Future 21cm surveys and non-Gaussianity

Antony LewisInstitute of Astronomy, Cambridge

http://cosmologist.info/

work with Anthony Challinor & Richard Shaw + (mostly) review

Hu & White, Sci. Am., 290 44 (2004)

Evolution of the universe

Opaque

Transparent

Easy

Hard

Dark ages

30<z<1000

• CMB great way to measure perturbations down to silk damping scale• To observe small scale perturbations, need to see the CDM or baryons• How can light interact with the baryons (mostly neutral H + He)?

Credit: Sigurdson

triplet

singlet

Define spin temperature Ts to quantify occupation numbers:

After recombination essentially only one transition at low enough energy:

- hyperfine spin-flip transition of hydrogen

Spontaneous emission: n1 A10 photons per unit volume per unit proper time

Rate: A10 = 2.869x10-15 /s (decay time 107 years)

Stimulated emission: net photons (n1 B10 – n0 B01)Iv

0

1

h v = E21

Net emission or absorption if levels not in equilibrium with photon distribution- observe baryons in 21cm emission or absorption if Ts <> TCMB

What can we observe?

In terms of spin temperature:

Total net number of photons:

Thermal history

What’s the linear-theory power spectrum?

Use Boltzmann equation for change in CMB due to 21cm absorption:

Background: Perturbation:

Fluctuation in density of H atoms,+ fluctuations in spin temperature

CMB dipole seen by H atoms:more absorption in direction of gas motion relative to CMB

l >1 anisotropies in TCMB

Doppler shiftto gas rest frame

+ self-absorption and reionization re-scattering terms

Solve Boltzmann equation in Newtonian gauge

Redshift distortionsMain monopolesource Effect of local

CMB anisotropy

Tiny Reionization sourcesSachs-Wolfe, Doppler and ISW change to redshift

For k >> aH good approximation is

(+ few percent self-absorption effects)

Lewis & Challinor: astro-ph/0702600

Observable angular power spectrum:

‘White noise’from smaller scales

Baryonpressuresupport

1/√N suppressionwithin window(bandwidth)

baryon oscillations

z=50

Integrate over window in frequency

Comparison with CMB power spectrum

Kleban et al. hep-th/0703215

Non-linear evolution

Small scales see build up of power from many larger scale modes - important

But probably accurately modelled by 3rd order perturbation theory:

On small scales non-linear effects many percent even at z ~ 50

Lewis & Challinor: astro-ph/0702600

Shaw & Lewis, 2008 in prep. also Scoccimarro 2004

Non-linear redshift distortions

Exact non-linear result (for Gaussian fields on flat sky):

Non-Gaussianity

• Primordial non-Gaussianity, e.g. fNl

• Non-linear evolution• Non-linear redshift distortions• Lensing• First sources• Foregrounds• Observational things

Pillepich, Porciani, Matarrese: astro-ph/0611126

fNL=1

Squeezed bispectrum for shell at z=50 (0.1MHz bandwidth)

- need to calculate non-linear contribution accurately to subtract off - have large cosmic variance

Cumulative S/N for one redshift shell at z=50, fNl=1

Pillepich, Porciani, Matarrese: astro-ph/0611126

SqueezedEquilateral

Cooray: astro-ph/0610257Can do better with full redshift dependence: claims of fNL ~ 0.01

Redshift distortion bispectrum

• Mapping redshift space -> real space nonlinear, so non-Gaussian

Linear-theory source

Can do exactly, or leading terms are:

Not attempted numerics as yetAlso Scoccimarro et al 1998, Hivon et al 1995

Lensing

- Generally small effect on power spectrum as 21cm spectrum quite smooth

- Effect of smoothing primordial bispectrum (Cooray et al, 0803.4194) - Small bispectrum, potentially important trispectrum

Dark-age observational prospects

No time soon…

- (1+z)21cm wavelengths: ~ 10 meters for z=50

- atmosphere opaque for z>~ 70: go to space?

- fluctuations in ionosphere: phase errors: go to space?

- interferences with terrestrial radio: far side of the moon?

- foregrounds: large! use signal decorrelation with frequency

See e.g. Carilli et al: astro-ph/0702070, Peterson et al: astro-ph/0606104

But: large wavelength -> crude reflectors OK

After the dark ages

• First stars and other objects form• Lyman-alpha and ionizing radiation present:

Wouthuysen-Field (WF) effect: - Lyman-alpha couples Ts to Tg

- Photoheating makes gas hot at late times so signal in emission

Ionizing radiation: - ionized regions have little hydrogen – regions with no 21cm signal

Over-densities start brighter (more hot gas), but ionize first, so end off dimmer

Highly non-linear complicated physics

• Lower redshift, so less long wavelengths:- much easier to observe! GMRT (z<10), MWA, LOFAR (z<20), SKA (z<25)….

• Discrete sources: lensing, galaxy counts (~109 in SKA), etc.

Mellema, Iliev, Pen, Shapiro:astro-ph/0603518

Non-linear implies large non-Gaussianities…

Detect skewness ‘soon’with MWA Stuart et al: astro-ph/0703070

Lots of potentially useful information:clumping of IGM, mass of ionizing sources, source bias, ionization redshift, etc…- but probably not directly about primordial fNL Wyithe & Morales: astro-ph/0703070

Conclusions• Huge amount of information in dark age perturbation spectrum

- could constrain early universe parameters to many significant figures

• Dark age baryon perturbations in principle observable at 30<z< 500 up to l<107 via observations of CMB at (1+z)21cm wavelengths.

• Non-linear effects small but important even at z ~ 50

• Dark ages very challenging to observe (e.g. far side of the moon)

• After dark ages physics is complicated – mostly learn about astrophysics, but also - BAO standard ruler (dark energy) - lensing - non-linear bias, etc. - SKA, LOFAR, GMRT, MWA should actually happen

Non-Gaussianity?

• Lots, but much the largest from non-linear evolution (+ redshift distortions). Different angular dependence from fNl

• Bispectrum ultimately may in theory give fNl<1.- Calculations currently incomplete and highly idealized e.g. what happens if you filter large scales as when removing foregrounds?

- Complicated modelling of high-order perturbation theory of the signal from non-linear evolution

• Trispectrum (+ higher); e.g. see gNL >~ 10 Cooray, Li, Melchiorri 0801.3463

• Possibly other powerful non-Gaussianity probes, e.g. non-linear biasc.f. Dalal et al 0710.4560, Verde & Matarrese 0801.4826, Slosar & Seljak in prep.

Other things you could do with precision dark age 21cm

• High-precision on small-scale primordial power spectrum(ns, running, features [wide range of k], etc.)e.g. Loeb & Zaldarriaga: astro-ph/0312134, Kleban et al. hep-th/0703215

• Varying alpha: A10 ~ α13 (21cm frequency changed: different background and perturbations)Khatri & Wandelt: astro-ph/0701752

• Isocurvature modes(direct signature of baryons; distinguish CDM/baryon isocurvature)Barkana & Loeb: astro-ph/0502083

• CDM particle decays and annihilations, primordial black holes(changes temperature evolution)Shchekinov & Vasiliev: astro-ph/0604231, Valdes et al: astro-ph/0701301, Mack & Wesley 0805.1531

• Lots of other things: e.g. cosmic strings, warm dark matter, neutrino masses, early dark energy/modified gravity….

Why the CMB temperature (and polarization) is great

Why it is bad

- Probes scalar, vector and tensor mode perturbations

- The earliest possible observation (bar future neutrino anisotropy surveys etc…)

- Includes super-horizon scales, probing the largest observable perturbations

- Observable now

- Only one sky, so cosmic variance limited on large scales

- Diffusion damping and line-of-sight averaging: all information on small scales destroyed! (l>~2500)

- Only a 2D surface (+reionization), no 3D information

Instead try to observe the baryons…

- Fall into CDM potential wells after recombination

- not erased by photon diffusion power on all scales down to baryon sound horizon at recombination

- full 3D distribution of perturbations

How does the information content compare with the CMB?

CMB temperature, 1<l<~2000: - about 106 modes - can measure Pk to about 0.1% at l=2000 (k Mpc~ 0.1)

Dark age baryons at one redshift, 1< l < 106: - about 1012 modes - measure Pk to about 0.0001% at l=106 (k Mpc ~ 100)

About 104 independent redshift shells at l=106

- total of 1016 modes - measure Pk to an error of 10-8 at 0.05 Mpc scales

What about different redshifts?

e.g. running of spectral index:

If ns = 0.96 maybe expect running ~ (1-ns)2 ~ 10-3

Expected change in Pk ~ 10-3 per log k

- measure running to 5 significant figures!?

So worth thinking about… can we observe the baryons somehow?

What determines the spin temperature?

• Interaction with CMB photons (stimulated emission): drives Ts towards TCMB

• Collisions between atoms: drives Ts towards gas temperature Tg

TCMB = 2.726K/a

At recombination, Compton scattering makes Tg=TCMB

Later, once few free electrons, gas cools: Tg ~ mv2/kB ~ 1/a2

Spin temperature driven to Tg < TCMB by collisions: - atoms have net absorption of 21cm CMB photons

14 000 Mpc

Dark ages~2500Mpc

Opaque ages ~ 300MpcComoving distance

z=30

z~1000

New large scaleinformation?- potentials etccorrelated with CMB

l ~ 10

Non-linear redshift distortions

Power spectrum from:

Exact non-linear result (for Gaussian fields on flat sky):

Shaw & Lewis, 2008 in prep. also Scoccimarro 2004

Cooray: astro-ph/0610257

Power spectrum

weightedbispectrumfor fNl=1

Non-linear growth

Cosmic varianceon bispectrum

Idealised fNl constraint from redshift slice

z=100

…Can do better with full redshift dependence: claims fNL ~ 0.01