Future 21cm surveys and non-Gaussianity Antony Lewis Institute of Astronomy, Cambridge work with Anthony Challinor & Richard Shaw + (mostly) review

Hu & White, Sci. Am., (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 T s to quantify occupation numbers: After recombination essentially only one transition at low enough energy: - hyperfine spin-flip transition of hydrogen

Spontaneous emission: n 1 A 10 photons per unit volume per unit proper time Rate: A 10 = 2.869x /s (decay time 10 7 years) Stimulated emission: net photons (n 1 B 10 – n 0 B 01 ) I v 0 1 h v = E 21 Net emission or absorption if levels not in equilibrium with photon distribution - observe baryons in 21cm emission or absorption if T s <> T CMB What can we observe? In terms of spin temperature: Total net number of photons:

Thermal history

Whats 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 T CMB Doppler shift to gas rest frame + self-absorption and reionization re-scattering terms

Solve Boltzmann equation in Newtonian gauge Redshift distortions Main monopole source Effect of local CMB anisotropy Tiny Reionization sources Sachs-Wolfe, Doppler and ISW change to redshift For k >> aH good approximation is (+ few percent self-absorption effects) Lewis & Challinor: astro-ph/

Observable angular power spectrum: White noise from smaller scales Baryon pressure support 1/N suppression within window (bandwidth) baryon oscillations z=50 Integrate over window in frequency

Comparison with CMB power spectrum Kleban et al. hep-th/

Non-linear evolution Small scales see build up of power from many larger scale modes - important But probably accurately modelled by 3 rd order perturbation theory: On small scales non-linear effects many percent even at z ~ 50 Lewis & Challinor: astro-ph/

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. f Nl Non-linear evolution Non-linear redshift distortions Lensing First sources Foregrounds Observational things

Pillepich, Porciani, Matarrese: astro-ph/ f NL =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, f Nl =1 Pillepich, Porciani, Matarrese: astro-ph/ Squeezed Equilateral Cooray: astro-ph/ Can do better with full redshift dependence: claims of f NL ~ 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 yet Also Scoccimarro et al 1998, Hivon et al 1995Scoccimarro

Lensing - Generally small effect on power spectrum as 21cm spectrum quite smooth - Effect of smoothing primordial bispectrum (Cooray et al, ) Cooray 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/ , Peterson et al: astro-ph/ 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 T s to T g - 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 (~10 9 in SKA), etc.

Mellema, Iliev, Pen, Shapiro: astro-ph/ Non-linear implies large non-Gaussianities… Detect skewness soon with MWA Stuart et al: astro-ph/

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

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<10 7 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 f Nl Bispectrum ultimately may in theory give f Nl <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 g NL >~ 10 Cooray, Li, Melchiorri Possibly other powerful non-Gaussianity probes, e.g. non-linear bias c.f. Dalal et al , Verde & Matarrese , Slosar & Seljak in prep.

Other things you could do with precision dark age 21cm High-precision on small-scale primordial power spectrum (n s, running, features [wide range of k], etc.) e.g. Loeb & Zaldarriaga: astro-ph/ , Kleban et al. hep-th/ Varying alpha: A 10 ~ α 13 (21cm frequency changed: different background and perturbations) Khatri & Wandelt: astro-ph/ Isocurvature modes (direct signature of baryons; distinguish CDM/baryon isocurvature) Barkana & Loeb: astro-ph/ CDM particle decays and annihilations, primordial black holes (changes temperature evolution) Shchekinov & Vasiliev: astro-ph/ , Valdes et al: astro-ph/ , Mack & Wesley 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 10 6 modes - can measure P k to about 0.1% at l=2000 (k Mpc~ 0.1) Dark age baryons at one redshift, 1< l < 10 6 : - about modes - measure P k to about % at l=10 6 (k Mpc ~ 100)

About 10 4 independent redshift shells at l= total of modes - measure P k to an error of at 0.05 Mpc scales What about different redshifts? e.g. running of spectral index: If n s = 0.96 maybe expect running ~ (1-n s ) 2 ~ Expected change in P k ~ 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 T s towards T CMB Collisions between atoms: drives T s towards gas temperature T g T CMB = 2.726K/a At recombination, Compton scattering makes T g =T CMB Later, once few free electrons, gas cools: T g ~ mv 2 /k B ~ 1/a 2 Spin temperature driven to T g < T CMB by collisions: - atoms have net absorption of 21cm CMB photons

Mpc Dark ages ~2500Mpc Opaque ages ~ 300Mpc Comoving distance z=30 z~1000 New large scale information? - potentials etc correlated 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/ Power spectrum weighted bispectrum for fNl=1 Non-linear growth Cosmic variance on bispectrum Idealised f Nl constraint from redshift slice z=100 …Can do better with full redshift dependence: claims f NL ~ 0.01