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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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Primordial perturbations and precision cosmology from the Cosmic Microwave Background Antony Lewis CITA, University of Toronto

Primordial perturbations and precision cosmology from the Cosmic Microwave Background Antony Lewis CITA, University of Toronto

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