David J. E. Marsh

David J. E. Marsh Phys. Rep. 643, 1 (2016)

Axion Cosmology, and the Lightest Possible Dark Matter Candidate

David J. E. Marsh

David J. E. Marsh

Initial Conditions and Relic Density

Symmetry Breaking and Inflation

David J. E. Marsh

Cold condensate from SSB.

The axion is born:

Vacuum Realignment

David J. E. Marsh

Axion acquires mass*, evolves according to Klein-Gordon:

(* I am ignoring T-dependence and

h i iti )

Axion is “frozen” by Hubble friction term.

Light axions are “DE-like”

Vacuum Realignment

David J. E. Marsh

Axion acquires mass*, evolves according to Klein-Gordon:

(* I am ignoring T-dependence and

h i iti )

Field oscillates & damps. WKB (or exact)

Osc. scalar ~ matter

David J. E. Marsh

Relic Density of Cold Axions

David J. E. Marsh

Ultralight axions: • Relic abundance

natural for GUT scale decay constants!

• SSB occurs before/during inflation.

Universe is one θ patch.

CMB B-pol BICEP/Planck (2014)

Scales of Interest

David J. E. Marsh

Non-thermal compare mass to Hubble (not T).

Physics: Hubble:

[eV]

Non-linear

Linear perts: LSS and the CMB

Size of dSph

“Fuzzy DM”, v. non-linear. Solitons in galaxies. ν<<1 Hz

Galaxy formation, halo model.

“WDM-like”

Equality

“DM-like” “DE/ν-like”

BBN

UV physics? Non-thermal epoch? Miniclusters?

Today

Field frozen: behave as Λ

Rough DM lower bound Precision DM cosmology

Precision Cosmology: Perturbations and Linear

Observables

CMB download: github.com/dgrin1/axionCAMB Cosmosis module coming soon…

Axion DM is “Fuzzy”

David J. E. Marsh

Clustering suppressed relative to CDM on small scales. Heuristically: de Broglie wavelength from Hubble flow.

Uncertainty in position: Recession veocity:

Q: how far away does cosmic DM have to be for r>λ?

Parametrically, this is borne out in cosmological PT…

The Axion Jeans Scale

David J. E. Marsh

Gradient energy scalar DM has effective sound

speed:

pressure gravity

WKB approx, e.g. Park et al (2012)

Exact solutions possible in axion-dominated Universe. e.g. DJEM (2016)

Fits for “transfer function” relative to CDM. Hu et al (2000)

The Axion Jeans Scale

David J. E. Marsh

Numerical solution* in Boltzmann code axionCAMB.

Fig. Hlozek, DJEM et al (2014)

(*un-normalized)

CMB Temperature Power

David J. E. Marsh

DM-like axions change during rad. dom. epoch acoustic peak

heights.

DE-like axions change angular scale and

evolution of Φ. SW

effect. Hlozek, DJEM et al (2014)

Physics: early w=-1 evolution changes expansion rate.

Constraints from Planck TT

David J. E. Marsh Hlozek, DJEM et al (2014)

Marginalised constraints via nested sampling with MultiNest.

Constraints from Planck TT

David J. E. Marsh Hlozek, DJEM et al (2014)

Interpretation as constraints on decay constant if φi~fa.

The Future: CMB-S4

David J. E. Marsh Hlozek, DJEM et al (2016)

Array of ground based telescopes for ~2020*. Advantage over Planck for DM: high-l lensing power.

CMB-S4 Science Book

S4 forecast

Axi

on D

M F

raction

Planck “forecast”

Axi

on D

M F

raction Improve lower bound on DM

particle mass by 102.

Allow detection of 1% departures from CDM at 5σ. S4 can do precision tests

of the CDM paradigm! Ωa~fa

2 improve fa bound.

Challenge: modelling effects of non-linear clustering.

(*near term also “Simons array”)

Non-Linear Scales and Galaxy Formation

Fig: Schive et al (2014) Fig: Schwabe et al (2016)

Halo Model download: github com/DoddyPhysics/HMcode

Overview: Hui et al (2016)

The Halo Mass Function

David J. E. Marsh DJEM & Silk (2013), Du et al (2016)

Physics: pressure/λdB suppresses galaxy formation. Methodology: Press-Schechter and/or N-body sims. Physics: pressure/λdB suppresses galaxy formation. Methodology: Press-Schechter and/or N-body sims.

Corasaniti, DJEM et al (2016)

HUDF cumulative luminosity. Data: Bouwens et al (2014).

100%

50%

10-22eV

10-23eV 50%

CDM

High-z Galaxy Formation

David J. E. Marsh Bozek, DJEM et al (2015); Schive et

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

Abundance matching: HMF UV luminosity. Less clustering later halo formation, fewer high-z

galaxies.

Bright Faint

JWST No

fainter galaxies

Different techniques (matching, SFR, HMF), different data (observations, redshifts, binning) all reach the same conclusions:

is consistent with the data.

Ionized fraction inc. astro. uncertainties.

CDM 10-22eV 10-21eV

Reionization and CMB τ

David J. E. Marsh Bozek, DJEM et al (2105)

High-z galaxies reionize the Universe optical depth. Fewer galaxies later reionization lower τ Planck.

CMB uncertain. But will improve with better EE & kSZ.

Ionized fraction inc. astro. uncertainties. Integrate…

tension

“Axion Stars” and Galaxy Cores

David J. E. Marsh Schive et al (2014+), Schwabe et al (2016+)

ULAs gravitationally condense on small scales inside halos.

David J. E. Marsh

“Axion Stars” and Galaxy Cores

Schive et al (2014+), Schwabe et al (2016+)

R>λdB NFW

Soliton core

• Cores are local ground state soliton soln.

• Cores size shrinks with increasing density.

• Scaling relationship: • Large scale

incoherence NFW.

• Parameterise density profile with transition.

simulation results…

The Cusp-Core Problem?

David J. E. Marsh Walker & Penarrubia (2011)

(e.g.) Slopes of Fornax & Sculptor density profiles:

Velocity dispersion at half-light measures enclosed mass. Two populations constrain slope of DM halo.

Pure

cusp

exc

lude

d >99%

Constraints From Cores

David J. E. Marsh Gonzalez-Morales, DJEM et al

(2016) DJEM & Pop (2015) Chen et al

Use of mock data shows that Jeans analysis is biased and cannot discriminate between models (β-degeneracy).

Slopes method + improved estimator is unbiased.

Jeans Slope

s New

0.4

x10

-22eV

Hig

h-z

gala

xies • All evidence points

to cores. • BUT axions (just)

too light c.f. WDM. • Assume negligible

baryonic feedback. • Testable in future

via (non-)universality.

Extra Topics

David J. E. Marsh

David J. E. Marsh

Let’s take a break...

m~10-22 eV appears special: Limit of our ignorance for DM. Possible source of dSph cores.

Can we ever detect such an axion?

Detecting ULAs with

nEDM: Paving the

Way for CASPEr

David J. E. Marsh

Fig: Harris (2007)

The neutron EDM Experiment

David J. E. Marsh

Ultracold neutrons spinning “in a jar” in E and B fields. Ran at RAL/ILL from 1998 giving best static nEDM limit:

Baker et al (2006); Pendlebury et al (2015)

Measures energy splitting relative to Larmour freq. of Hg:

Cycles: 130s; E-flips: hourly; “Run” measures dn every day.

Sensitive to tiny energy shifts:

Q: can we use the time series to search for axions?

Axions and nEDM

David J. E. Marsh Graham & Rajendran (2013)

Ayres, Rawlik, DJEM et al (in prep.)

Graham & Rajendran: assumed no signal on cycle scales, and averaged. Published data not available for this. For m-1>run, ILL limit ~ 10 times worse than published:

(unpublished) cycle level PSI data + 4 years ILL:

David J. E. Marsh

nEDM (blinded)

Nicholas Ayres and Michal Rawlik for nEDM:

nEDM also sensitive to “axion wind”, but cannot beat SNe…

Numerical GR for Axion Stars

David J. E. Marsh

Fig: Helfer, DJEM et al (2016)

David J. E. Marsh

GRChombo, Clough et al (2015)

Katy Clough Thomas Helfer

(3+1) numerical GR with a scalar cosine potential (any V!).

Stability Solution Space

David J. E. Marsh

Core Collapse I: BHs

David J. E. Marsh Helfer, DJEM et al (2016)

• Above critical MADM and fa axion stars collapse to BHs.

• Appears hard to realise for axion stars from DM structure.

• Mergers and BH formation signals?

Core Collapse II: Axion Emission

David J. E. Marsh Helfer, DJEM et al (2016)

Fig: Levkov et al (2016)

• Below critical fa, quartic interactions axion

emission. • Destabilise galaxy cores

for fa<1015 GeV. CDM

HDM?

ULA Endgame: Can We Exclude 10-22 eV?

David J. E. Marsh

ULA Endgame: 21cm and 10-18 eV

David J. E. Marsh

Scale Mpc-1

CDM w/ vel CDM no vel

Sensitivity early LW

21cm

Pow

er S

pect

rum

z=2

0

Fig. Visbal et al (2012)

DM-baryon relative v modulates large scale 21cm power. Effect can be measured by e.g. LOFAR.

Tseliakhovich & Hirata (2010) Visbal et al (2012)

ULA Endgame: 21cm and 10-18 eV

David J. E. Marsh

Large scale 21cm power from baryon v coherence. Originates from small-scale P(k) effect absent for

ULAs.

Scale Mpc-1

CDM m<10-18 eV Sensitivity

early LW

21cm

Pow

er S

pect

rum

z=2

0

Fig. Visbal et al (2012)

DJEM (2015)

Problem: need to

understand SFR!

Caveats & Work in Progress

David J. E. Marsh

Anharmonic potentials: • Relic density lower fa. In prep w/ Diez-

Tejedor. • axionCAMB: modified perts. In prep w/ Leung. Iscourvature: precision CMB in prep w/ Hlozek.

Multiple axions? “Predicted” by string/M-theory. Can we do precision cosmology? In prep w/ Stott.

“Miniclusters”. Beyond the QCD axion

microlensing constraints. In prep w/ Quevillon.

Simulations with m~10-22 eV. More community input!

Direct detection: can it ever work at ultra-low frequency? Lyman-alpha forest: WTF? In prep w/ Bozek et al.

The Principle of Plenitude: “This best of all possible worlds will contain all possibilities, with our finite experience of eternity giving no reason to dispute nature’s perfection.”

Gottfried Leibniz (1646-1716), in Theodicee

Pangloss sometimes said to Candide: “There is a concatenation of events in this best of all possible worlds: for if you had not been kicked out of a magnificent castle for love of Miss Cunégonde–if you had not come under the Inquisition–if you had not walked over America–if you had not stabbed the Baron–if you had not lost all your sheep from the fine country of El Dorado– why, then, you would not be here, eating preserved citrons and pistachio-nuts.” “All that is very well,” answered Candide, “but let us cultivate our garden.”

Voltaire (1694-1778), in Candide

Quoted in “String Axiverse”