Cosmological constraints on (elastic) Dark Matter self-interactions

Transcription

1 Cosmological constraints on (elastic Dark Matter self-interactions Rainer Stiele Work done together with J. Schaffner-Bielich & T. Boeckel (University Heidelberg Institut für Theoretische Physik Goethe-Universität Frankfurt am Main 4. Kosmologietag Bielefeld May 8 th 2009 Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 1 / 13

2 Dark Matter: Collisionless? Self-interacting? Collisionless Dark Matter In cosmological standard model Dark Matter assumed to be collisionless: Weak interactions with baryonic matter and weak self-interactions. Dark Matter - baryonic matter interactions and Dark Matter annihilation cross-section strongly restricted by collider and scattering experiments. Self-interacting Dark Matter Present models with self-interactions above the nuclear scale (Carlson et al. 1992, ApJ 398; Spergel and Steinhardt 2000, Phys. Rev. Lett. 84 strongly constrained e.g. by galaxy cluster collisions (σ/m < 0.7 cm 2 /g, Randall et al. 2008, ApJ 679. Our approach: nuclear-like forces between Dark Matter particles. Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 2 / 13

3 Self-interacting Dark Matter Model Self-interacting Dark Matter model Consequence of predicted self-interaction between Dark Matter particles is additional energy density to this of Dark Matter particles: SIDM = DM + SI Describe self-interaction as two particle force ( n 2 DM with exchange particle of mass m SI and coupling constant α SI (interaction strength m SI / α SI : SI = α SI n 2 msi 2 DM Valid for m SI >, propagator independent on kinematics. For comparison: Equation of state: αweak m = G 1/2 F 293 GeV, p SI = SI = α SI n 2 msi 2 DM m strong αstrong 100 MeV repulsive interaction Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 3 / 13

4 Self-interacting Dark Matter Consequences Scaling behaviour of energy densities Friedman equations give following relation between energy density, pressure d and scale factor a : = 3 +p da a With eos p = α follows: = const. a 3(1+α Radiation: p rad = rad 3 rad a 4 (nonrelativistic Matter: p mat = 0 mat a 3 Dark Energy: p DE = DE DE = const. Self-interaction: p SI = SI SI a 6 Epoch of self-interaction domination prior to radiation-dominated era. Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 4 / 13

5 Self-interacting Dark Matter Parameters Model parameters SI n 2 DM ; SI a 6 n DM a 3 Naturally fulfilled after Dark Matter decoupling. Before decoupling only true for relativistic particles. Self-interacting Dark Matter has to decouple while still relativistic. Warm Dark Matter ( Free Boltzmann gas: n DM = g DM T 3 π 2 DM exp µdm Non-vanishing Dark Matter chemical potential: Boeckel and Schaffner-Bielich 2007, Phys. Rev. D 76. ( Entropy conservation: (a = g th eq (a g dec th eq 1/3 T(a Self-interacting Dark Matter model parameters: g dec th eq, g µ DM, DM m, m DM, αsi SI But they are not all independent. Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 5 / 13

6 Dark Matter particles Ω 0 DM constraints Parameter constraints via Ω 0 DM Today Dark Matter is nonrelativistic: 0DM = m DMnDM 0 Particle number conservation after decoupling: 0DM m DM g DM exp( µdm g dec T th eq DM n DM (a > a dec n dec DM ( adec 3 a Exact condition: g DM m DM g dec th eq exp( µdm = 3π m 2 Pl H2 0 T 3 0 Ω 0 DM g dec th eq = g DMm DM 193 ev g DM = 2, m DM = 1 kev g dec th eq 1107 For standard Warm Dark Matter particle masses (1 kev-10 kev additional degrees of freedom (particles at decoupling required. Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 6 / 13

7 Self-interacting Dark Matter Evolution Energy density evolution ( n DM = g DM T 3 π 2 DM exp µdm before decoupling n DM (a > a dec ndm dec ( adec 3 a after decoupling DM = 3 n DM while relativistic DM = m DM n DM when nonrelativistic SI = α SI n 2 msi 2 DM SIDM = DM + SI mdm = 1 kev, g DM = 2, µ DM = 0, g dec th eq = 1107 Only very strong interactions would have an impact on the very early Universe. BBN perfect test! Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 7 / 13

8 Dark Matter particles BBN constraints Allowed energy density during BBN In standard model energy density during BBN given by radiation ( a 4. Additional energy density parametrized as additional neutrino families N ν : BBN rad = BBN γ + (3 + N ν BBN ν Analysis of primordial element abundances: N ν 0.3 (Simha and Steigman 2008, JCAP 6 Condition on SIDM: msi αsi n f.o. DM ( N ν f.o. ν f.o. DM 1/2 + BBN e f.o. SIDM Nν f.o. ν Denominator restricts particle parameters: < Nν f.o. ν f.o. DM m DM > /3 m 7π Pl 2 H2 0 T Ω 0 DM N ν g dec 1/3 th eq Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 8 / 13

9 Self-interacting Dark Matter Constraints Allowed energy density at n/p freeze-out SI a 6 constrain interaction strength via earliest stage of BBN: n/p freeze-out. f.o. tot = f.o. SIDM + f.o. rad (1 + csidm f.o. rad, 0 c SIDM < 1 Additional energy density increases (n/p f.o. increases 4 He abundance Y P Upper limit of measured primordial 4 He abundance: Y P < (Steigman 2007, Annu. Rev. Nucl. Part. Sci. 57 m αsi f.o. SIDM f.o. rad m SI αsi n f.o. DM (0.373 f.o. rad f.o. DM 1/2 const 1 m 1 DM const 2 const 3 g dec 1/3 1/2 th eq m 1 DM Dark Matter particles can interact with the strength of the strong interaction... and even stronger! Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 9 / 13

10 Self-interacting Dark Matter Combined Constraints Allowed self-interaction strength Cross-section for exchange of intermediate vector boson: σ SI α2 SI m 2 msi 4 DM σ SI m DM = Prefered range of Spergel and Steinhardt 2000, Phys. Rev. Lett. 84 to explain observed Halo properties (no cusp, small number of satellites: σ SI /m DM = cm 2 /g Upper limit from galaxy cluster collisions (Randall et al. 2008, ApJ 679: σ SI /m DM < 0.7 cm 2 /g ( αsi 4 mdm m SI Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 10 / 13

11 Self-interacting Dark Matter Decoupling Dark Matter decoupling in a self-interaction dominated Universe Decoupling: Γ A = H Warm Dark Matter: Γ A = n DM σv = n DM σ A 1. Friedman equation: H = (8π/3 1/2 m 1 Pl 1/2 σ A = (8π/3 1/2 m 1 Pl Standard model: dec = dec σ A dec rad 1/2 /n dec DM ( 1/2 dec /n dec DM rad Self-interaction dominated Universe: dec = dec SI = α SI m 2 SI ndm dec 2 σ A = (8π/3 1/2 mpl 1 αsi m SI σ weak T 0 3 m Pl GeV cm 2 H2 0 Strong Dark Matter self-interactions conform with superweak DM-baryonic interactions. Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 11 / 13

12 Self-interacting Dark Matter Structure formation Structure formation of Self-interacting Dark Matter Analyse relativistic structure formation of linear perturbations: = 0 + δ ; δ = δ / 0 self-interaction domination: δ a relativistic: δ = const. nonrelativistic: δ { ln a a during radiation domination when matter dominated m SI αsi = 1 kev, m DM = 5 kev, g DM = 2, µ DM = 0, g dec th eq = 104 Calculations performed by T. Boeckel All modes inside Hubble horizon during self-interaction domination grow already. Concerns only very small, non-cosmological scales (M 10 3 M. Washed-out due to free-streaming? Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 12 / 13

13 Summary Standard cosmological models suppress something very important: Short-range superstrong Dark Matter self-interactions conform with observations! Crucial consquence self-interaction energy density contribution has only an impact on very early Universe. Today s Dark Matter energy density can be used to restrict particle parameters: Ω 0 DM = m DM g DM exp µdm g dec = m = 1 10 kev g dec th eq DM th eq > Big Bang Nucleosynthesis ultimate test to restrict self-interaction strength: m SI αsi m 1 DM : m SI αsi (m DM =1 kev 1.51 kev, m SI αsi (m DM =10 kev 151 ev Superstrong Dark Matter self-interactions conform with superweak DM-baryonic interactions: αsi σ A : σ msi m A SI αsi =1 kev σ weak, σ msi A αsi =100 MeV σ weak Linear structure growth while Dark Matter self-interaction dominated: Superstrong short-range Dark Matter self-interactions are possible! δ a Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 13 / 13

14 Thank You for Your attention! Standard cosmological models suppress something very important: Short-range superstrong Dark Matter self-interactions conform with observations! Crucial consquence self-interaction energy density contribution has only an impact on very early Universe. Today s Dark Matter energy density can be used to restrict particle parameters: Ω 0 DM = m DM g DM exp µdm g dec = m = 1 10 kev g dec th eq DM th eq > Big Bang Nucleosynthesis ultimate test to restrict self-interaction strength: m SI αsi m 1 DM : m SI αsi (m DM =1 kev 1.51 kev, m SI αsi (m DM =10 kev 151 ev Superstrong Dark Matter self-interactions conform with superweak DM-baryonic interactions: αsi σ A : σ msi m A SI αsi =1 kev σ weak, σ msi A αsi =100 MeV σ weak Linear structure growth while Dark Matter self-interaction dominated: Superstrong short-range Dark Matter self-interactions are possible! δ a Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 13 / 13

15 Back up Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 14 / 13

16 Cosmological Background Combined results Results of CMB observation, studying SNe Ia and LSS observations (BAO depend in differing ways on composition of the Universe (Ω x - relative amount of component x, Λ: Dark Energy, m: Matter. Combination of different methods leads to consistent result and allows narrow constraints. NASA / WMAP Science Team, Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 15 / 13

17 Theoretical background Friedman equations Central comsological equations describing expansion behaviour of the Universe: ( 2 3 ȧ a + 3 k = 8πG a ( ä a + ȧ a + k = 8πGp a 2 Energy density Definition of relative energy densities. If tot = crit Universe is flat (k = 0. Ω x x crit, Ω tot = x Ω x Ω tot = 1, the crit 3H2 8πG Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 16 / 13

18 WMAP 5 years results Cosmological parameters from CMB, LSS and SNe observations. Hinshaw et al. 2008, arxiv: v1 [astro-ph] Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 17 / 13

19 Direct empirical proof of the existence of Dark Matter Collision of two Galaxy Clusters Before collision: Galaxies, intergalactic gas, Dark Matter (? same spatial localistaion. Collision: Galaxies (low density and interacting intergalactic gases spatially separated. Without Dark Matter: Largest accumulation of mass central intergalactic gas. Hubble and Chandra Composite of the Galaxy Cluster MACS J , releases/2008/32 With Dark Matter: Offset between largest accumulations of mass and central gas. Graphics: Clowe 2007, 11th Paris Cosmology Colloquium 2007 Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 18 / 13

20 CDM decoupling in radiation-dominated Universe Standard scenario of decoupling Cold Dark Matter: Γ A = n DM σv = n DM σ A ( 1/2 T m DM Expansion rate in radiation-dominated Universe: H = (8π/3 1/2 m 1 1/2 Pl rad Decoupling: Γ A = H m DM T dec = ln [ ( [ ln 2 π 3 m Pl g DM g dec eff g DM g dec eff Fixes m DM /T dec, only logarithmic corrections. geff dec 1 2 gth dec eq ( 3 mdm T dec ( 2 σ weak 1 2 ( σa σ weak Fixes σ A with today s Dark Matter energy density. σ A 1 2 σ A m DM ] (mdm GeV ] Ω 0 DM h Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 19 / 13

21 Structure formation Structure growth of cold matter Describe Universe as perfect fluid characterized by energy density distribution (t, x, velocity field v(t, x and entropie S(t, x which fulfill continuity equation, Euler equations and entropie conservation. Analyzing fluctuations of linear order and describing structure formation as adiabatic process leads to: δ + 2H δ c2 s a 2 δ 4πG 0 δ = 0 or via Fourier transformation: δ k + 2H δ k + ( c 2 s k 2 a 2 4πG 0 δ k = 0 For pressureless Cold Dark Matter summands proportional to δ or k 2 can be neglected. Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 20 / 13

22 Cold Dark Matter ΛCDM model favours Dark Matter that is cold and collisionless Definition Cold: Dark Matter particles are so massive that they are already nonrelativistic when they decouple. Problems with Cold Dark Matter Simulations of the structure formation with Cold Dark Matter fit to large-scale structure oberservations (galaxy clusters,... but fail on subgalactic scales: Substructure problem Cusp vs. core problem Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 21 / 13

23 Cold Dark Matter The substructure problem Substructure problem Cold Dark Matter predicts hierarchical structure formation (bottom-up scenario: Smaller structures form first, cluster to larger structures but survive as substructures Galaxies as substructures of galaxy clusters: Fit Satellite galaxies as substructures of galaxies: Failure Moore et al. 1999, ApJ 524 Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 22 / 13

24 Cold Dark Matter The cusp vs. core problem Cusp vs. core problem In structure formation simulations Cold Dark Matter halos show universal density profiles which diverge to the center: Cusp 1 (r r rs 1+ r rs 2 ; r s : scale radius 10 0 Observations of the most Dark Matter dominated galaxies (dsphs: dwarf spheroidal galaxies indicate shallow inner density profiles: Core ρ (M pc Ursa Minor Draco LeoII LeoI Carina Sextans 1/r Gilmore et al. 2007, ApJ r (kpc Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 23 / 13

25 Cold Dark Matter vs. Warm Dark Matter Solution to both problems Lighter Dark Matter particles with a larger velocity dispersion: Warm Dark Matter Smooth-out inner regions Its free-streaming prevents formation of smallest scale (subgalactic structure Tegmark, Zaldarriaga 2008, arxiv: v1 [astro-ph] Frenk 2008, 12th Paris Cosmology Colloquium 2008 Warm Dark Matter: Particles decouple while still relativistic Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 24 / 13

26 Thermodynamics in the SIDM model Thermodynamics n DM = g DM (2π 3 fdm ( k d 3 k DM = g DM (2π 3 EDM ( kf DM ( k d 3 k p DM = g DM (2π 3 k 2 3E DM ( k f DM( k d 3 k g DM : multiplicity of DM particles Maxwell-Boltzmann distribution function f DM (k DM = exp( µdm E DM µ DM : chemical potential ( Boeckel and Schaffner-Bielich 2007, Phys. Rev D 76 Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 25 / 13

27 Thermodynamics in the SIDM model Thermodynmamics n DM = g DM (2π 3 fdm ( k d 3 k, p DM = g DM (2π 3 k 2 3E DM ( k f DM( k d 3 k; DM = g DM (2π 3 EDM ( kf DM ( k d 3 k, g DM : multiplicity of DM particles Maxwell-Boltzmann distribution function: f DM (k DM = exp( µdm E DM general solution ( ( n DM = g DM m 2 2π 2 DM K mdm 2 exp µdm [ DM = g DM 2π 2 m 2 DM p DM = g DM 2π 2 m 2 DM T 2 DM K 2 3 K 2 ( mdm ( mdm exp ( µdm ( ] ( + m DM K mdm 1 exp µdm = n DM Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 25 / 13

28 Thermodynamics in the SIDM model general solution ( ( n DM = gdm m 2 2π 2 DM K mdm 2 exp µdm [ ( DM = gdm m 2 2π 2 DM 3 K mdm 2 p DM = gdm 2π 2 m 2 DM T 2 DM K 2 ( mdm exp ( µdm + m DM K 1 ( mdm ] exp = n DM Modified Bessel function of the second kind ( µdm K ν (z = π 1 2 ( 1 2 zν exp( zt Γ(ν ( t 2 1 ν 1 2 dt Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 25 / 13

29 Thermodynamics in the SIDM model general solution ( n DM = gdm m 2 2π 2 DM T m DM K DM 2 exp [ ( DM = gdm m 2 2π 2 DM 3 K mdm 2 p DM = gdm 2π 2 m 2 DM T 2 DM K 2 relativistic limit n DM = g DM π 2 DM = 3 g DM π 2 p DM = g DM π 2 ( mdm ( TDM 3 exp µdm exp ( µdm ( µdm + m DM K 1 ( mdm ] exp = n DM T 4 DM exp ( µdm = 3 n DM ( TDM 4 exp µdm = n DM = DM 3 ( µdm Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 25 / 13

30 Thermodynamics in the SIDM model general solution ( ( n DM = gdm m 2 2π 2 DM K mdm 2 exp µdm [ ( DM = gdm m 2 2π 2 DM 3 K mdm 2 p DM = gdm 2π 2 m 2 DM T 2 DM K 2 nonrelativistic limit n DM = g DM ( mdm 2π ( mdm exp ( µdm 3 2 exp( µdm m DM + m DM K 1 ( mdm ] exp = n DM ( DM = g DM m TDM 2 DM 2π exp( µdm m DM = m DM n DM p DM = g DM T 5 ( 2 mdm 3 2 DM 2π exp( µdm m DM = n DM ( µdm Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 25 / 13

31 Numerical calculations Central equations Friedman equations and n DM a 3 : d x da = 3 a ( x dn + p x, DM da = 3 a n DM Solve with 4th order Runge-Kutta method. Temperature and chemical potential Calculate temperature and chemical potential with Newton-Raphson root finding: ( n i+1 F( x = DM n DM( x i+1 DM DM( x x = ( TDM µ DM g DM = 2, µ DM = 1 Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 26 / 13

32 SIDM energy density contributions Individual energy density contributions m αsi = 1 MeV, m DM = 1 kev, g DM = 2, µ DM = 0, g dec th eq = Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 27 / 13

33 Energy density, pressure and particle density of SIDM Comparison of SIDM, p SIDM and n SIDM m αsi = 1 MeV, m DM = 1 kev, g DM = 2, µ DM = 0, g dec th eq = 1107 Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 28 / 13

34 SIDM equations of state Different equations of state of SIDM during evolution 1. SI domination: p SIDM p SI = SI SIDM 2. SIDM DM = x n DM, x = 3 (rel., x = m DM (nrel. p SIDM p SI = α SI m 2 SI n 2 DM m DM = 1 kev, g DM = 2, µ DM = 0, g dec th eq = 1107 p SIDM = 1 x 2 α SI m 2 SI 2SIDM 3. Particle domination: SIDM DM p SIDM p DM = y DM y SIDM, y = 1/3 (rel., y = /m DM < 1/3 (nrel. m SI αsi = 1 kev, m DM = 100 kev, g DM = 3, µ DM = 5, gth dec eq = Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 29 / 13

35 BBN n/p freeze-out How strong the self-interactions between Dark Matter particles can be (m SI / α SI? How much additional energy density is conform with evolution of the Universe? First physical process sensitive to energy content of the Universe: Big Bang Nucleosynthesis. Freeze-out of n/p ratio Steigman 2007, Annual Review of Nuclear and Particle Science 57 Kick-off of Big Bang Nucleosynthesis is freeze-out of n/p ratio when n + ν e p + e and n + e + p + ν e out of equlibrium (Γ np < H. m Before freeze-out: (n/p eq = exp `, T m m n m p 1.29 MeV After freeze-out free n decay: n/p (t = (n/p f.o. exp( 2 t/τ n, τ n = (885.7 ± 0.8 s n/p ratio very sensitive to moment of freeze-out! Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 30 / 13

36 Big Bang Nucleosynthesis Primordial element abundances First fusion process: n + p D + γ. But photo-dissociation of D: Deuterium bottleneck ( 250 s. Smith et al. 1993, ApJS 85 After sufficient cooling synthesis of T, 3 He, 4 He. No stable nuclei with five and eight nucleons. Nearly all n s captured into 4 He. Primordial 4 He abundance ideal probe to n/p freeze-out! Mukhanov 2004, International Journal of Theoretical Physics 43 Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 31 / 13

37 Big Bang Nucleosynthsis Energy density dependence of BBN Primordial element abundances very sensitive to expansion rate, e.g. via n/p at Γ np < H and time for n s to decay during Deuterium bottleneck. Expansion rate H depends directly on total energy density: H 1/2 (1. Friedman equation. Smith et al. 1993, ApJS 85 Higher energy density leads to more 4 He because of larger (n/p f.o. more D and 3 He because of less time for further processing less 7 Li because less time for production via 7 Be Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 32 / 13

38 BBN 4 He mass abundance Y P Possible energy density at beginning of BBN For restriction via N ν assumed a 4 like radiation. True for energy density of relativistic Dark Matter particles DM but not for self-interaction SI a 6. Better to analyze possible additional energy density at earliest stage of BBN: freeze-out of n/p ratio. f.o. tot = f.o. SIDM + f.o. rad (1 + csidm f.o. rad, 0 c SIDM < 1 Additional energy density increases (n/p f.o. increases 4 He abundance Y P Upper limit of measured primordial 4 He abundance: Y P < f.o. SIDM f.o. rad Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 33 / 13

39 T f.o. energy dependence Energy dependence of freeze-out temperature 4 ( 3 ( ( Tf.o. Q Tf.o. Q Tf.o. Q g f.o. 2 eff (1 + c SIDM 1 2 Q m n m p = ( ± MeV Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 34 / 13

40 Neutron concentration at freeze-out and BBN Energy dependence of relative neutron concentration X f.o. n Relative neutron concentration X n : nn n p = Xn 1 X n ( R exp g 1 eff 2 (1 + c SIDM 1 yr h i h i x x exp x 1 dy dx 0 0 2y 2h i 1+cosh 1y 1 t f.o. = 45 2 m 16 π 3 Pl geff f.o. 1 2 (1 + c SIDM 2 1 T 2 f.o. t bbbn 243 s X bbbn n ( = Xn f.o. exp t τ n t = t bbbn t f.o. Y P = 2 nn np bbbn 1+ nn np bbbn Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 35 / 13

41 Self-interaction strength Allowed self-interaction strength depending on g dec th eq, g DM, µ DM / m αsi n f.o. DM (0.373 f.o. Str f.o. 2 DM 1 = π π 2 g µdm f.o. exp g th dec T eq DM π g DM µdm g th dec 4 exp 5 3 eq Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 36 / 13

42 Constraint on SI coupling constant Constraint on α SI at n/p freeze-out Remember: Ansatz SI = α SI n 2 msi 2 DM only true for m SI > α SI > (10.75/gdec th eq 2/3 Tf.o. 2 (m SI / α SI 2 at n/p freeze-out. For f.o. SIDM = f.o. rad : T f.o. 882 kev Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 37 / 13

43 Cluster collision SI constraint Constraint on SI strength from galaxy cluster collisions σ/m < 0.7 cm 2 /g = ev 3, Randall et al. 2008, ApJ 679 σ SI = α2 SI m 4 SI m 2 DM σ SI m DM = ( αsi 4 mdm m SI m SI αsi > ev 3/4 m 1/4 DM Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 38 / 13

44 SIDM mean free path Mean free path of Self-interacting Dark Matter ( 4 mean free path : λ DM = 1 σ SI n DM = msi αsi m 2 DM n 1 DM n DM = DM m DM λ DM = ( msi αsi 4 m 1 DM 1 DM mean galactic DM density: DM = 0.4 GeV cm ev 4 λ DM msi αsi 4 m 1 DM ev 4 Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 39 / 13

45 Combined limits on self-interaction strength All limits on Self-interacting Dark Matter Rainer Stiele (Goethe-Univ. Frankfurt Self-interacting Dark Matter 4. Kosmologietag Bielefeld 40 / 13