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:

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

CMB temperature

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

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

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

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

Baryon and dark matter linear perturbation evolution

If only we could observe the baryon or CDM perturbations! 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?

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

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:

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

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)

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/

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….

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

Recent paper: arXiv:

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)

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) ….

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…)

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

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

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

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

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

+ 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.

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

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

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

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

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

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

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

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. Dark ages very challenging to observe (e.g. far side of the moon) Easier to observe at lower z, but complicated astrophysics Lensing and redshift-distortions probe matter density (hence cosmology) BUT: non-linear effects important on small scales - more sophisticated non-linear separation methods may be required

Correlation function z=10