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

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Hu & White, Sci. Am., (2004) Evolution of the universe Opaque Transparent Easy Hard Dark ages 30

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CMB temperature

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Observed CMB temperature power spectrum Primordial perturbations + known physics Observations Constrain theory of early universe + evolution parameters and geometry Hinshaw et al.

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e.g. curvature flat closed θ θ We see:

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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

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Mpc Dark ages ~2500Mpc Opaque ages ~ 300Mpc Comoving distance z=30 z~1000 z=0

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Baryon and dark matter linear perturbation evolution

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If only we could observe the baryon or CDM perturbations! CMB temperature, 1

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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?

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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 Credit: Sigurdson triplet singlet Define spin temperature T s

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Spontaneous emission: n 1 A 10 photons per unit volume per unit proper time Rate: A 10 = 2.869x /s 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:

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What determines the spin temperature? Interaction with CMB photons: drives T s towards T CMB Collisions between atoms: drives T s towards gas temperature T g (+Interaction with Lyman-alpha photons - not important during dark ages) 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 below T CMB by collisions: - atoms have net absorption of 21cm CMB photons

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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 (+re-scattering effects)

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21cm does indeed track baryons when T s < T CMB So can indirectly observe baryon power spectrum at 30< z < via 21cm z=50 Kleban et al. hep-th/

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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 (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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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 See e.g. Carilli et al: astro-ph/ , Peterson et al: astro-ph/ But: large wavelength -> crude reflectors OK Current 21cm: LOFAR, PAST, MWA: study reionization at z <~12 SKA: still being planned, z<~ 12

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Recent paper: arXiv:

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What can we observe after the dark ages? Electromagnetic radiation as a function of frequency and angle on the sky Distances only measured indirectly as a redshift (e.g. from ratio of atomic line frequency observed to that at source) Diffuse radiation (e.g. 21cm) discrete sources (counts, shapes, luminosities, spectra)

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21cm 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 Both highly non-linear: very complicated physics Lower redshift, so less long wavelengths: - much easier to observe! GMRT (z<10), MWA, LOFAR, SKA (z<13) ….

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Angular source count density in linear theory Challinor & Lewis 2020 What we think we are seeingActually seeing v z1z1 z2z2 Most source densities depend on complicated astrophysics (evolution of sources, interactions with environment, etc…)

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So how do we get cosmology from this mess?? Look at gravitational potentials (still nearly linear everywhere) - Friedman equations still good approximation Most of the complicated stuff is baryons and light: dark matter evolution is much simpler

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

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Weak lensing Last scattering surface Inhomogeneous universe - photons deflected Observer Changes power spectrum, new B modes, induces non-Gaussianity - but also probes potentials along the line of sight

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Galaxy weak lensing and actually… Bridle et al,2008 Integral constraint – most useful for dark energy rather than power spectrum

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A closer look at redshift distortions x y x y(z) Real spaceRedshift space

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+ Density perturbed too. In redshift-space see More power in line-of-sight direction -> distinguish velocity effect Both linear (+higher) effects – same order of magnitude. Note correlated.

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Linear power spectrum: Messy astrophysicsDepends only on velocities -> potentials (n.k) 4 component can be used for cosmology Barkana & Loeb astro-ph/

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Are redshift distortions linear? RMS velocity Radial displacement ~ MPc Megaparsec scale Looks like big non-linear effect! Real Space Redshift space BUT: bulk displacements unobservable. Need more detailed calculation. M(x + dx) M(x) + M(x) dx Define 3D redshift-space co-ordinate

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

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Significant effect Depending on angle z=10 Small scale power boosted by superposition of lots of large-scale modes

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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… Need more sophisticated separation methods to measure small scales. z=10 Shaw & Lewis, 2008

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

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Non-linear density evolution Small scales see build up of power from many larger scale modes - important At high redshift accurately modelled by 3 rd order perturbation theory: On small scales non-linear effects many percent even at z ~ 50 Very important at lower redshifts : need good numerical simulations

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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

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Correlation function z=10

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