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Interacting Dark Matter Markus R. Mosbech Linear Modeling of Baryon-Dark Matter Interactions with CLASS Introducing a Novel Resonance Interaction Type Markus Rasmussen Mosbech February 21, 2020 Interacting Dark Matter Markus R. Mosbech

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Interacting Dark Matter Markus R. Mosbech

Linear Modeling of Baryon-Dark Matter Interactions with CLASS

Introducing a Novel Resonance Interaction Type Markus Rasmussen Mosbech February 21, 2020

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Interacting Dark Matter Markus R. Mosbech

Overview

1 Evolution 2 Dark Matter Interactions 3 Numerics 4 Results

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Structure Formation

Primordial perturbations Gravity Pressure

Figure: simulations were performed

at the National Center for Supercomputer Applications by Andrey Kravtsov (The University of Chicago) and Anatoly Klypin (New Mexico State University). Visualizations by Andrey Kravtsov.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

The CMB spectrum

Observable Recombination Linear

Figure: by ESA/Planck collaboration

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

The CMB spectrum

Observable Recombination Linear

Figure: by ESA/Planck collaboration

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

The CMB spectrum

Observable Recombination Linear

500 1000 1500 2000 2500 l 1 2 3 4 l(l + 1)ClTT ×10−9

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Perturbation Theory

Small deviation from average Early universe Advantages in Fourier space

10−6 10−5 10−4 10−3 10−2 a 10−2 100 102 104 |δb| (k = 0.5 Mpc−1)

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Perturbation Theory

Small deviation from average Early universe Advantages in Fourier space

10−6 10−5 10−4 10−3 10−2 a 10−2 100 102 104 |δb| (k = 0.5 Mpc−1)

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Perturbation Theory

Small deviation from average Early universe Advantages in Fourier space

10−6 10−5 10−4 10−3 10−2 a 10−2 100 102 104 |δb| (k = 0.5 Mpc−1)

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

The Boltzmann Equations

Dark Matter Baryons Photons ˙ δcdm = −θcdm + 3 ˙ Φ, ˙ θcdm = − ˙ a aθcdm + k2Ψ.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

The Boltzmann Equations

Dark Matter Baryons Photons ˙ δb = −θb − 3 ˙ Φ, ˙ θb = − ˙ a aθb + c2

sk2δb

+ 4¯ ργ 3¯ ρb aneσT (θγ − θb) + k2Ψ.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

The Boltzmann Equations

Dark Matter Baryons Photons ˙ δγ = −4 3θγ + 4 ˙ Φ ˙ θγ = k2 1 4δγ − σγ

  • + aneσT (θb − θγ) + k2Ψ
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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Temperature

Photons Baryons Cold dark matter EDGES

10−4 10−3 10−2 10−1 100 a 100 101 102 103 104 T [K] Tb Tγ

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Temperature

Photons Baryons Cold dark matter EDGES

10−4 10−3 10−2 10−1 100 a 100 101 102 103 104 T [K] Tb Tγ

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Temperature

Photons Baryons Cold dark matter EDGES

10−4 10−3 10−2 10−1 100 a 100 101 102 103 104 T [K] Tb Tγ

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Temperature

Photons Baryons Cold dark matter EDGES

10−4 10−3 10−2 10−1 100 a 100 101 102 103 104 T [K] Tb Tγ

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Basic Premise

Nonzero interaction Velocity dependence Nonzero temperature

∆ p χ p χ

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Basic Premise

Nonzero interaction Velocity dependence Nonzero temperature

∆ p χ p χ

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Basic Premise

Nonzero interaction Velocity dependence Nonzero temperature

∆ p χ p χ

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Modifjed Boltzmann equations

Baryons Dark Matter ˙ δb = −θb − 3 ˙ Φ, ˙ θb = − ˙ a aθb + c2

sk2δb

+ 4¯ ργ 3¯ ρb aneσT (θγ − θb) + k2Ψ. + ρχ ρb Rχ (θχ − θb) Rχ = aρb mχ + mH σv FHe

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Modifjed Boltzmann equations

Baryons Dark Matter ˙ δcdm = −θcdm + 3 ˙ Φ, ˙ θcdm = − ˙ a aθcdm + k2Ψ + Rχ (θb − θχ) Rχ = aρb mχ + mH σv FHe

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Power Law Interaction

Coulomb Dipole

10−4 10−3 10−2 10−1 100 a 10−1 101 103 T [K] Tb Tb ref. Tχ Tγ

Rχ = acnρbσ0 mχ + mH Tb mH + Tχ mχ + V 2

rms

3 n+1

2

FHe

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Power Law Interaction

Coulomb Dipole

10−4 10−3 10−2 10−1 100 a 10−4 10−2 100 102 104 T [K] Tb Tb ref. Tχ Tγ

Rχ = acnρbσ0 mχ + mH Tb mH + Tχ mχ + V 2

rms

3 n+1

2

FHe

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Resonance interaction

Assumptions Velocity dependence

10−4 10−3 10−2 10−1 a 10−7 10−5 10−3 10−1 101 R/aH mχ = 10000 mχ = 10 mχ = 1 mχ = 1000 mχ = 100

Rχ = aρbσ0 mχ + mH xbxχQ3/2 mHmχ K1 Q 2 √xbxχ

  • FHe
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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Resonance interaction

Assumptions Velocity dependence

10−4 10−3 10−2 10−1 a 10−7 10−5 10−3 10−1 101 R/aH mχ = 10000 mχ = 10 mχ = 1 mχ = 1000 mχ = 100

Rχ = aρbσ0 mχ + mH xbxχQ3/2 mHmχ K1 Q 2 √xbxχ

  • FHe
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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

CLASS

Boltzmann solver Linear Modular

Figure: from class-code.net

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

CLASS

Boltzmann solver Linear Modular

Figure: from class-code.net

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

CLASS

Boltzmann solver Linear Modular

Figure: from class-code.net

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Thermodynamics

Interactions Temperature Recombination + reionisation

−20 ∆xe/xe,ref [%] Interacting ΛCDM 101 102 103 104 z 10−3 10−1 xe

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Thermodynamics

Interactions Temperature Recombination + reionisation

−20 ∆xe/xe,ref [%] Interacting ΛCDM 101 102 103 104 z 10−3 10−1 xe

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Thermodynamics

Interactions Temperature Recombination + reionisation

−20 ∆xe/xe,ref [%] Interacting ΛCDM 101 102 103 104 z 10−3 10−1 xe

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Perturbations

Modifjed Boltzmann equations Tight coupling ap- proximation

10−6 10−5 10−4 10−3 10−2 a 10−2 100 102 104 |δb| (k = 0.5 Mpc−1) Interacting ΛCDM

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Perturbations

Modifjed Boltzmann equations Tight coupling ap- proximation

10−6 10−5 10−4 10−3 10−2 a 10−2 100 102 104 |δb| (k = 0.5 Mpc−1) Interacting ΛCDM

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Upper limit ∆Cls

500 1,000 1,500 2,000 2,500 1 2 3 4 ·10−9 l l(l + 1)ClTT ΛCDM Power law Resonance

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Upper limit ∆Cls

−3 −2 −1 ∆TT/TTref [%] Resonance 10 MeV Resonance 100 MeV Power law 1 MeV Power law 100 MeV 500 1000 1500 2000 2500 l −3 −2 −1 1 ∆EE/EEref [%]

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Coulomb-like

10−4 10−3 10−2 10−1 100 a 10−3 10−1 101 103 T [K] Tb Power law 1 MeV Tχ Power law 1 MeV Tb Power law 100 MeV Tχ Power law 100 MeV

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Coulomb-like

mχ 1 MeV 100 MeV σ0 (95% CL.) 2.2 × 10−41 cm2 2.3 × 10−41 cm2 Tb(z = 17.2) 0.01 K 0.14 K

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Resonance

10−4 10−3 10−2 10−1 100 a 10−5 10−3 10−1 101 103 T [K] Tχ Resonance 10 MeV Tb Resonance 10 MeV Tχ Resonance 100 MeV Tb Resonance 100 MeV

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Resonance

mχ 10 MeV 100 MeV σ0 (95% CL.) 5.2 × 10−9 1.9 × 10−7 ˜ σ0 (95% CL.) 1.2 × 10−51 cm2 1.4 × 10−52 cm2 Tb(z = 17.2) 6.97 K 6.71 K

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Further Results

ǫ [MeV] mχ = 10 MeV mχ = 100 MeV 1 × 10−11 σ0 = 1.05 × 10−8 σ0 = 3.46 × 10−7 1 × 10−10 σ0 = 2.52 × 10−9 σ0 = 8.36 × 10−8 1 × 10−9 σ0 = 1.39 × 10−9 σ0 = 2.09 × 10−8 1 × 10−8 σ0 = 2.84 × 10−9 σ0 = 1.61 × 10−8 1 × 10−7 σ0 = 9.88 × 10−8 σ0 = 5.29 × 10−8 ǫ [MeV] mχ = 1000 MeV mχ = 5000 MeV 1 × 10−11 σ0 = 1.05 × 10−5 σ0 = 1.25 × 10−4 1 × 10−10 σ0 = 2.59 × 10−6 σ0 = 2.95 × 10−5 1 × 10−9 σ0 = 6.79 × 10−7 σ0 = 7.09 × 10−6 1 × 10−8 σ0 = 1.93 × 10−7 σ0 = 2.25 × 10−6 1 × 10−7 σ0 = 2.07 × 10−7 σ0 = 2.52 × 10−6

Table:

Inferred 95% confjdence upper limits of σ0. Obtained with MontePython using Planck 2015 TT+TE+EE data.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Further Results

ǫ [MeV] mχ = 10 MeV mχ = 100 MeV 1 × 10−11 ˜ σ0 = 4.43 × 10−52 cm2 ˜ σ0 = 5.29 × 10−53 cm2 1 × 10−10 ˜ σ0 = 3.36 × 10−52 cm2 ˜ σ0 = 4.04 × 10−52 cm2 1 × 10−9 ˜ σ0 = 5.86 × 10−50 cm2 ˜ σ0 = 3.19 × 10−51 cm2 1 × 10−8 ˜ σ0 = 3.79 × 10−48 cm2 ˜ σ0 = 7.78 × 10−50 cm2 1 × 10−7 ˜ σ0 = 4.17 × 10−45 cm2 ˜ σ0 = 8.08 × 10−48 cm2 ǫ [MeV] mχ = 1000 MeV mχ = 5000 MeV 1 × 10−11 ˜ σ0 = 1.29 × 10−53 cm2 ˜ σ0 = 1.48 × 10−53 cm2 1 × 10−10 ˜ σ0 = 1.00 × 10−52 cm2 ˜ σ0 = 1.10 × 10−52 cm2 1 × 10−9 ˜ σ0 = 8.36 × 10−52 cm2 ˜ σ0 = 8.38 × 10−51 cm2 1 × 10−8 ˜ σ0 = 7.52 × 10−51 cm2 ˜ σ0 = 8.41 × 10−51 cm2 1 × 10−7 ˜ σ0 = 2.55 × 10−49 cm2 ˜ σ0 = 2.98 × 10−49 cm2

Table:

Inferred 95% confjdence upper limits of ˜ σ0. Obtained with MontePython using Planck 2015 TT+TE+EE data.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Further Results

100 101 102 103 104

z

10−7 10−5 10−3 10−1 101

Rχ/aH ǫ = 10−10 MeV mχ = 10 MeV ǫ = 10−10 MeV mχ = 100 MeV ǫ = 10−10 MeV mχ = 1000 MeV ǫ = 10−10 MeV mχ = 5000 MeV

Figure: The evolution of the momentum exchange rate Rχ for

ǫ = 1 × 10−10 MeV, using the inferred CMB upper limits for σ0.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Further Results

−2 −1

∆CT T

l

/CT T

l,ref [%]

mχ =10 MeV mχ =100 MeV mχ =1000 MeV mχ =5000 MeV

500 1000 1500 2000 2500

l

−3 −2 −1 1

∆CEE

l

/CEE

l,ref [%]

Figure: Percent residuals of the TT (upper) and EE (lower) spectra with

respect to ΛCDM for ǫ = 1 × 10−10 MeV, using the inferred CMB upper limits for σ0.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Further Results

100 101 102 103 104

z

10−7 10−5 10−3 10−1 101

Rχ/aH ǫ = 10−11 MeV mχ = 100 MeV ǫ = 10−10 MeV mχ = 100 MeV ǫ = 10−9 MeV mχ = 100 MeV ǫ = 10−8 MeV mχ = 100 MeV ǫ = 10−7 MeV mχ = 100 MeV

Figure: The evolution of the momentum exchange rate Rχ for

mχ = 100 MeV, using the inferred CMB upper limits for σ0.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Further Results

−3 −2 −1

∆CT T

l

/CT T

l,ref [%]

ǫ = 10−11 MeV ǫ = 10−10 MeV ǫ = 10−9 MeV ǫ = 10−8 MeV ǫ = 10−7 MeV

500 1000 1500 2000 2500

l

−2

∆CEE

l

/CEE

l,ref [%]

Figure: Percent residuals of the TT (upper) and EE (lower) spectra with

respect to ΛCDM for mχ = 100 MeV, using the inferred CMB upper limits for σ0.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Further Results

10−8 10−6 10−4

σ0

10−10 10−8

ǫ [MeV]

10−51 10−48 10−45

˜ σ0 [cm2] mχ = 10 MeV mχ = 100 MeV mχ = 1000 MeV mχ = 5000 MeV

Figure: Inferred 95% upper limits for σ0 (upper fjgure) and ˜

σ0 (lower fjgure) as a function of ǫ for each tested mχ.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Further Results

10−8 10−6 10−4

σ0 ǫ = 10−11 MeV ǫ = 10−10 MeV ǫ = 10−9 MeV ǫ = 10−8 MeV ǫ = 10−7 MeV

101 102 103

Mχ [MeV]

10−51 10−48 10−45

˜ σ0 [cm2]

Figure: Inferred 95% upper limits for σ0 (upper fjgure) and ˜

σ0 (lower fjgure) as a function of mχ for each tested ǫ.

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Conclusion

Upper Limits EDGES Other constraints

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Conclusion

Upper Limits EDGES Other constraints

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Interacting Dark Matter Markus R. Mosbech Evolution DM Interactions Numerics Results

Conclusion

Upper Limits EDGES Other constraints