Model-Independent Approaches

Matter

Model-Independent Approaches

By tiziana scarnà

Service de Physique Théorique Université Libre de Bruxelles

doctoral thesis in theoretical physics

December 2014

Academic Advisor: Prof. Thomas Hambye Academic Co-advisor: Prof. Michel Tytgat

En espérant que vous auriez été fières.

T

he focus of this thesis is on Dark Matter, and more precisely on a type of signal it could produce, namely gamma-ray lines. The nature of Dark Matter remains a mystery, and what is known about its properties is discussed in the first chapter. In particular, the relevance of gamma-ray lines in the search of Dark Matter is stressed. This thesis is aimed at the study of the connections between this type of potential Dark Matter signature and other indirect and direct detection signals, as well as, much more briefly, collider phenomenology. The goal is to establish the possibility to discriminate among different models and/or to obtain model-independent constraints.

In order to do so, in the second chapter, the methodology allowing for the model-independent study of a given phenomenology is introduced. It is based on the use of effective operators, and its applicability as well as its validity domain are discussed. Then, from the third to the fifth chapter, the original work carried out for this thesis is presented. First, the study of the production of gamma- ray lines from the decay of neutral Dark Matter particles is discussed. Second, an analogous study in the case of a Dark Matter candidate which is also metastable, but now carries a millicharge is exposed. Finally, the case of a Dark Matter candidate producing monochromatic photons through an annihilation accompanied by another annihilation into gluons is analyzed.

In the case of metastable Dark Matter, for both the neutral and millicharged instances, the emphasis laid on the interplay between the production of gamma-ray lines and the production of cosmic rays, unavoidable in the scenarios discussed here. For the neutral Dark Matter, the production of cosmic rays moderately constrains the possibility to emit a strong gamma-ray line, while for a millicharged Dark Matter candidate, the constraints are such that many effective operators could be ruled out if a simultaneous detection of a gamma-ray line and an excess of cosmic rays were to be confirmed. In the third scenario discussed here, the production of gluons allows to constrain this scenario thanks, once more, to the production of cosmic rays. Furthermore, it also enables the use of the direct detection and LHC data to exclude simple realizations of this scenario.

I

l faut commencer par le commencement, et avant d’exposer par le menu le travail accompli dans le cadre de cette thèse, je voudrais remercier chaleureusement celui sans qui elle n’aurait sans doute pas vu le jour, mon promoteur Prof. Thomas Hambye. Je suis consciente de la chance que j’ai eue d’être encadrée par une personne qui, outre le fait de me faire patiemment profiter de sa vaste expertise en physique des particules, a fait montre d’un enthousiasme contagieux et d’un réel intérêt pour mon futur académique. J’ai appris énormément durant ces quatres années, en un mot comme en cent, merci Thomas.

Je voudrais également remercier mon co-promoteur Prof. Michel Tytgat pour les discussions en- richissantes et les conseils prodigués tout au long de cette thèse. Merci également pour sa disponibilité et son aide pour préparer l’après-thèse. Un grand merci aussi au Prof. Petr Tinyakov, aux côtés de qui enseigner s’est révélé amusant et stimulant à la fois. Merci au Prof. Jean-Marie Frère, qui a également contribué à ma formation de physicienne (et indirectement à ma formation, non moins importante, d’apprentie skieuse).

I would like to particularly thank my collaborators, Michael Gustafsson and Chaïmae El Aisati. It has been a pleasure to do physics with you, you both are very meticulous, very passionate, and I am lucky to have you as colleagues and friends. I am also very grateful to the members of my jury, Prof.

Thomas Hambye, Prof. Michel Tytgat, Prof. Glenn Barnich, Prof. Marco Cirelli, Prof. Barbara Clerbaux and Prof. Alejandro Ibarra, for their availability to read and comment this thesis.

I very much enjoyed my PhD years, not only thanks to the physics, but also thanks to the friendly environment at the Service de Physique Théorique. Mik, Federico, Federica, Lorenzo, Bryan, Sabir, Simon, Maxim, Laura, Josemi, Germano, Yong... Thank you for making (or having made) this place so much fun! These PhD years in Brussels gave me the occasion to meet lots of crazy and amazing people, Almu, Sofi, Sara, Euli and all the "bzz group", I will miss you girls.

Et puis, il y a ceux qui ont toujours été là ou presque, ma famille, mes amis de longue date, mon amour. En particulier ma petite maman, Audrey, Thibaut, et bien sûr toi mon mari (si si, il faut s’habituer). Cet été, à la difficulté de l’écriture sont venus s’ajouter deux douloureux deuils, et sans vous j’aurais sans aucun doute perdu le cap. Vous êtes mes amarres, merci.

“ ”

Page

List of Tables v

List of Figures vii

Introduction 1

1 The dark matter puzzle: evidences, properties and unknowns 3

1.1 Evidences for dark matter . . . . 4

1.1.1 Cosmological scales . . . . 4

1.1.2 Clusters of galaxies scales . . . . 7

1.1.3 Galactic scales . . . . 8

1.2 Properties of dark matter . . . . 11

1.2.1 Particle dark matter . . . . 11

1.2.2 Stable dark matter . . . . 12

1.2.3 Neutral dark matter . . . . 14

1.2.4 Cold dark matter . . . . 17

1.2.5 Collisionless dark matter . . . . 19

1.2.6 Dark matter production . . . . 20

1.2.7 Dark matter velocity distribution . . . . 22

1.3 The search for non-gravitational evidences for dark matter . . . . 23

1.3.1 Direct detection . . . . 24

1.3.2 Colliders searches . . . . 30

1.3.3 Indirect detection . . . . 33

1.3.4 The photon line as a smoking-gun signature . . . . 41

2 Effective approaches to the dark matter phenomenology 45 2.1 Effective approach implementation . . . . 46

2.1.1 A famous example: Fermi effective theory for weak interactions . . . . 46

2.1.2 Effective approach to beyond the Standard Model physics . . . . 48

2.1.3 Choice of the operators basis . . . . 50

2.1.4 Symmetries and effective field theory . . . . 51

2.2 Validity of the effective approach . . . . 53

3 Neutral dark matter decay into photon lines 59 3.1 The set up . . . . 60

3.1.1 Dark matter decay and effective approach . . . . 60

3.1.2 Effective approach implications . . . . 61

3.2 Operators . . . . 63

3.3 Phenomenological aspects: multiple lines spectrum signal . . . . 67

3.4 Phenomenological aspects: cosmic ray continuum signal . . . . 70

3.4.1 Upper bounds on the monochromatic photons over cosmic rays ratios . . . . . 71

3.4.2 Linear combinations of operators . . . . 73

3.4.3 Derivation of the constraints . . . . 76

3.4.4 Results . . . . 79

3.5 Main messages . . . . 86

4 Millicharged dark matter decay into photon lines 89 4.1 The set up . . . . 90

4.1.1 Massless scenario: millicharge from kinetic mixing . . . . 90

4.1.2 Massive scenario: millicharge from Stueckelberg mechanism . . . . 91

4.2 Operators . . . . 93

4.2.1 Fermionic dark matter . . . . 94

4.2.2 Scalar and vector dark matter . . . . 95

4.3 Phenomenological Aspects: Cosmic Ray Continuum Signal . . . . 97

4.3.1 Upper bounds on the dark matter millicharge . . . . 97

4.3.2 Upper bounds on the monochromatic photons over cosmic rays ratios . . . . . 98

4.3.3 Constraints on the_DµDνψσ¯ ^µν_{ψD M}operator . . . . 100

4.3.4 Constraints on the_DµDνψσ¯ ^µν_{ψD Mφ}operator . . . . 101

4.3.5 Constraints on the_ψσ¯ ^µνD_µD_{νψD Mφ}operator . . . . 101

4.3.6 Constraints on the_Dµψσ¯ ^µνD_{νψD Mφ}operator . . . . 101

4.3.7 Results . . . . 102

4.4 Phenomenological aspects: polymonochromatic signal . . . . 108

4.4.1 Dark matter mass above_MZ . . . . 108

4.4.2 Dark matter mass below_MZ . . . . 109

4.4.3 Tentative 3.5 KeV Line . . . . 110

4.5 Main messages . . . . 111

5 Dark matter annihilation into photon and gluon lines 113 5.1 The set up . . . . 114

5.2 Phenomenological aspects: anti-proton flux . . . . 117

5.3 Phenomenological aspects: direct detection . . . . 122

5.3.1 Case 1. Gamma-ray line, quartic interactions . . . . 122

5.3.2 Case 2. Gamma-ray line, s-channel exchange . . . . 125

5.3.3 Case 3. Box-shaped spectrum, t-channel . . . . 128

5.3.4 Case 4. Box-shaped spectrum, quartic coupling and s-channel . . . . 130

5.4 Phenomenological aspects: collider constraints . . . . 131

5.4.1 Case 1. Gamma-ray line quartic interactions . . . . 131

5.4.2 Case 2. Gamma-ray line, s-channel exchange . . . . 132

5.4.3 Case 3. Box-shaped spectrum, t-channel . . . . 132

5.4.4 Case 4. Box-shaped spectrum, quartic coupling and s-channel . . . . 133

5.5 Main messages . . . . 133

Conclusions and outlook 137 A Acronyms 141 B Neutral dark matter appendix 143 Explicit expressions of the_FY/Land_G^R/I Y/Lratios . . . . 143

C Millicharged dark matter appendix 145 C.1 Massive kinetic mixing and the abscence of millicharge generation . . . . 145

C.2 Explicit model of millicharged vector dark matter . . . . 146

C.3 Cosmic rays production for the_Dµψσ¯ ^µνD_{νψD Mφ}with non-singlet DM . . . . 147

Bibliography 149

Table Page

1.1 Upper bounds on the DM self-interaction . . . . 20

1.2 Propagation parameters . . . . 34

3.1 Dimension-five operators . . . . 65

3.2 Dimension-six operators . . . . 66

3.3 Signal scenarios for hyperchargeless DM candidate . . . . 84

3.4 Signal scenarios for inert scalar doublet DM candidate . . . . 86

4.1 Millicharged DM Operators . . . . 94

5.1 Direct detection operators . . . . 122

Figure Page

1.1 Planck temperature power spectrum . . . . 5

1.2 DM halo profiles . . . . 9

1.3 DM Lifetime constraints . . . . 13

1.4 Constraints on millicharged particles . . . . 15

1.5 Constraints on strongly interacting massive particles . . . . 16

1.6 Dark matter production mechanisms . . . . 21

1.7 Direct detection experiments types . . . . 25

1.8 Direct detection results for spin-independent interaction . . . . 27

1.9 Direct detection results for spin-dependent interaction . . . . 29

1.10 DM production at colliders . . . . 31

1.11 Constraints on DM at colliders . . . . 32

1.12 Positron-to-electron ratio and DM implications . . . . 36

1.13 Antiproton flux measurement and DM implications . . . . 37

1.14 DM constraints from photon diffuse flux measurement . . . . 41

1.15 DM constraints from neutrino flux measurement . . . . 42

2.1 Feynman diagrams for DM pair production with initial state radiation . . . . 54

2.2 UV theory predictions versus effective theory predictions . . . . 55

3.1 DM decays into monochromatic photons . . . . 68

3.2 Bounds dependence on propagation and halo models . . . . 77

3.3 Upper bounds on the decay rate into gamma-ray lines from antiprotons and diffuse photons 80 3.4 Compared upper bounds on the decay rate into monochromatic photons . . . . 82

3.5 Upper bounds on the decay rate into monochromatic photons for SM final states . . . . . 83

4.1 Upper bounds on the decay of a millicharged DM into gamma-ray lines . . . . 103

4.2 Upper bounds on the decay of millicharged and neutral DM into gamma-ray lines . . . . . 105

4.3 Upper bounds on the gamma-ray line intensity as a function of_g⁰_Q⁰ . . . . 106

5.1 Topologies with pairs of gamma-ray lines . . . . 114

5.2 Topologies giving to a box-shaped gamma spectrum . . . . 115

5.3 Anti-proton fluxes from a WIMP candidate of_MDM=130GeV . . . . 119

5.4 Upper bounds on the annihilation cross section of DM into gluon pairs . . . . 120

5.5 Upper bounds on the annihilation cross section of DM into photon pairs . . . . 121

5.6 Direct detection bounds on the scattering cross-section induced by gluons . . . . 124

F

inding out what is our place in the Universe is an old human preoccupation, and somehow it seems that the more we know about the Universe, the smaller our place in it seems to be. In particular, the matter we are made of and the matter we know about, whose building blocks are the elementary particles of the Standard Model, turn out to account for a very small fraction of the matter content of the Universe. How small? The Planck satellite gave us the latest number in 2013, 85 % of the matter content of the Universe is under the form of a non-visible component, called dark matter. This result is the last one of a long series of gravitational evidence for the existence of dark matter, started almost one century ago. We observed its effects at many scales, ranging from galaxies to cosmological scales. But we are clueless with respect to what is its very nature.

As the dark matter presence is detected through its gravitational effects, it is fair to wonder whether the mismatch between the visible matter and the gravitationally sensed matter is not due to an incomplete understanding of gravity. Several modifications of gravity have been considered in order to account for dark matter, but so far none of them managed to consistently explain the observations at every involved scale. If the puzzle is not solved by modifying gravity, the only other solution is to consider the existence of a new, non-visible matter component. If this component is an elementary particle, as already anticipated it is not a Standard Model particle. A particle physics explanation of the origin of dark matter therefore requires beyond the Standard Model physics. This conclusion nurtures the hope for new discoveries after the one of the Standard Model scalar, and is backed by one other missing element in the Standard Model, an explanation for the mass of the neutrinos.

Saying that particle physicists have been prolific in building dark matter models is a euphemism.

Among the most popular candidates, the lightest supersymmetric particle, sterile neutrinos, axions, or inert doublets have a place of choice. So far the dark matter searches have not reported a clear positive detection, and therefore none of these numerous possible candidates has been singled out.

On top of searching for a striking non-gravitational signature of the presence of dark matter, it is of utmost importance to find ways to use the existing and growing data, independently of a given model, in order to be able to put generic constraints on dark matter properties.

This motivates the approach followed in this thesis, which focuses on the connections between one type of signal considered as a very clear hint towards the detection of dark matter, namely gamma-ray lines, and other possible signals associated with the production of such lines. While a gamma-ray line detection would strongly suggest a discovery of dark matter, the study of associated

signals might allow to discriminate among various models accounting for a given line. This work mainly focuses on associated cosmic rays production, which provides a way to probe dark matter through indirect detection. However, direct detection – the detection of the scattering of dark matter off nuclei – and colliders phenomenology – based on the potential production of dark matter at LHC (and Tevatron) – will also be discussed, even if more briefly.

During my PhD years, I have witnessed twice the excitement generated by the tentative detection of monochromatic photon lines. The first time took place in 2012, when a tentative gamma-ray line with an energy of 130 GeV originating from our Galactic Center was reported. In 2014, another line at an energy of 3.5 KeV has been observed in the X-ray spectrum of several clusters of galaxies. Although the dark matter origin and even the mere existence of these tentative lines has since then been heavily challenged, these examples illustrate how vivid is the search for this type of dark matter signature.

Those years have also been the years of the release of many direct and indirect detection experiments results. Among others, LUX, and XENON for the direct detection searches, AMS and Fermi-LAT for the indirect detection searches, have provided cutting-edge data for the dark matter hunt. Of course, the LHC dark matter searches complete this dynamical experimental landscape.

In the light of this impressive series of new experimental probes of the DM particle, beside many studies which have analyzed what are its consequences for specific models, and complementarily to these studies, it is absolutely necessary to think about ways to consider the search for DM as model-independently as possible. A model-independent approach allows to build a bridge linking the generic phenomenological consequences of different types of searches, such as a potential gamma-ray line observation and (in)direct and colliders constraints.

In this thesis, three types of scenarios of gamma-ray line production are analyzed without relying on an explicit dark matter model. The first analyzed scenario, presented in Chapter 3 and based on the work carried on in Ref. [1], involves a neutral dark matter particle with a mass above the Z boson mass, producing gamma-ray lines through a slow decay. In this context, the use of a model-independent approach based on effective operators is fully justified. Therefore the effective theory of such decay is established and the constraints from cosmic rays observation are derived. In Chapter 4, a similar scenario with a millicharged dark matter instead of a neutral dark matter is discussed, following the original work of Ref. [2]. The third scenario, under scrutiny in Chapter 5 and based on Ref. [3], focuses on the possibility that the production mechanism of photon lines –an annihilation instead of a decay as in the previous chapters– implies the production of gluon lines. This framework implies a very rich and interconnected phenomenology, and allows to relate the intensity of the gamma-ray line to other signals and constraints. The latest experimental results in dark matter search are introduced in Chapter 1, while the effective theory background used in the bulk of this thesis to make dark matter predictions is described in Chapter 2. But before reviewing the required tools to delve into a particular dark matter phenomenology, our current general knowledge about dark matter should be summarized.

This is why an important part of the first chapter is dedicated to a review of the evidence for the existence of dark matter as well as of its properties.

C h a p t

1

The dark matter puzzle: evidences, properties and unknowns

F

or almost a century, scientists have been wondering about the existence of invisible matter in our Universe. From the works of E. Opïk (1915) [4], J.C. Kapteyn (1922) [5] and F. Zwicky (1933) [6] to the latest result of the Planck Collaboration (2013) [7], the matter content that can be inferred through various gravitational effects has been confronted with the amount of detected visible matter. And evidence for a blatant mismatch between these two quantities has been accumulating with time, for systems ranging from stars around the galactic plane up to the entire visible Universe. This mismatch could be solved in two ways, either the theory of gravity used to compute the gravitational effects has to be modified in such a way that the deduced mass corresponds to the visible matter, either a dark (non-electromagnetically interacting) matter component has to be assumed to exist. The dark matter (DM) hypothesis is able to account for the discrepancies at all the scales at which they appeared, whereas in the case of Modified Gravity it is more difficult, especially when dealing with the larger scales such as cosmological scales (see Sec. 1.1.1) and clusters of galaxies scales (see Sec.

1.1.2). This thesis focuses on the DM hypothesis. More precisely, it focuses on the possibility that this matter component is made of a particle. This chapter aims to briefly review what are the evidences for the existence of DM in our Universe (Sec. 1.1), to summarize what are the required properties for a particle to account for DM (Sec. 1.2), and finally to review the state of the art in the effort to identify DM particles (Sec. 1.3).

1.1 Evidences for dark matter

The scale of the Universe involved in establishing the presence of DM, ranging from the largest up to the smallest, has been chosen as the ordering criterion to present the evidence for the existence of DM.

This allows to start with one of the most global, as well as the most recently reconfirmed indication of the presence of DM in our Universe.

1.1.1 Cosmological scales

Making the assumptions that our Universe is spatially homogeneous and isotropic at large scales, and that the evolution of space-time obeys General Relativity, a precise picture of the history of the Universe back to very early times emerges, the Big Bang Model. The early Universe consisted of a hot plasma of elementary particles, whose temperature cooled down as time went by due to the expansion of the Universe. During its first seconds, the Universe went through many radical changes, such as the electroweak and QCD phase transitions, that implied a drastic change in the way the elementary particles interacted, and then the nucleosynthesis, responsible for the formation of the primordial nuclei. However, as the purpose here is to focus straightaway on observations related to DM, we will skip the first 380 000 years of the history of the Universe to reach the moment at which the Universe became transparent to photons after the temperature dropped below₃₀₀₀K, because the temperature was then low enough to bind electrons and protons into hydrogen atoms. This particular event is called the photon decoupling. The photons present at that time have since then been streaming freely to reach us today, to form the Cosmic Microwave Background (CMB), whose features allow to deduce many global characteristics of our Universe, among which the amount of DM it contains.

The temperature of the CMB is highly homogeneous and isotropic, however there are temperature fluctuations with respect to the CMB mean temperature of the order of _∆T/T≤10⁻⁵_.Primordial fluctuations are thought to have been created in an early phase of the Universe called Inflation. The study of how the CMB temperature fluctuations are distributed over the sky as a function of the angular scale delivers much information about the feature of the Universe, like its geometry or, more importantly to us, about its content. The variation of the CMB temperature as a function of the direction_nˆof the sky we look at can be parametrized as a series of spherical harmonic functions:

(1.1) ^∆

T( ˆn)

T₀ =T( ˆn)−T₀ T₀ =

X∞ l=0

+l

X

m=−l

a_lmY_lm( ˆn),

where_{T0=2.72548±0.00057}K [8] is the mean CMB temperature and the coefficients of the expansion are given by

(1.2) _alm=

Z 2π 0

d_φ Z _π

−φd_θ∆T( ˆn)Y_lm^∗ ( ˆn).

The quantity that is used to parametrized the anisotropy of the CMB temperature is the angular power spectrum_Cl of the temperature fluctuations, which is defined as the variance of the harmonic

2 10 50 0

1000 2000 3000 4000 5000 6000

D

[ µ K

]

90^◦ 18^◦

500 1000 1500 2000

Multipole moment, `

1^◦ 0.2^◦ 0.1^◦

Angular scale

Figure 1.1. Temperature power spectrum (foreground-subtracted) as measured by Planck.

At low multipoles (_l≤50), the x-axis is logarithmic, whereas for_l≥50it is linear. The shaded region represents the cosmic variance, which is not included in the error bars.

Note that reference angular scales have been placed in front of their corresponding multipole. Figure taken from [9].

coefficients

(1.3) ^­_alma^∗

l⁰m⁰

®=C_lδll0δmm⁰.

The delta functions arise because of the anisotropy of our Universe. As we only have one Universe to take samples and perform the average in Eq. (1.3), there is an intrinsic limitation to the maximum number of independent_mmodes. This maximum number is equal to_2l+1, so the value of_Clthat can actually be computed is

(1.4) _Cl= ¹

2l+1

l

X

l=−l

­|a_lm|²® ,

and this definition of_Cl has an associated error equal to_∆Cl=^p_2/(2l+1). This intrinsic error is called the cosmic variance. The quantity_{Dl≡Cl/(2l+1)}as a function of the multipole moment_lis represented in Fig. 1.1 as it has been measured by the Planck Satellite.

The power spectrum can be separated in three parts as a function of the multipole moment (or the angular scale). A first part at_2≤l.¹⁰⁰, where the angular power spectrum features a plateau, called

the Sachs-Wolfe plateau [10]. This part of the spectrum essentially contains information about the initial conditions of the density perturbations. In the second part of the spectrum, from₁₀₀.^l.¹⁰⁰⁰, large acoustic oscillations are present. This is the part of the spectrum we will focus on, because it is the one that tells us about the matter content of the Universe. In the third part of the spectrum, at higher multipoles (smaller scales), the oscillations are smoothed out, this is the damping tail of the spectrum. There are two main reasons why oscillations on small scales are damped: the first is that the baryon-photon fluid is not perfectly isotropic, and this translates into a shear viscosity term. The second reason is that as recombination occurs, photons acquire a mean free path that will allow the hot photons to travel towards colder regions. As hot and cold photons mix, the temperature gradient is smoothed out.

A key feature to understand why the oscillations start at_l=100is that this value of the multipole moment, meaning_θH=1^◦, corresponds to the size of the horizon at the time when CMB photons were emitted. For angular scales smaller than_θH=1^◦, the dynamics of the baryon-photon plasma at the time of recombination explains the presence of acoustic oscillations. Put in very simple words, on the one hand gravity tends to compress the baryon-photon fluid inside the potential wells, but the radiation pressure due to the photons resists the compression from gravity, and as a result acoustic oscillations arise. The baryon-photon fluid density undergoes a series of compression and rarefaction phases, which are respectively translated into an increase and a decrease of the temperature, and DM enters as responsible for the potential wells. The first acoustic peak corresponds to a wavelength which went through exactly one compression since entering the horizon, whereas the second peak corresponds to one rarefaction cycle. Taking the ratio of the heights of the second over the first peak, it is possible to know about the baryonic matter density of our Universe. Basically, the effect of the baryon density is to increase the mass in a given potential well, therefore the baryon-photon fluid goes deeper inside the well, so the compression phase will be enhanced with respect to the rarefaction one (baryon load effect). In order to know about DM, it is necessary to consider at least the third peak as well. Dark matter has two main effects on the spectrum: increasing the DM density reduces the overall amplitude of the peaks and boosts the third peak with respect to the second one. What mainly determines the amplitude of the oscillations during the radiation-dominated era is the so-called radiation driving, which stands for the fact that during the rarefaction phase, the photon pressure causes the potential wells to decay, so the fluid expands further and the amplitude of the oscillations is boosted. If the DM density is increased, the potential wells are deeper, thus the driving effect is less important and the overall amplitude of the peaks is reduced. Increasing the DM density enhances the third peak with respect to the second one because the deeper the potential well, the more effective the baryon load effect is. Having a third peak that is boosted to a height comparable to the second peak like what is observed indicates that DM dominated the matter density in the plasma before recombination. For a review about CMB anisotropies, seee.g.[11].

To put numbers on this qualitative picture, let us introduce the quantity that is used to define the cosmological densities of the components of our Universe. The geometry of our Universe is observed

to be flat, and the total energy density of a flat universe is given by the value_ρC≡^3H

2

8πG, a quantity called the critical density. The energy density of a given component_Xis usually given in terms of a fraction of the critical density,

(1.5) _{ρX =ΩXρC=ΩXh}²_1.88×10⁻²⁹g cm⁻³_,

The most recent best-fit values for the matter energy densities of the baryons and the DM obtained by the Planck Collaboration are [7]:

(1.6) _Ωbh²_{=0.02205±0.00028} and _{ΩD Mh}²_{=0.1199±0.0027,}

for the baryons and the DM respectively. These numbers mean that not only is DM present in our Universe, but it is dominating by far its matter content. Before closing this section, let us point out that when putting together Big Bang Nucleosynthesis predictions of primordial light nuclei abundances and actual measurements of the latter, an independent confirmation of the above CMB value for the baryon density is found, with a larger error though.

1.1.2 Clusters of galaxies scales

The mass of galaxy clusters In 1933, F. Zwicky computed the velocities of galaxies ininside the Coma Cluster [6]. Making use of the virial theorem, he calculated its mass content and compared it to an estimate of the luminous matter inside the cluster. Zwicky deduced that a mass-to-light ratio of at least 400 solar masses per solar luminosity was necessary in order to explain the velocities he had obtained. Numerous results have since then been confirming that galaxy clusters are dark matter dominated environments [12]. These results involve other clusters, and also different techniques in order to compute the cluster mass, as for example gravitational lensing or temperature measurements of hot gas inside the cluster. The gravitational lensing method relies on the distortion of the image of background objects due to the gravitational mass of an astrophysical object to infer the shape of its potential well and thus its mass. As for the temperature measurements, if the cluster is assumed to be in hydrostatic equilibrium, the temperature at a given radius is expected to be proportional to the enclosed mass. Again, comparing the temperature measurements to what corresponds to the visible mass, a clear disagreeement is found.

Bullet Cluster Along with the CMB anisotropy spectrum, the Bullet Cluster provides what is believed to be the best evidence of the existence of dark matter so far. It refers to the observation of a collision between two clusters of galaxies, more precisely to the smallest of the two colliding clusters.

In these clusters, the main baryonic matter component is known to be present under the form of gas rather than stars. During the collision, the stars and the gas of the clusters behave differently. On the one hand, the gas components of the two clusters interact electromagnetically, and these interactions will affect the spatial distribution of the plasma. On the other hand, the stars belonging to the galaxies of the clusters will go through the collision almost undisturbed, they are said to be collisionless. So the

stars and the gas are expected to exhibit a significant offset after the collision. Indeed, observations show that the collisionless stellar component and the X-ray emitting gas are spatially separated.

Thanks to gravitational lensing, the gravitational wells of the clusters have been traced back [13].

And this is where dark matter enters the story, because the lensing maps show that the centers of the two potential wells approximately coincide with the distribution of galaxies, and not with the gas distribution. So it means that the gravitational mass is mainly distributed where the stars are, and not where the gas – the main baryonic mass component – is. As a consequence, there must be an unseen matter component, which does not self-interact too much in order to go through the collision as the stars. So, on top of telling us about the presence of DM in the system, the Bullet Cluster places bounds on the self-interaction of DM. In Sec. 1.2.5, this point will further be investigated.

Large scale structures Clusters are not the largest scale structures observed in the Universe. The clusters themselves are found to lie in filaments, bubbles and sheet-like structures. These structures were formed out of primordial density fluctuations with initial power spectrum dictated by the CMB.

These fluctuations first grow linearly, but a phase of non-linear evolution follows, requiring numerical simulations to be computed. These N-body simulations take only dark matter into account in the matter budget, with an abundance agreeing with the CMB-derived value [14]. The velocity of the particles at decoupling determines whether the structure formation history will be top-down (large scale structures form first and then fragment) or bottom-up (small scale structures form first and then merge.) If the particles were relativistic at decoupling, then the structure formation evolves in a top-down fashion, whereas if they were not, then the bottom-up formation occurs. The two scenarios result in different galaxy distributions, with more filaments in the case of the top-down formation, and more clumps in the case of bottom-up history. The second picture shows a good agreement with the distribution of galaxies observed by redshift surveys like SDSS [15]. This indicates that DM was non-relativistic at the time of decoupling, which is referred as cold dark matter (CDM), see Sec. 1.2.4.

1.1.3 Galactic scales

Galaxy rotation curves At the galactic scale, the most direct evidence for dark matter appears.

Rotation curves of galaxies consist in the graph of circular velocities of stars and gas as a function of their distance from the galactic center. In 1931, the rotation curve of the Andromeda galaxy has been obtained [16]. The expected behaviour of such curves at large radii is_v(r)∼^p_r⁻¹, just out of newtonian dynamics,

(1.7) ^v

2

r =G M(r) r² ,

where_M(r)=^R_ρ(r)4πr²_dr, which, if no DM were present, would be constant beyond the optical disc.

However, what is observed is that the velocity remains approximately constant at large radii, which implies the existence of a halo with_M(r)∼rand thus_ρ(r)∼r⁻². A similar behaviour has since then been observed in galaxies with kpc-100 kpc sizes.

10⁻³ 10⁻² 10⁻¹ 10⁰ 10¹ 10² r[kpc]

10⁻² 10⁻¹ 10⁰ 10¹ 10² 10³ 10⁴

ρDM[GeV/cm3]

NFW Moore Iso

Profile _{α β γ ρs rs}

[GeV_/cm³_{] [}kpc_]

NFW [17] 1 3 1 0.184 24.42

Moore [18] 1 3 1.16 0.105 4.38

Iso [19] 2 2 0 1.387 30.28

Figure 1.2. DM halo profiles plots and parameters for two popular numerical simulation results (Moore and NFW) and for an the truncated isothermal halo. The values of_ρs and_rsreported here correpond to the Milky Way halo.

Dark matter halo profile From the considerations of the previous paragraph, the behaviour of the DM halo profile at large radii is known to be_ρ(r)∼r⁻². N-body simulations have also been used to understand the DM density at galactic scales, and they suggest the existence of a universal dark matter profile, with the same shape for all masses and input power spectra [17], for systems ranging from clusters to dwarf spheroidal galaxies. In many cases, the halo shape can be parametrized as

(1.8) _ρ(r)= ^ρs

(r/r_s)^γ[1+(r/r_s)^α]^(β−γ)/α,

but various groups ended up with different values for the parameters_α,β,γ, which translates into a different spectral shape in the innermost regions of galaxies and clusters. In Fig. 1.2 the plots of three profiles are reported, as well as the corresponding sets of parameters. Two of them (NFW and Moore) are simulations results, whereas the truncated isothermal profile is a convenient parametrization for a profile with a flat core at small radii. Fig. 1.2 shows clearly that simulations have a tendency to prefer cuspy profiles.

Numerical simulations of DM halos agree very well with what is know about DM halos at scales larger than about 1 Mpc. However, at smaller scales, there are some discrepancies between numerical simulations predictions and astrophysical observations. These discrepancies can be separated into three main issues which are listed below.

Core versus cusp problem While numerical simulations prefer cuspy profiles in the inner regions of the halo, flat cores are observed in astrophysical objects such as the low surface brightness galaxies and some dwarf shperoidal galaxies, which prefer a profile much closer to the truncated isothermal one [20–22]. Whether a cusp is really not compatible is still under debate.

Missing satellite problem There is a discrepancy between the number of satellite galaxies of the Milky Way and Andromeda and the number of subhaloes of compatible mass predicted by DM simulations [23].

Too-big to fail problem Numerical simulations predict that the Milky Way should have at least six subhalos with maximal circular velocities higher than 30 km/s and infall masses of_{[0.2−0.4]×10}¹⁰_M¯, and yet none of the observed Milky way satellite with luminosities higher than_5L¯are compatible with this prediction. So, if the Milky Way is not a statistical anomaly, the possible explanations of these non-observations are two: either these massive subhalos are present but not detected because they are faint, or they do not exist. Both explanations would require some refinements of the structure formation theory [24].

These three types of tension between numerical simulation results and astrophysical observations might be eased either by blaming incomplete astrophysical observations or by advocating some mechanisms involving baryons in the halo formation. Baryonic processes, which are not included in numerical simulations, may indeed affect the DM distribution on small scales by heating it to larger radii. Another direction of investigation followed to relieve these tensions is to alter what are considered to be the standard properties of the dark matter, see Sec. 1.2.4-1.2.5.

Dark matter local density After tracing back the DM at galactic and larger scales, it is natural to wonder what is the DM halo shape of our own galaxy and the DM abundance at our very position, in the solar system. It is tricky to infer the Milky Way halo shape, because it is not possible to directly observe the radial velocities of the stars of our own Galaxy. For the stars that are within the sun’s radius around the galactic center, it is possible to compute the radial velocity knowing the maximal line-of-sight velocity of the star, which is done with Doppler shift measurements, and the sun’s position and velocity. To apply this method for outer stars, it is necessary to know their position as well, which introduces a large uncertainty in the velocity rotation curve [25]. Another difficulty is to discriminate the stellar mass distribution from the dark matter distribution. Using dynamical modeling of the Milky Way it is possible to do this to some extent, but so far the DM halo reconstruction is not precise enough to allow for a discrimination between cuspy and shallower profiles [26].

As for_ρ¯, the local value of the DM density, it is possible to determine it relying of the global modelling of the halo, and integrating the DM density up to the sun’s distance to the galactic center.

This has been done in [27], where they obtain the value quoted in Eq. (1.9a). However, a subsequent work did not confirm their result, especially the claimed uncertainty [25]. The authors of the latter work find a range of consistent values for_ρ¯, given in Eq. (1.9b). A derivation independent of the mass modelling of the entire galaxy has been carried out in [28], with a result presented in Eq. (1.9c).

ρ¯=0.389±0.025GeV_/cm³_, (1.9a)

ρ¯∈[0.2−0.4]GeV_/cm³_, (1.9b)

ρ¯=0.43±0.11±0.10GeV_/cm³_. (1.9c)

A word should be spent on what is meant here by local DM density. As explained above, this value is determined by the dynamics of the galactic halo. Nothing prevents this value to vary within the solar system, particularly at the precise position of the sun. At this scale, there are only upper bounds on ρ_¯ originating from planetary motions, which are at the level of_ρ¯.¹⁰⁵GeV_/cm³ [29, 30]. So the DM density might be locally bigger than the values reported in Eqs. (1.9), as long as the contribution to the integrated mass is negligible. In the following, when computing potential signals from dark matter, the conservative value_ρ¯=0.3GeV_/cm³ will be used.

1.2 Properties of dark matter

A network of evidence, some of them quickly reviewed in the previous section, indicates that matter is mainly under the form of dark matter at galactic scales and beyond. We know that DM should be around because we see its gravitational effects, but what else do we know about it? Its nature is elusive, but nevertheless some properties can be deduced indirectly and will be listed in this section. As some of these accepted properties are challenged in the work carried out for this thesis, it is important to know how much a departure from the standard picture is legitimate. This is why some time will now be spent to precisely assess these properties.

1.2.1 Particle dark matter

As already anticipated, in this thesis the DM is assumed to consist of an elementary particle and it should be checked whether this is a well-motivated assumption. First, there are contributions to the non-luminous matter which are known not to be under the form of elementary particles, as planets or stellar remnants like brown and red dwarfs. However, these astrophysical objects are made of baryons, and we know from CMB that the baryons cannot account for the total matter density, at least at cosmological scales, see Eq. (1.6) though at the galactic scale they could in principle contribute to a larger fraction of the total mass. Second, there are other potential candidates for dark matter which are not elementary particles and that could account for the total of the DM amount, the primordial black holes (PBHs). These PBHs can form in the early Universe when the density perturbations become large. As PBHs were produced before PBHs and non-luminous astrophysical objects belong to the category of massive compact objects and can therefore act as gravitational lens, producing an effect called gravitational microlensing that can be used to put constraints on the abundance of such objects in our Galaxy.

Gravitational microlensing consist in an apparent brightening of a source due to the passage of a gravitational lens in the foreground. It is a transient phenomenon, which allows to detect objects with masses₁₀⁻⁷_M¯.^M.^10M¯[31]. The MACHO and EROS surveys have been looking for such signal in the Magellanic Clouds, and found no events corresponding to masses₁₀⁻⁷_M

¯.^M.^10−3M¯, which excludes that compact objects with this mass range could form a fraction larger than 10 % of the galactic halo [32]. Combined results of MACHO and EROS-2 collaboration roughly exclude that

compact objects constitute more than 10 % of the galactic halo for masses₁₀⁻⁷_M¯.^M.^10M¯[31].

PBHs mass range is much wider than what is probed by MACHO and EROS, but other constraints, such as lifetime requirements (putting a lower bound on the possible PBH mass as DM) are narrowing the window of PBHs masses compatible with PBHs as unique DM component, and the current viable window could even be closed in a near future [33].

As massive compact objects cannot provide an explanation for the total amount of DM, assuming that DM is mainly made of an elementary particle is one of the simplest things to do. What kind of particle could it be? The general properties exposed below provide guidelines to answer this question.

1.2.2 Stable dark matter

Lifetime requirements We see the effect of dark matter in today’s Universe, but its production mechanism took place in the very Early Universe, around₁₀⁻¹²-₁₀⁻⁶s after the Big Bang (see Sec.

1.2.6), so the DM particle must be extremely long-lived. A minimal requirement would then be that its lifetime is greater then the age of the Universe,_{τDM≥τU '4×10}¹⁷s. In order to meet such a large lifetime requirement, either DM can be considered as completely stable or its lifetime could be finite, but should be very long. Exactly how long depends on the kind of particles produced by the decay. If the DM decays into SM particles, there is a possibility that these SM particles produce a detectable signal. Ultimately, whatever SM particle produced by the decay of the DM particle will decay into stable particles like electrons and positrons, protons and antiprotons, neutrinos and photons. This is the principle of indirect detection, that will be explained in more details in Sec. 1.3.3. For the time being, it is enough to know that the DM lifetime is constrained by indirect detection searches to be of the order of_{τD M}&¹⁰²⁴-₁₀²⁹s, depending on the decay channel considered [34–37].

Of course, these bounds are model-dependent, because they depend on how much the DM will produce of these particles. Moreover, if the DM decays into other hidden sector particles, then none of the previous bounds would apply. Other types of approaches aim to put an upper bound on_τDM without looking to specific SM final decay products. The idea is to look for consequences of the mere fact that there is a decay, which are either an energy release or a DM mass loss. Motivated by the missing satellite problem mentioned in Sec. 1.1.3, a particular set-up has been studied in which the DM particle decays into a slightly less massive stable particle and a light particle. The stable daughter particle receives a small kick velocity _vk=c∆M/M where_∆M is the mass difference between the parent and the daughter particles and_Mis the parent particle mass. Such a kick velocity might affect the evolution of structure formation, erasing small-scale structures, which up to a certain point helps with the missing satellite problem, but if the effect is too large, structure formation is compromised.

Along this line, several works have been putting constraints on the DM lifetime of the order of τD M&¹⁰¹⁷-₁₀²⁰s [39–42].

Recently, a work investigated the consequences of a DM decay inside a neutron star after its capture [43]. Note that a necessary condition for the DM capture inside the neutron star is a sizeable DM-nucleon cross-section. The claim is that the energy released by a decay could trigger a phase