David J. E. Marsh

The High-z Universe as a Probe of Warm and Fuzzy Dark Matter

What do we really know about DM?“Cold”: (if thermal) non-relativistic when produced.“Collisionless”: no interactions beyond gravity.Produced some time before CMB formation.Many scales: present in galaxies, clusters, and on CMB scales.Forms bound objects down to at least 106 Msol.Not made up of bound objects (no MACHOs, PBHs).One component (+ few % neutrinos).

Everything we know about DM comes from gravitational physics.All statements are scale dependent, and some have to break down.

CMB, galaxiesBullet cluster, CMB

high-z galaxies

Tidal streamsMicrolensing

CMB, galaxies

2 10 100 500 2000Multipole `

0

1000

2000

3000

4000

5000

6000

`(`

+1)

CT

T`

/2

[µK

2 ]

CDM (a/d ! 0)

a/d = 0.01, ma = 1027 eV

a/d = 0.05, ma = 1027 eV

a/d = 0.1, ma = 1027 eV

a/d = 0.5, ma = 1027 eV

a/d = 1, ma = 1027 eV

Planck

Two models of CDMWIMPs

Predicted ~1970’sNaturally come from SUSY.

Heavy, nucleon mass.Thermal.

“Traditional” search strategies.…

AxionsPredicted ~1970’s

Come from strong-CP.v. light, sub-neutrino mass.

Non-thermal.“Non-traditional” search strategies.

…Cold due to small thermal

velocitiesCollisions necessary for

production

“Cold” due to coherence and small wavelengthInteractions via wave

equations

We will explore two limits of these models and how reionization probes them

Aside: on axions and WIMPs

Predicted interaction strength for WIMPs has already been excluded.Soon experiments will hit the “neutrino floor”.

Fig. RESONAANCES.blogspot

Aside: on axions and WIMPs

The QCD axion is essentially a one-parameter model.Only one experiment has got into the range to probe DM.

Warm DM Bond & Szalay (1984); Bode et al (2000)

Any DM with initial velocities imprinted à free-streaming.Thermal particle that decouples while relativistic à gravitino.Other candidates have “thermal equivalent mass” e.g. sterile neutrino.

SM neutrinos m~0.1eV are too hot, WIMP CDM is “a little bit warm”. à WDM is the limit of our knowledge of WIMPs and neutrinos.

Connection to SUSY?

kfs 10 Mpc1 ) mth. 1 keV

“All we do is lower the WIMP mass”? No, also require new d.o.f.’s to lower T.

Fuzzy DM Khlopov et al (1985); Hu et al (2000);

Any bosonic field can have a coherent waves à classical uncertainty.Klein-Gordon eq. gradient energy à effective pressure à Jeans scale. Real scalar from SSB + non-perturbative potential à axion.Other candidates e.g. complex scalar or arbitrary potential.

kJ 10 Mpc1 ) ma 1022 eV

“All we do is lower the QCD axion mass”? No. Need new NP effects to lower m.

FDM is on a continuum with dark energy and quintessence.Limit on FDM mass is lowest possible DM mass.

Connection to string theory?

Linear Transfer FunctionsExact computations with axionCAMB (FDM) or CLASS (WDM).Fitting functions are useful for analytic comparisons of certain cases.

100 101 102

Wavenumber k [Mpc1]

0.0

0.2

0.4

0.6

0.8

1.0

T(k

)

ma = 1023 eV

ma = 1022 eV

ma = 1021 eV

T (k) = X/CDM

Half-mode match:mth. = 0.84 keVm0.39

22

Free-streaming à power-law cut-off.Jeans scale à exponential cut-off + acoustic oscillations.

DJEM (2016)Hlozek, DJEM, et al (2015);

Lesgourgues (2011)

Power suppression reduces structure formation relative to CDM.à These models indirectly change the reionization history

Halo Formation

e.g. DJEM & Silk (2014); Barkana et al (2001)Wang & White (2007); Schneider et al (2013)

Consider Press-Schechter model: halos for super-critical density.Mass function suppressed. How much? Naïve PS has no cut-off.

106 108 1010 1012 101410ï7

10ï5

10ï3

10ï1

101

103

M [h−1M⊙]

dn

dln

M[M

pc/

h]−

3

ΛCDM

Ωc/Ω

d

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Dashed: no cut-offSolid: barrier cut-off

Cut-offs:1) SimulationSpurious structure removal.Non-linear streaming/waves.2) AnalyticSharp-k window.Fitting functions.Modified barrier. FDM: m22 = 1, z=0

Gunn-Peterson BoundBode et al (2000)

Gnedin & Ostriker (1997); Fan et al (2000,2006)

High-z quasars do not show absorption from neutral Hydrogen à Universe must be fully ionized at quasar redshifts, z~6.Rough bound bydemanding a specific PS collapsed fraction at this z.

Z=7Z=6

Z=5Z=4

Z=3

COBE cosmology.σ8 =0.9 (solid) 1 (dashed)

Non-linear fraction ~ 10-3 for reion.

WDM with m<0.6 keV excluded.

Gunn-Peterson Bound DJEM & Silk (2014)Gnedin & Ostriker (1997);

Fan et al (2000,2006)

0 5 10 15 20

10ï4

10ï3

10ï2

10ï1

100

z

F(M

>M

min)

ΛCDMma = 10−20 eV

ma = 10−21 eV

ma = 10−22 eV

FDM with m>10-23 eV consistent with quasars.

WMAP cosmology

High-z quasars do not show absorption from neutral Hydrogen à Universe must be fully ionized at quasar redshifts, z~6.Rough bound bydemanding a specific PS collapsed fraction at this z.

High-z Galaxies Kuhlen & Faucher-Giguere (2012); Schultz et al (2014);

Bozek, DJEM et al (2014)

Concordance models assign UV flux to DM halos by abundance matchingFit observed flux, φ, with Schechter and integrate to get Φ:

(< MUV, z) = n(> Mh, z) ) Mh(MUV, z)

Schultz et alCDM, simsMatch used for WDM

HUDFJWST

Bozek et alMatching model-by-modelAnalytic HMF

50% FDM100% FDM

WDM (Schultz et al):HUDF excludes 0.8 keV, 1.3 keV is marginal.JWST could reach 2.6 keV

FDM (Bozek, DJEM et al):HUDF excludes 10-23 eV, 10-22 eV is marginal.JWST could reach 50% FDM.

A Complete Study Corasaniti, Agarwal, DJEM, Das (2016)

High resolution sims of half-mode matched WDM, FDM and LFDM.Fit HMF over z. Correct low z LF, match SFR(Mh) using HAM, compute LF at high z from SFR PDF. Predict higher SFR at low M than CDM

Data: Bouwens et al; Atek et al; Livermore et al. z=6,7,8.

mW0.81.01.5

[Livermore z=6 steep faint slope can change conclusions]

Exclusions:mW>=1.5 keV; zf>= 106

No axion constraint.:ma>=1.5 x 10-22 consistent.[P(k) shape matters!]

Modeling Reionization Kuhlen & Faucher-Giguere (2012); Bozek, DJEM et al (2014)

Use concordance LF to model ionizing fraction:

nion = fesc.

Z 1

Mlim

(MUV)ion(MUV)dMUV

Model parameters

0.2< fesc < 0.5 -13 <Mlim < -10

50%<FDM<100%

Non-CDM models predict later and faster reionization, with less uncertainty (min Mlim)

[Note: have not used data to get these Q: these are the priors]

Modeling Reionization Kuhlen & Faucher-Giguere (2012); Bozek, DJEM et al (2014)

Use concordance LF to model ionizing fraction:

nion = fesc.

Z 1

Mlim

(MUV)ion(MUV)dMUV

Model parameters

0.2< fesc < 0.5 -13 <Mlim < -10

50%<FDM<100%

Non-CDM models predict later and faster reionization, with less uncertainty (min Mlim)

[Note: have not used data to get these Q: these are the priors]

Optical Depth CDM: Kuhlen & Faucher-GiguereFIT/MIN/MAX are LF fit params.

Integrate Q(z) à τ(<z)Here, CMB values PlanckTT+WMAP-EE à higher values of τ.

Low τ requires more “extreme”models of CDM

Optical DepthIntegrate Q(z) à τ(<z)Here, CMB values PlanckTT+WMAP-EE à higher values of τ.

WDM: Schultz et al

Optical DepthIntegrate Q(z) à τ(<z)Here, CMB values PlanckTT+WMAP-EE à higher values of τ.

FDM: Bozek, DJEM et al

Reionization UncertaintitesFDM (and WDM) prefer low-z, rapid, reionisation and low optical depth.

Competitive with high-z and Ly-a on mass constraints.Future?

Duration of reion via patchy kSZ at high l in AdvACT: σ(δz)~0.2.è break degeneracy of high mass models with CDM à 10-21 eV?

1023 1022 1021

Axion Mass ma [eV]

0.025

0.050

0.075

0.100

0.125

Opt

ical

Dep

th

Planck HFI

Planck + WP

Modeling

1023 1022 1021

Axion Mass ma [eV]

4

6

8

10

Rei

on.R

edsh

iftz r

e

Epilogue: Novel Features of FDM and Axions

FDM PhysicsFuzzy DM is fundamentally different from CDM/WDM/SIDM etc.Non-rel limit of Klein-Gordon-Einstein à Schrodinger-Poisson:

e.g. Widrow & Kaiser (1993); Chavanis (2011+);DJEM (2015,2016); Hui et al (2016)

i +1

2m2a

r2 ma = 0; r2 = 4GN | |2

Related to the smoothed Vlasov equation. Field equation not a particle distribution function à “non-linear optics” regime.

+ ~v ·r = (1 + )r · ~v

Madelung transformation (polar co-ords) à fluid system:

~v + (~v ·r)~v = r(+Q)

Q = 1

2m2

r2p1 + )p1 +

continuity

Euler

“Quantum Pressure”: source of interference effects

Schive et al (2014)

FDM Simulations

Schwabe et al (2016)

FDM Simulations

Novel AstrophysicsSolitons/Axion Stars

Interference Fringes

Black Hole Superradiance

Pressure Oscillations

Halo “Granules”

Detecting AxionsAxions are a great model for FDM. The symmetry structure tells us exactly what types of operators axions can couple to:E.B of electromagnetism, electric dipole moments, fermion spins

e.g. Graham et al (2015); Graham & Rajendran (2013)

ABRACADABRA

MADMAXQUAXFDM

Detecting ULAs Kim & DJEM (2015); Abel, DJEM et al (2017); Garcon et al (2017)

Two challenges: 1) build a model of FDM and compute the couplings.2) Most experiments work by resonance, and can’t probe low freq.

Detecting ULAs Kim & DJEM (2015); Abel, DJEM et al (2017); Garcon et al (2017)

Two challenges: 1) build a model of FDM and compute the couplings.2) Most experiments work by resonance, and can’t probe low freq.

1024 1016 108 102

m [eV]

1032

1026

1020

1014

108

|gN|[G

eV

1 ]

ZN models (constructed)

ZN models (required)

Highz Probes

CASPEr-Wind (reach)

SN1987A (excluded)

QCD axion

Detecting ULAs Kim & DJEM (2015); Abel, DJEM et al (2017); Garcon et al (2017)

Two challenges: 1) build a model of FDM and compute the couplings.2) Most experiments work by resonance, and can’t probe low freq.

1024 1016 108 102

m [eV]

1032

1026

1020

1014

108

|gN|[G

eV

1 ]

ZN models (constructed)

ZN models (required)

Highz Probes

CASPEr-Wind (reach)

SN1987A (excluded)

QCD axion

CASPEr at low frequency?Low field NMR.

10-7 Hz 1 Hz

Detecting ULAs Kim & DJEM (2015); Abel, DJEM et al (2017); Garcon et al (2017)

Two challenges: 1) build a model of FDM and compute the couplings.2) Most experiments work by resonance, and can’t probe low freq.

Detecting ULAs Kim & DJEM (2015); Abel, DJEM et al (2017); Garcon et al (2017)

Two challenges: 1) build a model of FDM and compute the couplings.2) Most experiments work by resonance, and can’t probe low freq.

Any models there?

log10(ma/eV)

3" 23"9"

Decays" Axion"infla1on"

0"

Thermal"axions"

818" 83"833" 812"824"

Linear"Cosmology:"CMB,"LSS"

Lyman8a,"High8z,"21cm"

QCD"axion:"ADMX,"CASPEr,"stellar"

String"theory"axions?"

BHSR:"supermassive,"stellar."eLISA?"

CMB"pol."rota1on""

Solve"CDM"crises?"

ULAs"

Dark"en

ergy"