Cosmological observables after recombination

Antony LewisInstitute of Astronomy, Cambridge

http://cosmologist.info/

Anthony Challinor (IoA, DAMTP); astro-ph/0702600 + in prep.Richard Shaw (IoA), arXiv:0808.1724

Following work by Scott, Rees, Zaldarriaga, Loeb, Barkana, Bharadwaj, Naoz, Scoccimarro + many more …

Work with:

Hu & White, Sci. Am., 290 44 (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

ObservationsConstrain theory of early universe+ evolution parameters and geometry

Hinshaw et al.

e.g. curvature

flat closed

θθ

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

14 000 Mpc

Dark ages~2500Mpc

Opaque ages ~ 300MpcComoving 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 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 0.0001% at l=106 (k Mpc ~ 100)

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

What about different redshifts?

e.g. running of spectral index:

If ns = 0.96 maybe expect running ~ (1-ns)2 ~ 10-3

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?

• 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 Ts

Spontaneous emission: n1 A10 photons per unit volume per unit proper time

Rate: A10 = 2.869x10-15 /s

Stimulated emission: net photons (n1 B10 – n0 B01)Iv

0

1

h v = E21

Net emission or absorption if levels not in equilibrium with photon distribution- observe baryons in 21cm emission or absorption if Ts <> TCMB

What can we observe?

In terms of spin temperature:

Total net number of photons:

What determines the spin temperature?

• Interaction with CMB photons: drives Ts towards TCMB

• Collisions between atoms: drives Ts towards gas temperature Tg

• (+Interaction with Lyman-alpha photons - not important during dark ages)

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

Solve Boltzmann equation in Newtonian gauge:

Redshift distortionsMain monopolesource Effect of local

CMB anisotropy

Tiny Reionization sourcesSachs-Wolfe, Doppler and ISW change to redshift

For k >> aH good approximation is

(+re-scattering effects)

21cm does indeed track baryons when Ts < TCMB

So can indirectly observe baryon power spectrum at 30< z < 100-1000 via 21cm

z=50

Kleban et al. hep-th/0703215

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/0312134, Kleban et al. hep-th/0703215

• Varying alpha: A10 ~ α13 (21cm frequency changed: different background and perturbations)Khatri & Wandelt: astro-ph/0701752

• Isocurvature modes(direct signature of baryons; distinguish CDM/baryon isocurvature)Barkana & Loeb: astro-ph/0502083

• CDM particle decays and annihilations(changes temperature evolution)Shchekinov & Vasiliev: astro-ph/0604231, Valdes et al: astro-ph/0701301

• Primordial non-Gaussianity(measure bispectrum etc of 21cm: limited by non-linear evolution)Cooray: astro-ph/0610257, Pillepich et al: astro-ph/0611126

• 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/0702070, Peterson et al: astro-ph/0606104

But: large wavelength -> crude reflectors OK

Current 21cm:

LOFAR, PAST, MWA: study reionization at z <~12SKA: still being planned, z<~ 12

Recent paper: arXiv:0902.0493

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 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, SKA (z<13) ….

Angular source count density in linear theory

Challinor & Lewis 2020

What we think we are seeing Actually seeing

v

z1 z2

• 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

ObserverChanges 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 space Redshift 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 astrophysics Depends only on velocities -> potentials

(n.k)4 component can be used for cosmology

Barkana & Loeb astro-ph/0409572

Are redshift distortions linear?

RMS velocity 10-4-10-3 Radial displacement ~ 0.1-1 MPc

Megaparsecscale

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 effectDepending on angle

z=10

Small scale power boostedby superposition of lots oflarge-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 detectionRedshift-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 1995

Non-linear density evolution

Small scales see build up of power from many larger scale modes - important

At high redshift accurately modelled by 3rd 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<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

• 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