Scalar field dark matter and the Higgs field
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1 Scalar field dark matter and the Higgs field Catarina M. Cosme in collaboration with João Rosa and Orfeu Bertolami Phys. Lett., B759:1-8, 2016 COSMO-17, Paris Diderot University, 29 August 2017
2 Outline Introduction and Motivation; Oscillating scalar field as dark matter candidate; Inflation and initial conditions; Possible scenarios Non-renormalizable interactions model; Warped extra-dimension model; Conclusions and future work. 29/08/2017 Scalar field dark matter and the Higgs field 2
3 Introduction and motivation Dark matter (DM) 26.8 % of the mass-energy content of the Universe [Planck Collaboration 2015]; 29/08/2017 Scalar field dark matter and the Higgs field 3
4 Introduction and motivation Dark matter (DM) 26.8 % of the mass-energy content of the Universe [Planck Collaboration 2015]; Evidence of DM come from different sources; 29/08/2017 Scalar field dark matter and the Higgs field 4
5 Introduction and motivation Dark matter (DM) 26.8 % of the mass-energy content of the Universe [Planck Collaboration 2015]; Evidence of DM come from different sources; Several candidates; 29/08/2017 Scalar field dark matter and the Higgs field 5
6 Introduction and motivation Dark matter (DM) 26.8 % of the mass-energy content of the Universe [Planck Collaboration 2015]; Evidence of DM come from different sources; Several candidates; What is dark matter made of? 29/08/2017 Scalar field dark matter and the Higgs field 6
7 Introduction and motivation Dark matter (DM) 26.8 % of the mass-energy content of the Universe [Planck Collaboration 2015]; Evidence of DM come from different sources; Several candidates; What is dark matter made of? We propose: oscillating scalar field as DM candidate, coupled to the Higgs boson; 29/08/2017 Scalar field dark matter and the Higgs field 7
8 Introduction and motivation Dark matter (DM) 26.8 % of the mass-energy content of the Universe [Planck Collaboration 2015]; Evidence of DM come from different sources; Several candidates; What is dark matter made of? We propose: oscillating scalar field as DM candidate, coupled to the Higgs boson; Previous works: Higgs-portal DM models: abundance of DM is set by the decoupling and freeze-out from thermal equilibrium m ~ GeV TeV (Weakly Interacting Massive Particles - WIMPs) [Silveira, Zee 1985; Bento, Bertolami, Rosenfeld 2001; Burgess, Pospelov, ter Veldhuis 2001; Tenkanen 2015]. 29/08/2017 Scalar field dark matter and the Higgs field 8
9 Oscillating scalar field as DM candidate Our proposal: Oscillating scalar field, φ, as DM candidate; φ acquires mass through the Higgs mechanism; Feeble interactions with the Higgs boson m φ ev ; extremely small selfinteractions oscillating scalar condensate that is never in thermal equilibrium. 29/08/2017 Scalar field dark matter and the Higgs field 9
10 Oscillating scalar field as DM candidate When does it start to oscillate? KG: φ + 3H φ+m 2 φ φ=0 29/08/2017 Scalar field dark matter and the Higgs field 10
11 Oscillating scalar field as DM candidate When does it start to oscillate? KG: φ + 3H φ+m 2 φ φ=0 friction term 29/08/2017 Scalar field dark matter and the Higgs field 11
12 Oscillating scalar field as DM candidate When does it start to oscillate? KG: φ + 3H φ+m 2 φ φ=0 friction term Before the electroweak phase transition (EWPT) (T~100 GeV): m φ < H 29/08/2017 Scalar field dark matter and the Higgs field 12
13 Oscillating scalar field as DM candidate When does it start to oscillate? KG: φ + 3H φ+m 2 φ φ=0 friction term Before the electroweak phase transition (EWPT) (T~100 GeV): m φ < H Overdamped regime. No oscillations. 29/08/2017 Scalar field dark matter and the Higgs field 13
14 Oscillating scalar field as DM candidate When does it start to oscillate? KG: φ + 3H φ+m 2 φ φ=0 friction term Before the electroweak phase transition (EWPT) (T~100 GeV): m φ < H Overdamped regime. No oscillations. After the EWPT: m φ > H 29/08/2017 Scalar field dark matter and the Higgs field 14
15 Oscillating scalar field as DM candidate When does it start to oscillate? KG: φ + 3H φ+m 2 φ φ=0 friction term Before the electroweak phase transition (EWPT) (T~100 GeV): m φ < H Overdamped regime. No oscillations. After the EWPT: m φ > H Underdamped regime. The field oscillates. 29/08/2017 Scalar field dark matter and the Higgs field 15
16 Oscillating scalar field as DM candidate When does it start to oscillate? KG: φ + 3H φ+m 2 φ φ=0 friction term Before the electroweak phase transition (EWPT) (T~100 GeV): m φ < H Overdamped regime. No oscillations. After the EWPT: m φ > H Underdamped regime. The field oscillates. H rad = π 90 g T 2 M Pl ρ ϕ,0 = 1 2 m ϕ 2 a 0 3 ϕ i 2 n φ s = ρ ϕ /m φ 2π 2 45 g ST 3 = const 29/08/2017 Scalar field dark matter and the Higgs field 16
17 Oscillating scalar field as DM candidate DM abundance: Ω φ,0 ρ ϕ,0 2 φi 2 = m φ ρ c,0 6H 2 0 M2 Pl g s,0 g s T 0 T osc 3 H EW ~10 5 ev 29/08/2017 Scalar field dark matter and the Higgs field 17
18 Oscillating scalar field as DM candidate DM abundance: Ω φ,0 ρ ϕ,0 2 φi 2 = m φ ρ c,0 6H 2 0 M2 Pl g s,0 g s T 0 T osc 3 H EW ~10 5 ev T osc 29/08/2017 Scalar field dark matter and the Higgs field 18
19 Oscillating scalar field as DM candidate DM abundance: Ω φ,0 ρ ϕ,0 2 φi 2 = m φ ρ c,0 6H 2 0 M2 Pl g s,0 T 0 g s T3 osc H EW ~10 5 ev T osc m φ > H at T EW 29/08/2017 Scalar field dark matter and the Higgs field 19
20 Oscillating scalar field as DM candidate DM abundance: Ω φ,0 ρ ϕ,0 2 φi 2 = m φ ρ c,0 6H 2 0 M2 Pl g s,0 T 0 g s T3 osc H EW ~10 5 ev T osc m φ > H at T EW T EW 29/08/2017 Scalar field dark matter and the Higgs field 20
21 Oscillating scalar field as DM candidate DM abundance: Ω φ,0 ρ ϕ,0 2 φi 2 = m φ ρ c,0 6H 2 0 M2 Pl g s,0 T 0 g s T3 osc H EW ~10 5 ev T osc m φ > H at T EW T EW m φ φ i = g 100 1/2 ϕ i GeV 1 ev 29/08/2017 Scalar field dark matter and the Higgs field 21
22 Oscillating scalar field as DM candidate DM abundance: Ω φ,0 ρ ϕ,0 2 φi 2 = m φ ρ c,0 6H 2 0 M2 Pl g s,0 T 0 g s T3 osc H EW ~10 5 ev T osc m φ > H at T EW m φ < H at T EW T EW m φ φ i = g 100 1/2 ϕ i GeV 1 ev 29/08/2017 Scalar field dark matter and the Higgs field 22
23 Oscillating scalar field as DM candidate DM abundance: Ω φ,0 ρ ϕ,0 2 φi 2 = m φ ρ c,0 6H 2 0 M2 Pl g s,0 T 0 g s T3 osc H EW ~10 5 ev T osc m φ > H at T EW m φ < H at T EW T EW T = 90 π 2 1/4 1/4 g MPl m ϕ m φ φ i = g 100 1/2 ϕ i GeV 1 ev 29/08/2017 Scalar field dark matter and the Higgs field 23
24 Oscillating scalar field as DM candidate DM abundance: Ω φ,0 ρ ϕ,0 2 φi 2 = m φ ρ c,0 6H 2 0 M2 Pl g s,0 T 0 g s T3 osc H EW ~10 5 ev T osc m φ > H at T EW m φ < H at T EW T EW T = 90 π 2 1/4 1/4 g MPl m ϕ m φ φ i = g 100 1/2 ϕ i GeV 1 ev m φ φ i = g 100 1/2 ϕ i GeV 4 ev 29/08/2017 Scalar field dark matter and the Higgs field 24
25 Inflation and initial conditions If the Higgs field is the unique source of mass during inflation m ϕ ~O(EW scale) Light field de-sitter fluctuations ~ H inf sizeable Cold Dark Matter (CDM) isocuvature modes 2π in the CMB spectrum ruled out (do not respect the observational constraints on the CDM isocurvature perturbations). 29/08/2017 Scalar field dark matter and the Higgs field 25
26 Inflation and initial conditions If the Higgs field is the unique source of mass during inflation m ϕ ~O(EW scale) Light field de-sitter fluctuations ~ H inf sizeable Cold Dark Matter (CDM) isocuvature modes 2π in the CMB spectrum ruled out (do not respect the observational constraints on the CDM isocurvature perturbations). Gravitational interactions during inflation L int = c 2 φ 2 V χ 2 m φ ~ H inf Massive field; M Pl 29/08/2017 Scalar field dark matter and the Higgs field 26
27 Inflation and initial conditions If the Higgs field is the unique source of mass during inflation m ϕ ~O(EW scale) Light field de-sitter fluctuations ~ H inf sizeable Cold Dark Matter (CDM) isocuvature modes 2π in the CMB spectrum ruled out (do not respect the observational constraints on the CDM isocurvature perturbations). Gravitational interactions during inflation L int = c 2 φ 2 V χ M Pl 2 m φ ~ H inf Massive field; Constraints on CDM isocurvature perturbations lead to: ϕ i α H inf, α ; 29/08/2017 Scalar field dark matter and the Higgs field 27
28 Inflation and initial conditions If the Higgs field is the unique source of mass during inflation m ϕ ~O(EW scale) Light field de-sitter fluctuations ~ H inf sizeable Cold Dark Matter (CDM) isocuvature modes 2π in the CMB spectrum ruled out (do not respect the observational constraints on the CDM isocurvature perturbations). Gravitational interactions during inflation L int = c 2 φ 2 V χ M Pl 2 m φ ~ H inf Massive field; Constraints on CDM isocurvature perturbations lead to: ϕ i α H inf, α ; H inf r GeV, r < [Planck Collaboration 2015]. r t 2 R 2 29/08/2017 Scalar field dark matter and the Higgs field 28
29 Initial conditions Results m φ ~ 10 5 ev m ϕ > H EW m ϕ ~ 10 6 ev m ϕ < H EW 29/08/2017 Scalar field dark matter and the Higgs field 29
30 Non-renormalizable interactions model Hidden sector DM field Visible sector Higgs boson (and Standard Model fields) 29/08/2017 Scalar field dark matter and the Higgs field 30
31 Non-renormalizable interactions model Hidden sector DM field Heavy messengers, Gravity Visible sector Higgs boson (and Standard Model fields) 29/08/2017 Scalar field dark matter and the Higgs field 31
32 Non-renormalizable interactions model Hidden sector DM field L int = a h 4 ϕ2 M 2 Heavy messengers, Gravity Visible sector Higgs boson (and Standard Model fields) 29/08/2017 Scalar field dark matter and the Higgs field 32
33 Non-renormalizable interactions model Hidden sector DM field L int = a h 4 ϕ2 M 2 Heavy messengers, Gravity Visible sector Higgs boson (and Standard Model fields) Electroweak symmetry breaking 29/08/2017 Scalar field dark matter and the Higgs field 33
34 Non-renormalizable interactions model Hidden sector DM field Heavy messengers, Gravity Visible sector Higgs boson (and Standard Model fields) L int = a h 4 ϕ2 M 2 m φ = a 6 v 2 M ~ a 6 M M Pl Electroweak symmetry breaking 1 ev; 29/08/2017 Scalar field dark matter and the Higgs field 34
35 Non-renormalizable interactions model Hidden sector DM field Heavy messengers, Gravity Visible sector Higgs boson (and Standard Model fields) L int = a h 4 ϕ2 M 2 m φ = a 6 v 2 M ~ a 6 M M Pl Electroweak symmetry breaking 1 ev; If M = M Pl m φ ~10 5 ev 29/08/2017 Scalar field dark matter and the Higgs field 35
36 Non-renormalizable interactions model Hidden sector DM field Heavy messengers, Gravity Visible sector Higgs boson (and Standard Model fields) L int = a h 4 ϕ2 M 2 m φ = a 6 v 2 M ~ a 6 M M Pl Electroweak symmetry breaking 1 ev; If M = M Pl m φ ~10 5 ev Interesting hierarchy: m φ v ~ v M Pl 29/08/2017 Scalar field dark matter and the Higgs field 36
37 Warped extra-dimension model Randall-Sundrum inspired model: Planck brane [L. Randall, R. Sundrum 1999] 5D bulk Φ v e kl M P Higgs Visible/Infrared brane e kl ~ y L Metric: ds 2 = e 2k y g μν dx μ dx ν + dy 2 S = d 4 x dy G 1 2 GMN M Φ N Φ 1 2 M Φ 2 Φ 2 + δ y L G MN M h N h V h g 5 2 Φ 2 h 2 29/08/2017 Scalar field dark matter and the Higgs field 37
38 Warped extra-dimension model Decompose Φ into Kaluza-Klein modes: Φ x μ,y = 1 2L n=0 ϕ n x μ f n y ; 29/08/2017 Scalar field dark matter and the Higgs field 38
39 Warped extra-dimension model Decompose Φ into Kaluza-Klein modes: Φ x μ,y = 1 2L n=0 ϕ n x μ f n y ; The DM field corresponds to the zero-mode : f 0 y 2kL ; 29/08/2017 Scalar field dark matter and the Higgs field 39
40 Warped extra-dimension model Decompose Φ into Kaluza-Klein modes: Φ x μ,y = 1 2L n=0 ϕ n x μ f n y ; The DM field corresponds to the zero-mode : f 0 y 2kL ; Φ 0 x μ,l = ϕ 0 x μ k L int = 1 2 g 5 2 ke 2kL ϕ 0 2 h 2 Rescale: h e kl h g 4 ~ g 5 2 ke kl O 1 v M Pl ~10 16 g 5 2 ~ 1 k ; k M Pl 29/08/2017 Scalar field dark matter and the Higgs field 40
41 Warped extra-dimension model Decompose Φ into Kaluza-Klein modes: Φ x μ,y = 1 2L n=0 ϕ n x μ f n y ; The DM field corresponds to the zero-mode : f 0 y 2kL ; Φ 0 x μ,l = ϕ 0 x μ k L int = 1 2 g 5 2 ke 2kL ϕ 0 2 h 2 Rescale: h e kl h g 4 ~ g 5 2 ke kl O 1 v M Pl ~10 16 g 5 2 ~ 1 k ; k M Pl m ϕ ~ v2 M Pl ~ 10 5 ev 29/08/2017 Scalar field dark matter and the Higgs field 41
42 Warped extra-dimension model Decompose Φ into Kaluza-Klein modes: Φ x μ,y = 1 2L n=0 ϕ n x μ f n y ; The DM field corresponds to the zero-mode : f 0 y 2kL ; Φ 0 x μ,l = ϕ 0 x μ k L int = 1 2 g 5 2 ke 2kL ϕ 0 2 h 2 Rescale: h e kl h g 4 ~ g 5 2 ke kl O 1 v M Pl ~10 16 g 5 2 ~ 1 k ; k M Pl m ϕ ~ v2 M Pl ~ 10 5 ev Mass in the required range. Interesting hierarchy again: m φ v ~ v M Pl 29/08/2017 Scalar field dark matter and the Higgs field 42
43 Warped extra-dimension model Decompose Φ into Kaluza-Klein modes: Φ x μ,y = 1 2L n=0 ϕ n x μ f n y ; The DM field corresponds to the zero-mode : f 0 y 2kL ; Φ 0 x μ,l = ϕ 0 x μ k L int = 1 2 g 5 2 ke 2kL ϕ 0 2 h 2 Rescale: h e kl h g 4 ~ g 5 2 ke kl O 1 v M Pl ~10 16 g 5 2 ~ 1 k ; k M Pl m ϕ ~ v2 M Pl ~ 10 5 ev Mass in the required range. Interesting hierarchy again: m φ v ~ v M Pl Planck-suppressed non-renormalizable operator Renormalizable interaction in a higherdimensional warped geometry. 29/08/2017 Scalar field dark matter and the Higgs field 43
44 Conclusions & Future work DM candidate: oscillating scalar field φ, which acquires mass through the Higgs mechanism. Lower bound: m ϕ ev ; m ϕ ~ v2 M P ~10 5 ev obtained through either non-renormalizable interactions between φ and the Higgs field or through a warped extra-dimension model. Future work: Extend the model study the effect of self-interactions; Find out ways of testing our model (astrophysical signatures, ongoing experiments...); Thank you for your attention! 29/08/2017 Scalar field dark matter and the Higgs field 44
45 Backup slides 29/08/2017 Scalar field dark matter and the Higgs field 45
46 Introducing the problem Dark Matter 26.8% of the massenergy content of the Universe [Planck Collaboration 2015]. Dark Matter (DM) Evidence from: Galaxy rotation curve; Gravitational lensing; Anisotropies of the CMB; Bullet Cluster; Candidates: Weakly Interacting Massive Particles (WIMPs); Axions; Supersymmetric particles;... 29/08/2017 Scalar field dark matter and the Higgs field 46
47 Introduction and motivation Why a scalar field dark matter? Fits: - evolution of cosmological densities [Matos, Vazquez-Gonzalez, Magana 2009]; - flat central density profile of the dark matter [Matos, Nunez 2003]; - acoustic peaks of CMB [Rodrigez-Montoya, Magana, Matos, Perez-Lorenzana 2010]; - observed properties of dwarf galaxies [Lee, Lim 2010]; Explains: - cusp and the missing satellite problems [Lee, Lim 2010; Lee 2009; Harko 2011]; - collision of galaxy clusters (e.g., Bullet Cluster) [Lee, Lim, Choi 2008]; 29/08/2017 Scalar field dark matter and the Higgs field 47
48 Oscillating scalar field as DM candidate Does an oscillating scalar field behave like non-relativistic matter? Potential: V φ = 1 2 m φ 2 φ 2 Generic cosmological epoch: a t = t t i p, p > 0. Hubble parameter: H = p t Klein-Gordon (KG) eq. : φ + 3 p t φ+m φ 2 φ=0 m φ t 1 φ t φ i a t 3 2 cos m φ t + δ φ Energy density: ρ φ = 1 2 φ2 + V φ ~a 3 Non-relativistic matter. 29/08/2017 Scalar field dark matter and the Higgs field 48
49 Inflation and initial conditions If the Higgs field is the unique source of mass during inflation m ϕ ~O(EW scale) Light field de-sitter fluctuations ~ H inf sizeable Cold Dark Matter (CDM) isocuvature modes 2π in the CMB spectrum ruled out (do not respect the observational constraints on the CDM isocurvature perturbations). Gravitational interactions during inflation L int = c 2 φ 2 V χ M Pl 2 m φ ~ H inf Massive field; Quantum fluctuations for a massive field: ν φ = 9 4 m 2 φ 2 H inf 1 2 δφ k H inf 2k 3 k ah inf 3 2 ν φ Integrating over all modes φ 2 1 H inf 3 2ν φ 2π 2 29/08/2017 Scalar field dark matter and the Higgs field 49
50 Inflation and initial conditions What is the minimum field s mass during inflation compatible with observational constraints on CDM isocurvature perturbations? Dimensionless isocurvature power spectrum: I 2 k3 2π 2 2 δφ φ 2 = 3 2νφ k ah inf 3 2 ν φ β iso k mid = 2 I k mid 2 R k mid + 2 < [Planck Collaboration 2015] ν φ 1.3 m φ 0.75 H inf I k mid Max: m φ ~ H inf Min: m φ ~ 0.75 H inf φ 2 = α 2 H inf 2, 0.1 α /08/2017 Scalar field dark matter and the Higgs field 50
51 Inflation and initial conditions Field remains overdamped until the EWPT φ 2 sets the initial amplitude for field oscillations in the post-inflationary era: φ i = φ 2 αh inf H inf r GeV, r < [Planck Collaboration 2015]. r t 2 R 2 m φ g 100 1/2 α 0.25 α r 0.03 r ev, mϕ > H EW. 2 ev, mϕ < H EW. 29/08/2017 Scalar field dark matter and the Higgs field 51
52 Warped extra-dimension model Bulk mass: M Φ 2 = ak 2 + bσ σ = k y ; σ = dσ dy = k sgn(y); σ = d2 σ d 2 y = 2k δ y δ y L EOM: e 2k y g μν μ ν + e 4k y y e 4k y y M Φ Φ x μ, y = 0; Decompose Φ into Kaluza-Klein modes: Φ x μ, y = 1 2L n=0 ϕ n x μ f n y ; The DM field corresponds to the zero-mode: f 0 y = 2kL b 1 e 2kL b 1 1 ebky ; Particular case: a = b = 0 The bulk scalar is scale invariant; 29/08/2017 Scalar field dark matter and the Higgs field 52
53 Warped extra-dimension model Do the heavier modes contribute to the DM density? m n n πke kl m n ~ O TeV m 0 DM, if they oscillate with large Could lead to an overabundance of amplitude after inflation. but f n L e kl f 0 L m n H inf super-planckian Might decay quickly through gravitational coupling. Only the zero-mode contributes to the present abundance of DM 29/08/2017 Scalar field dark matter and the Higgs field 53
54 Effects of field self-interactions Interactions with the Higgs field quartic coupling for the DM: λ~g 4 After inflation, φ i ~αh inf Contribution to the DM field mass: m φ 2 ~λ φ i 2 ~g 4 H inf 2 Since m φ 2 m φ 2 ~ H 2 inf 2 M Pl 1 May neglect the effect of these selfinteractions on the dynamics of the DM field. 29/08/2017 Scalar field dark matter and the Higgs field 54
55 Effects of the reheating period The mass of DM field vanishes in the radiation era, before the Electroweak symmetry breaking. How does the reheating period affect the results? During reheating: m φ 2 H 2 ~3c V χ V χ χ2 + ρ r V χ ρ r 1 2 m φ H 2 ~ 3 2 c There may be a period of inflaton matter-domination: φ t ~t α, α = c 29/08/2017 Scalar field dark matter and the Higgs field 55
56 Effects of the reheating period The interactions between the inflaton and φ may lead to the production of φ particles. L int = c φ 2 V χ 2 2 = c 2 M Pl m χ 2 2 M χ2 φ 2 + g 2 χ 2 φ 2 Pl m χ 2 = V χ 0 = 3ηH inf 2 g 2 ~10 12 η 0.01 r 0.01 Very small coupling. Do these particles contribute to the present DM abundance? 29/08/2017 Scalar field dark matter and the Higgs field 56
57 Effects of the reheating period φ-particles never thermalize in the cosmic history initial amplitude set by χ φ φ; n φi = B φ n χ = 2B φ π 2 30 g T R 4 m χ Contribution to the present DM abundance: Ω ϕ,0 0.01B φ m ϕ 10 5 ev T R GeV m χ GeV 1 Negligible We may neglect the reheating period effects in computing the present DM abundance. 29/08/2017 Scalar field dark matter and the Higgs field 57
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