Future 21cm surveys and nonGaussianity

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Future 21cm surveys and non-Gaussianity

• Antony Lewis
• Institute of Astronomy, Cambridge
• http//cosmologist.info/

work with Anthony Challinor Richard Shaw
(mostly) review
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Evolution of the universe
Opaque
Easy
Transparent
Dark ages
Hard
30ltzlt1000
Hu White, Sci. Am., 290 44 (2004)
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• 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)?

After recombination essentially only one
transition at low enough energy - hyperfine
spin-flip transition of hydrogen
triplet
Credit Sigurdson
singlet
Define spin temperature Ts to quantify occupation
numbers
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What can we observe?
Spontaneous emission n1 A10 photons per unit
volume per unit proper time
1
h v E21
Rate A10 2.869x10-15 /s (decay time 107 years)
0
Stimulated emission net photons (n1 B10 n0
B01)Iv
Total net number of photons
In terms of spin temperature
Net emission or absorption if levels not in
equilibrium with photon distribution - observe
baryons in 21cm emission or absorption if Ts ltgt
TCMB
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Thermal history
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Whats the linear-theory power spectrum?
Use Boltzmann equation for change in CMB due to
21cm absorption
Background
Perturbation
l gt1 anisotropies in TCMB
Fluctuation in density of H atoms, fluctuations
in spin temperature
Doppler shiftto gas rest frame
CMB dipole seen by H atomsmore absorption in
direction of gas motion relative to CMB
self-absorption and reionization re-scattering
terms
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Solve Boltzmann equation in Newtonian gauge
Lewis Challinor astro-ph/0702600
Redshift distortions
Main monopolesource
Effect of localCMB anisotropy
Sachs-Wolfe, Doppler and ISW change to redshift
Tiny Reionization sources
( few percent self-absorption effects)
For k gtgt aH good approximation is
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Observable angular power spectrum
Integrate over window in frequency
1/vN suppressionwithin window(bandwidth)
White noisefrom smaller scales
Baryonpressuresupport
baryon oscillations
z50
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Comparison with CMB power spectrum
Kleban et al. hep-th/0703215
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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
Lewis Challinor astro-ph/0702600
On small scales non-linear effects many percent
even at z 50
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Non-linear redshift distortions
Shaw Lewis, 2008 in prep. also Scoccimarro
2004
Exact non-linear result (for Gaussian fields on
flat sky)
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Non-Gaussianity

• Primordial non-Gaussianity, e.g. fNl
• Non-linear evolution
• Non-linear redshift distortions
• Lensing
• First sources
• Foregrounds
• Observational things

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Squeezed bispectrum for shell at z50 (0.1MHz
bandwidth)
fNL1

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

Pillepich, Porciani, Matarrese astro-ph/0611126
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Cumulative S/N for one redshift shell at z50,
fNl1
Squeezed
Equilateral
Pillepich, Porciani, Matarrese astro-ph/0611126
Can do better with full redshift dependence
claims of fNL 0.01
Cooray astro-ph/0610257
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Redshift distortion bispectrum

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

Linear-theory source
Can do exactly, or leading terms are
Not attempted numerics as yet
Also Scoccimarro et al 1998, Hivon et al 1995
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• 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

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Dark-age observational prospects

• No time soon

- (1z)21cm wavelengths 10 meters for z50-
atmosphere opaque for zgt 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
But large wavelength -gt crude reflectors OK
See e.g. Carilli et al astro-ph/0702070,
Peterson et al astro-ph/0606104
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After the dark ages

• First stars and other objects form
• Lyman-alpha and ionizing radiation
  presentWouthuysen-Field (WF) effect -
  Lyman-alpha couples Ts to Tg - Photoheating
  makes gas hot at late times so signal in
  emissionIonizing radiation - ionized regions
  have little hydrogen regions with no 21cm
  signalOver-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 (zlt10), MWA, LOFAR
  (zlt20), SKA (zlt25).
• Discrete sources lensing, galaxy counts (109 in
  SKA), etc.

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Non-linear implies large non-Gaussianities
Mellema, Iliev, Pen, Shapiroastro-ph/0603518
Detect skewness soonwith MWA Stuart et al
astro-ph/0703070
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Lots of potentially useful informationclumping
of IGM, mass of ionizing sources, source bias,
ionization redshift, etc- but probably not
directly about primordial fNL
Wyithe Morales astro-ph/0703070
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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 30ltzlt 500 up to llt107 via
  observations of CMB at (1z)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

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Non-Gaussianity?

• Lots, but much the largest from non-linear
  evolution ( redshift distortions). Different
  angular dependence from fNl
• Bispectrum ultimately may in theory give fNllt1.-
  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 gt 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.

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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 a13 (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.

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Why the CMB temperature (and polarization) is
great

• 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

Why it is bad
- Only one sky, so cosmic variance limited on
large scales - Diffusion damping and
line-of-sight averaging all information on
small scales destroyed! (lgt2500)- Only a 2D
surface (reionization), no 3D information
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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, 1ltllt2000 - about 106 modes
- can measure Pk to about 0.1 at l2000 (k Mpc
0.1) Dark age baryons at one redshift, 1lt l lt
106 - about 1012 modes - measure Pk to about
0.0001 at l106 (k Mpc 100)
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What about different redshifts?

• About 104 independent redshift shells at l106
• - total of 1016 modes - measure Pk to an
  error of 10-8 at 0.05 Mpc scales

e.g. running of spectral index If ns 0.96
maybe expect running (1-ns)2 10-3Expected
change in Pk 10-3 per log k - measure
running to 5 significant figures!?
So worth thinking about can we observe the
baryons somehow?
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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
TgTCMBLater, once few free electrons, gas
cools Tg mv2/kB 1/a2
Spin temperature driven to Tg lt TCMB by
collisions - atoms have net absorption of 21cm
CMB photons
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New large scaleinformation?- potentials
etccorrelated with CMB
Dark ages2500Mpc
l 10
14 000 Mpc
z30
Opaque ages 300Mpc
Comoving distance
z1000
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Non-linear redshift distortions
Shaw Lewis, 2008 in prep. also Scoccimarro
2004
Power spectrum from
Exact non-linear result (for Gaussian fields on
flat sky)
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Idealised fNl constraint from redshift slice
Cosmic variance on bispectrum
z100
Power spectrum
Non-linear growth
weightedbispectrumfor fNl1
Cooray astro-ph/0610257
Can do better with full redshift dependence
claims fNL 0.01