long before redshift z = 6 based on theLyαF [61,62].

FIG. 4. Measurements of the current (z = 0) power spec-trum of density fluctuations computed as described in [63],assuming the matter budget of [19] and reionization at z = 8.The CMB measurements combine the information from allexperiments to date as in [63]. LSS points are from a recentanalysis [64] of the 3D distribution of 2dF galaxies [11], andcorrecting them for bias shifts them vertically (b = 1.3 as-sumed here) and should perhaps blue-tilt them slightly. Thecluster error bars reflect the spread in the literature. Thelensing points are based on [65]. The LyαF points are froma reanalysis [66] of [52] and have an overall calibration uncer-tainty around 17%. The curve shows the concordance modelof [19].

Although the mere existence of a concordance modelis a striking success, inferences about things like the ex-pansion history, the matter budget and the early uni-verse involve many assumptions — about the nature ofdark energy and dark matter (e.g., interactions, tempera-ture, pressure, sound speed, viscosity [68]), about gravity,about galaxy formation, and so on. Since the avalancheof new cosmology data is showing no sign of slowing

down, it is becoming feasible to to raise the ambitionlevel to test rather than assume the underlying physics,probing the nature of dark energy, dark matter and grav-ity. Given the matter budget and the expansion his-tory H(z), theory predicts the complete time-evolutionof linear clustering, so measuring its redshift dependence(Fig. 3) offers redundancy and powerful cross-checks.Let us briefly summarize the status of our five power

spectrum probes in Fig. 3. Gravitational lensing usesphotons from distant galaxies as test particles to mea-sure the metric fluctuations caused by intervening mat-ter, as manifested by distorted images of distant objects.The first measurements of P (k, z) with this “weak lens-ing” technique [54] were reported in 2000 [55–60]. 3Dmapping of the universe with galaxy redshift surveysoffers another window on the cosmic matter distribu-tion, through its gravitational effects on galaxy cluster-ing. This field is currently being transformed by the 2degree Field (2dF) survey and the Sloan Digital Sky Sur-vey, which will jointly map more than 106 galaxies, andcomplementary surveys will map high redshifts and theevolution of clustering. Additional information can beextracted from galaxy velocities [69]. The abundance ofgalaxy clusters at different epochs, as probed by opti-cal, x-ray, CMB or gravitational lensing surveys, is a sen-sitive probe of P (k, z) on smaller scales [70–72] and theLyαF offers a new and exciting probe of matter cluster-ing on still smaller scales when the universe was merely10-20% of its present age [52,73,74,66]. CMB experi-ments probe P (k, z) through a variety of effects as farback as to redshifts z > 103 [75,76]. The MAP satellitewill publicly release CMB temperature measurements ofunprecedented quality in December 2002 [6], and two newpromising CMB fronts are opening up — CMB polar-ization (still undetected) and CMB fluctuations on tiny(arcminute) angular scales.There is a rich literature on how all these complemen-

tary probes can be combined to break each others’ degen-eracies and independently measure the matter budget,the primordial power spectrum and galaxy formation de-tails [45,46,68,77,78], so I will merely give a few exampleshere. The power spectra measured by CMB, LSS, lensingand LyαF are the product of the three terms: (i) the pri-mordial power spectrum, (ii) a so-called transfer functionquantifying the subsequent fluctuation growth, and (iii)(for LSS and LyαF only) a so called bias factor account-ing for the fact that the measured galaxies/gas cloudsmay cluster differently than the underlying matter.Disentangling bias and systematic errors:

Galaxy bias has now been directly measured from dataand found to be of order unity for typical 2dF galaxies[51,67], and LyαF bias may be computable with hydro-dynamics simulations [52,74,66]. Although CMB, LSS,lensing and LyαF each comes with caveats of their own,their substantial overlap (Fig. 3) should allow disagree-ments between data sets to be distinguished from dis-

6

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[M. Tegmark, arXiv: astro-ph/0207199]

Hot dark matter washes out small-scale structures .� . �FS<latexit sha1_base64="YiHY7OF1tlScXoc2MbZaGGB/tPo=">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</latexit><latexit 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HDM

8

When was the relic abundance formed?

Preface

This course is about 13.8 billion years of cosmic evolution:

At early times, the universe was hot and dense. Interactions between particles were frequent

and energetic. Matter was in the form of free electrons and atomic nuclei with light bouncing

between them. As the primordial plasma cooled, the light elements—hydrogen, helium and

lithium—formed. At some point, the energy had dropped enough for the first stable atoms

to exist. At that moment, photons started to stream freely. Today, billions of years later, we

observe this afterglow of the Big Bang as microwave radiation. This radiation is found to be

almost completely uniform, the same temperature (about 2.7 K) in all directions. Crucially, the

cosmic microwave background contains small variations in temperature at a level of 1 part in

10 000. Parts of the sky are slightly hotter, parts slightly colder. These fluctuations reflect tiny

variations in the primordial density of matter. Over time, and under the influence of gravity,

these matter fluctuations grew. Dense regions were getting denser. Eventually, galaxies, stars

and planets formed.

dark matter

dark

ene

rgy

baryons

radiation

Inflation

Dark MatterProduction

Cosmic MicrowaveBackground

StructureFormation

Big BangNucleosynthesis

dark matter (27%)

dark energy (68%)

baryons (5%)

present energy density

fract

ion

of e

nerg

y de

nsity

1.0

0.0

(Chapter 3)

(Chapter 3)

(Chapters 2 and 6)(Chapter 3)

(Chapters 4 and 5)

0-10-20-30 10

010

13.8 Gyr380 kyr3 min

0.1 MeV 0.1 eV0.1 TeV

This picture of the universe—from fractions of a second after the Big Bang until today—

is a scientific fact. However, the story isn’t without surprises. The majority of the universe

today consists of forms of matter and energy that are unlike anything we have ever seen in

terrestrial experiments. Dark matter is required to explain the stability of galaxies and the rate

of formation of large-scale structures. Dark energy is required to rationalise the striking fact that

the expansion of the universe started to accelerate recently (meaning a few billion years ago).

What dark matter and dark energy are is still a mystery. Finally, there is growing evidence

that the primordial density perturbations originated from microscopic quantum fluctuations,

stretched to cosmic sizes during a period of inflationary expansion. The physical origin of

inflation is still a topic of active research.

1

9

[D. Baumann, Cosmology Lectures]

n+ ⌫e ! p+ e�

Helium fusion via deuterium:

74 3. Thermal History

WMAP

4He

3He

DM

ass F

ract

ion

7Li

WMAP

Num

ber r

elativ

e to

H

Figure 3.10: Theoretical predictions (colored bands) and observational constraints (grey bands).

• ⌧n: a large neutron lifetime would reduce the amount of neutron decay after freeze-out

and therefore would increase the final helium abundance.

• Q: a larger mass di↵erence between neutrons and protons would decrease the n/p ratio

at freeze-out and therefore would decrease the final helium abundance.

• ⌘: the amount of helium increases with increasing ⌘ as nucleosythesis starts earlier for

larger baryon density.

• GN : increasing the strength of gravity would increase the freeze-out temperature, Tf /G

1/6

N, and hence would increase the final helium abundance.

• GF : increasing the weak force would decrease the freeze-out temperature, Tf / G�2/3

F,

and hence would decrease the final helium abundance.

Changing the input, e.g. by new physics beyond the Standard Model (BSM) in the early universe,

would change the predictions of BBN. In this way BBN is a probe of fundamental physics.

Light Element Synthesis⇤

To determine the abundances of other light elements, the coupled Boltzmann equations have to

be solved numerically (see fig. 3.11 for the result of such a computation). Fig. 3.10 shows that

theoretical predictions for the light element abundances as a function of ⌘ (or ⌦b). The fact that

we find reasonably good quantitative agreement with observations is one of the great triumphs

of the Big Bang model.

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after neutrino freeze-out:nn

nn + np⇠ 1

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p+ n ! 2H+ �

3He +

2H ! 4

He + p

2H+ p ! 3

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Dark matter should leave equilibrium before big bang nucleosynthesis.

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equilibrium above

Extra relativistic particles:

change abundance of light elementsHubble expansion around freeze-out H ⇠ p

g⇤T

2⌫

MPl⇡ �W ⇠ G

2FT

5⌫

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Big bang nucleosynthesis

10

Dark matter forms halos

m� & 10�22 eV

Boson: uncertainty principle

[halo surrounding Milky Way, ESO 2012]

dwarf galaxies:

(„fuzzy dark matter“)[Barkana et al., arXiv: astro-ph/0003365]

�x�p ⇠ (2Rhalo)(m�v) ⇠ 1

How light can dark matter be?

11

Dark matter forms halos

m� & 10�22 eV

Boson: uncertainty principle

[halo surrounding Milky Way, ESO 2012]

dwarf galaxies:

(„fuzzy dark matter“)[Barkana et al., arXiv: astro-ph/0003365]

�x�p ⇠ (2Rhalo)(m�v) ⇠ 1

How light can dark matter be?

m� & 0.7 keV

Fermion: Pauli exclusion

Mhalo = m�V

Zf(p)d3p . m�R

3halo(m�v)

3

dwarf galaxies:

dark matter halo:

Literature

12

Taoso et al., Dark Matter Candidates: A Ten-Point Test [https://arxiv.org/abs/0711.4996]

D. Cerdeno, IPPP Durham: Dark Matter 101 - Lecture notes

J. Garcia-Bellido, Cosmology and Astrophysics [https://arxiv.org/abs/astro-ph/0502139]

lecture notes on cosmology by D. Baumann: http://cosmology.amsterdam/education/cosmology/