cosmological observables after recombination antony lewis institute of astronomy, cambridge anthony...
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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:
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Hu & White, Sci. Am., 290 44 (2004)
Evolution of the universe
Opaque
Transparent
Easy
Hard
Dark ages
30<z<1000
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CMB temperature
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Observed CMB temperature power spectrum
Primordial perturbations + known physics
ObservationsConstrain theory of early universe+ evolution parameters and geometry
Hinshaw et al.
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e.g. curvature
flat closed
θθ
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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14 000 Mpc
Dark ages~2500Mpc
Opaque ages ~ 300MpcComoving 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<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)
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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?
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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 Ts
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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:
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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
• (+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
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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)
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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
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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/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….
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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/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
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Recent paper: arXiv:0902.0493
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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 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) ….
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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…)
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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
ObserverChanges 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 space Redshift 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 astrophysics Depends only on velocities -> potentials
(n.k)4 component can be used for cosmology
Barkana & Loeb astro-ph/0409572
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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
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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 effectDepending on angle
z=10
Small scale power boostedby superposition of lots oflarge-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 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
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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 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
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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
• 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
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Correlation function
z=10