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**High-redshift 21cm and redshift distortions**

Antony Lewis Institute of Astronomy, Cambridge Work with: Anthony Challinor (IoA, DAMTP); astro-ph/ Richard Shaw (IoA), arXiv: Following work by Scott, Rees, Zaldarriaga, Loeb, Barkana, Bharadwaj, Naoz, Scoccimarro + many more …

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**Evolution of the universe**

Opaque Easy Transparent Dark ages 30<z<1000 Hard Hu & White, Sci. Am., (2004)

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CMB temperature

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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! (l>~2500) - Only a 2D surface (+reionization), no 3D information

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**If only we could observe the CDM perturbations…**

- not erased by diffusion damping (if cold): power on all scales - full 3D distribution of perturbations What about the baryons? fall into CDM potential wells; also power on small scales full 3D distribution but baryon pressure non-zero: very small scales still erased 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 % at l=106 (k Mpc ~ 100)

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**What about different redshifts?**

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 e.g. running of spectral index: If ns = 0.96 maybe expect running ~ (1-ns)2 ~ 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?

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**How can light interact with the baryons (mostly neutral H + He)?**

- after recombination, Hydrogen atoms in ground state and CMB photons have hν << Lyman-alpha frequency * high-frequency tail of CMB spectrum exponentially suppressed * essentially no Lyman-alpha interactions * atoms in ground state: no higher level transitions either - Need transition at much lower energy * Essentially only candidate for hydrogen is the hyperfine spin-flip transition triplet singlet Credit: Sigurdson Define spin temperature Ts

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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 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 <> TCMB

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**What determines the spin temperature?**

Interaction with CMB photons: 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 below TCMB by collisions: - atoms have net absorption of 21cm CMB photons (+Interaction with Lyman-alpha photons - not important during dark ages)

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**What’s the power spectrum?**

Use Boltzmann equation for change in CMB due to 21cm absorption: Background: Perturbation: l >1 anisotropies in TCMB Fluctuation in density of H atoms, + fluctuations in spin temperature Doppler shift to gas rest frame CMB dipole seen by H atoms: more absorption in direction of gas motion relative to CMB + reionization re-scattering terms

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**Solve Boltzmann equation in Newtonian gauge:**

Redshift distortions Main monopole source Effect of local CMB anisotropy Sachs-Wolfe, Doppler and ISW change to redshift Tiny Reionization sources For k >> aH good approximation is (+re-scattering effects)

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**21cm does indeed track baryons when Ts < TCMB**

z=50 Kleban et al. hep-th/ So can indirectly observe baryon power spectrum at 30< z < via 21cm

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**Observable angular power spectrum:**

Integrate over window in frequency Small scales: 1/√N suppression within window ‘White noise’ from smaller scales Baryon pressure support baryon oscillations z=50

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**What about large scales (Ha >~ k)?**

Narrow redshift window <~ 1% effect at l<50 Extra terms largely negligible

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**New large scale information? - potentials etc correlated with CMB**

Dark ages ~2500Mpc l ~ 10 Mpc z=30 Opaque ages ~ 300Mpc Comoving distance z~1000

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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: On small scales non-linear effects many percent even at z ~ 50 + redshift distortions, see later.

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**Also lensing Modified Bessel function Unlensed Lensed Wigner functions**

Lensing potential power spectrum Lewis, Challinor: astro-ph/ c.f. Madel & Zaldarriaga: astro-ph/

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like convolution with deflection angle power spectrum; generally small effect as 21cm spectrum quite smooth Cl(z=50,z=50) Cl(z=50,z=52) Lots of information in 3-D (Zahn & Zaldarriaga 2006)

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**Observational prospects**

No time soon… - (1+z)21cm wavelengths: ~ 10 meters for z=50 - atmosphere opaque for z>~ 70: go to the moon? - fluctuations in ionosphere: phase errors: go to moon? - interferences with terrestrial radio: far side of the moon? - foregrounds: large! use signal decorrelation with frequency But: large wavelength -> crude reflectors OK See e.g. Carilli et al: astro-ph/ , Peterson et al: astro-ph/ Current 21cm: LOFAR, PAST, MWA: study reionization at z <20 SKA: still being planned, z< 25

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**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/ , Kleban et al. hep-th/ Varying alpha: A10 ~ α13 (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 (changes temperature evolution) Shchekinov & Vasiliev: astro-ph/ , Valdes et al: astro-ph/ Primordial non-Gaussianity (measure bispectrum etc of 21cm: limited by non-linear evolution) Cooray: astro-ph/ , Pillepich et al: astro-ph/ Lots of other things: e.g. cosmic strings, warm dark matter, neutrino masses, early dark energy/modified gravity….

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**Back to reality – 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 Both highly non-linear: very 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.

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**How do we get cosmology from this mess?**

Would like to measure dark-matter power on nearly-linear scales. Want to observe potentials not baryons 1. Do gravitational lensing: measure source shears probes line-of-sight transverse potential gradients (independently of what the sources are) 2. Measure the velocities induced by falling into potentials probe line-of-sight velocity, depends on line-of-sight potential gradients Redshift distortions

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**A closer look at redshift distortions**

Real space Redshift space y y(z) x x

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**+ Density perturbed too. In redshift-space see**

Both linear (+higher) effects – same order of magnitude. Note correlated. More power in line-of-sight direction -> distinguish velocity effect

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**Linear-theory n Redshift-space distance: Actual distance:**

Define 3D redshift-space co-ordinate Transform using Jacobian: Redshift-space perturbation Fourier transformed:

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**Linear power spectrum:**

Messy astrophysics Depends only on velocities > potentials (n.k)4 component can be used for cosmology Barkana & Loeb astro-ph/

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**Is linear-theory good enough?**

RMS velocity Radial displacement ~ MPc Megaparsec scale Real Space Redshift space Looks like big non-linear effect! M(x + dx) ≠ M(x) + M’(x) dx BUT: bulk displacements unobservable. Need more detailed calculation.

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**Non-linear redshift distortions**

Assume all fields Gaussian. Shaw & Lewis, 2008 also Scoccimarro 2004 Power spectrum from: Exact non-linear result (for Gaussian fields on flat sky):

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**Significant effect Depending on angle**

Small scale power boosted by superposition of lots of large-scale modes z=10

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**More important at lower redshift. Not negligible even at high z.**

Comparable to non-linear evolution z=10

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**Similar effect on angular power spectrum:**

(A ~ velocity covariance), u= (x-z,y-z’) (sharp z=z’ window, z=10)

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**What does this mean for component separation?**

Angular dependence now more complicated – all μ powers, and not clean. Assuming gives wrong answer… z=10 Need more sophisticated separation methods to measure small scales.

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**Also complicates non-Gaussianity detection Redshift-distortion bispectrum**

Mapping redshift space -> real space nonlinear, so non-Gaussian Linear-theory source Just lots of Gaussian integrals (approximating sources as Gaussian).. Zero if all k orthogonal to line of sight. Can do exactly, or leading terms are: Also Scoccimarro et al 1998, Hivon et al 1995 Not attempted numerics as yet

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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 30<z< 500 up to l<107 via observations of CMB at (1+z)21cm wavelengths. Dark ages very challenging to observe (e.g. far side of the moon) Easier to observe at lower z, but complicated astrophysics Redshift-distortions probe matter density – ideally measure cosmology separately from astrophysics by using angular dependence BUT: non-linear effects important on small scales - more sophisticated non-linear separation methods may be required

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Correlation function z=10

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