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Cosmological observables after recombination

Explore the evolution of the universe and observe the cosmic microwave background (CMB) temperature and power spectrum to constrain the early universe's theory and parameters.

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Cosmological observables after recombination

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  1. Cosmological observables after recombination Antony Lewis Institute of Astronomy, Cambridge http://cosmologist.info/ Work with: 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 …

  2. Evolution of the universe Opaque Easy Transparent Dark ages 30<z<1000 Hard Hu & White, Sci. Am., 290 44 (2004)

  3. CMB temperature

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

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

  6. 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

  7. Dark ages~2500Mpc z=0 14 000 Mpc z=30 Opaque ages ~ 300Mpc Comoving distance z~1000

  8. Baryon and dark matter linear perturbation evolution

  9. 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)

  10. 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 ~ 10-3Expected change in Pk ~ 10-3 per log k - measure running to 5 significant figures!? So worth thinking about… can we observe the baryons somehow?

  11. - 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 • How can light interact with the baryons (mostly neutral H + He)? - 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

  12. 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 0 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

  13. 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=TCMBLater, 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)

  14. Solve Boltzmann equation in Newtonian gauge: Redshift distortions Main monopolesource Effect of localCMB anisotropy Sachs-Wolfe, Doppler and ISW change to redshift Tiny Reionization sources For k >> aH good approximation is (+re-scattering effects)

  15. 21cm does indeed track baryons when Ts < TCMB z=50 Kleban et al. hep-th/0703215 So can indirectly observe baryon power spectrum at 30< z < 100-1000 via 21cm

  16. 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….

  17. 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/0702070, Peterson et al: astro-ph/0606104 Current 21cm: LOFAR, PAST, MWA: study reionization at z <~12SKA: still being planned, z<~ 12

  18. Recent paper: arXiv:0902.0493

  19. 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)

  20. 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 emissionIonizing radiation: - ionized regions have little hydrogen – regions with no 21cm signalBoth highly non-linear: very complicated physics • Lower redshift, so less long wavelengths:- much easier to observe! GMRT (z<10), MWA, LOFAR, SKA (z<13) ….

  21. Angular source count density in linear theory Challinor & Lewis 2020 What we think we are seeing Actually seeing v z2 z1 • Most source densities depend on complicated astrophysics(evolution of sources, interactions with environment, etc…)

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

  23. Want to observe potentials not baryons Would like to measure dark-matter power on nearly-linear scales via potentials. 1. Do gravitational lensing: measure source shears - probes line-of-sight transverse potential gradients (independently of what the sources are) Cosmic shear 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)

  24. 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

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

  26. A closer look at redshift distortions Real space Redshift space y(z) y x x

  27. 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

  28. Linear power spectrum: Messy astrophysics Depends only on velocities -> potentials (n.k)4 component can be used for cosmology Barkana & Loeb astro-ph/0409572

  29. Are redshift distortions linear? Radial displacement ~ 0.1-1 MPc RMS velocity 10-4-10-3 Define 3D redshift-space co-ordinate Megaparsec scale Redshift space Real Space Looks like big non-linear effect! M(x + dx) ≠ M(x) + M’(x) dx BUT: bulk displacements unobservable. Need more detailed calculation.

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

  31. Significant effectDepending on angle Small scale power boosted by superposition of lots oflarge-scale modes z=10

  32. What does this mean for component separation? Angular dependence now more complicated – all μ powers, and not clean. Assuming gives wrong answer… z=10 Shaw & Lewis, 2008 Need more sophisticated separation methods to measure small scales.

  33. Also complicates non-Gaussianity detectionRedshift-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

  34. 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

  35. 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

  36. Correlation function z=10

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