Primordial perturbations and precision cosmology from the Cosmic Microwave Background

1. Primordial perturbations and precision cosmology from the Cosmic Microwave Background Antony Lewis CITA, University of Toronto http://cosmologist.info

2. Outline • Introduction and current data • Parameter estimation • General primordial perturbations • Current constraints • CMB Polarization: E and B modes • Future constraints • Complications: E/B mixing; CMB lensing

3. Theory Observations Source: NASA/WMAP Science Team

4. Evolution of the universe Opaque Transparent Hu & White, Sci. Am., 290 44 (2004)

5. Perturbation evolutionCMB monopole source till 380 000 yrs (last scattering), linear in conformal timescale invariant primordial adiabatic scalar spectrum photon/baryon plasma + dark matter, neutrinos Characteristic scales: sound wave travel distance; diffusion damping length

6. CMB temperature power spectrumPrimordial perturbations + later physics diffusion damping acoustic oscillations primordial powerspectrum Hu & White, Sci. Am., 290 44 (2004)

7. (almost) uniform 2.726K blackbody Dipole (local motion) O(10-5) perturbations (+galaxy) Observations: the microwave sky today Source: NASA/WMAP Science Team

8. CMB observation history + numerous balloon and ground based observations Source: NASA/WMAP Science Team

9. WMAP + other CMB data Redhead et al: astro-ph/0402359 + Galaxy surveys, galaxy weak lensing, Hubble Space Telescope, supernovae, etc...

10. What can we learn from the CMB? • Initial conditionsWhat types of perturbations, power spectra, distribution function (Gaussian?); => learn about inflation or alternatives. • What and how much stuffMatter densities (Ωb, Ωcdm);; neutrino mass • Geometry and topologyglobal curvature ΩK of universe; topology • EvolutionExpansion rate as function of time; reionization- Hubble constant H0 ; dark energy evolution w = pressure/density • AstrophysicsS-Z effect (clusters), foregrounds, etc.

11. CMB Cl and statistics • Theory: Linear physics + Gaussian primordial fluctuations Theory prediction - variance (average over all possible sky realizations) linearized GR + Boltzmann equations Initial conditions + cosmological parameters Cl CAMB: http://camb.info

12. Observations: only one sky Use estimator for variance: “Cosmic Variance” WMAP low l Assume alm gaussian: - inverse gamma distribution(+ noise, sky cut, etc). l

13. Parameter Estimation • Can compute P( {ө} | data) = P( Cl({ө}) | clobs) • Often want marginalized constraints. e.g. • BUT: Large n integrals very hard to compute! • If we instead sample from P( {ө} | data) then it is easy: Can easily learn everything we need from set of samples

14. Markov Chain Monte Carlo sampling • Metropolis-Hastings algorithm • Number density of samples proportional to probability density • At its best scales linearly with number of parameters(as opposed to exponentially for brute integration) CosmoMC code athttp://cosmologist.info/cosmomcLewis, Bridle:astro-ph/0205436

15. CMB data alonecolor = optical depth Samples in6D parameterspace

16. Plot number density of samples as function of parameters e.g. CMB+galaxy lensing +BBN prior Contaldi, Hoekstra, Lewis: astro-ph/0302435

17. Primordial Perturbationsfluid at redshift < 109 • Photons • Nearly massless neutrinosFree-streaming (no scattering) after neutrino decoupling at z ~ 109 • Baryons + electronstightly coupled to photons by Thomson scattering • Dark MatterAssume cold. Coupled only via gravity. • Dark energyprobably negligible early on

18. Perturbations O(10-5) • Linear evolution • Fourier k mode evolves independently • Scalar, vector, tensor modes evolve independently • Various linearly independent solutions Scalar modes: Density perturbations, potential flows Vector modes: Vortical perturbations Tensor modes: Anisotropic space distortions – gravitational waves http://www.astro.cf.ac.uk/schools/6thFC2002/GravWaves/sld009.htm

19. General regular linear primordial perturbation -isocurvature- + irregular modes, neutrino n-pole modes, n-Tensor modes Rebhan and Schwarz: gr-qc/9403032+ other possible components, e.g. defects, magnetic fields, exotic stuff…

20. Adiabatic modesWhat is the primordial power spectrum? Parameters are primordial power spectrum bins P(ki)+ cosmological parameters On most scales P(k) ~ 2.3 x 10-9 Close to scale invariant Bridle, Lewis, Weller, Efstathiou: astro-ph/0302306

21. Matter isocurvature modes • Possible in two-field inflation models, e.g. ‘curvaton’ scenario • Curvaton model gives adiabatic + correlated CDM or baryon isocurvature, no tensors • CDM, baryon isocurvature indistinguishable – differ only by cancelling matter mode “CDM = baryon + (CDM-baryon)” Constrain B = ratio of matter isocurvature to adiabatic; ns = power law spectrum tiltNo evidence, though still allowed.Not very well constrained. Gordon, Lewis:astro-ph/0212248

22. General isocurvature models • General mixtures currently poorly constrained Bucher et al: astro-ph/0401417

23. Primordial Gravitational Waves(tensor modes) • Well motivated by some inflationary models- Amplitude measures inflaton potential at horizon crossing- distinguish models of inflation • Observation would rule out other models- ekpyrotic scenario predicts exponentially small amplitude - small also in many models of inflation, esp. two field e.g. curvaton • Weakly constrained from CMB temperature anisotropy - cosmic variance limited to 10% - degenerate with other parameters (tilt, reionization, etc) Look at CMB polarization: ‘B-mode’ smoking gun

24. CMB Polarization Generated during last scattering (and reionization) by Thomson scattering of anisotropic photon distribution Hu astro-ph/9706147 Observe Stokes’ parameters - - Q U Rank 2 trace free symmetric tensor

25. E and B polarization “gradient” modesE polarization “curl” modes B polarization e.g.

26. Why polarization? • E polarization from scalar, vector and tensor modes (constrain parameters, break degeneracies, reionization) • B polarization only from vector and tensor modes (curl grad = 0) + non-linear scalars ‘smoking gun’ for primordial vector and tensor modes

27. CMB polarization from primordial gravitational waves (tensors) Tensor B-mode Tensor E-mode Adiabatic E-mode Weak lensing Planck noise(optimistic) • Amplitude of tensors unknown • Clear signal from B modes – there are none from scalar modes • Tensor B is always small compared to adiabatic E Seljak, Zaldarriaga: astro-ph/9609169

28. Regular vector mode: ‘neutrino vorticity mode’ logical possibility but unmotivated (contrived). Spectrum unknown. B-modes Similar to gravitational wave spectrum on large scales: distinctive small scale Lewis: astro-ph/0403583

29. Other B-modes? • Topological defects Seljak, Pen, Turok: astro-ph/9704231 Non-Gaussian signals global defects: 10% local strings frombrane inflation: r=0.1 lensing Pogosian, Tye, Wasserman, Wyman: hep-th/0304188

30. Primordial inhomogeneous magnetic fields- Lorentz force on Baryons - Anisotropic stress sources vector and tensor metric perturbations e.g. Inhomogeneous field B = 3x10-9 G, spectral index n = -2.9 Tensor amplitude uncertain. Non-Gaussian signal. tensor vector Lewis, astro-ph/0406096.Subramanian, Seshadri, Barrow, astro-ph/0303014 Observable amplitudes probably already ruled out by cluster field observations Banerjee and Jedamzik: astro-ph/0410032

31. Complications • E/B mixing • Lensing of the CMB

32. Partial sky E/B separation problem Pure E: Pure B: Inversion non-trivial with boundaries Likely important as reionization signal same scale as galactic cut Use set of E/B/mixed harmonics that are orthogonal and complete over the observed section of the sphere. Project onto the `pure’ B modes to extract B. (Nearly) pure B modes do existLewis, Challinor, Turok astro-ph/0106536

33. Underlying B-modes Part-sky mix with scalar E Observation Separation method Recovered B modes‘map of gravity waves’ Lewis: astro-ph/0305545

34. Weak lensing of the CMB Last scattering surface Inhomogeneous universe - photons deflected Observer

35. Lensing potential and deflection angles LensPix sky simulation code: http://cosmologist.info/lenspix Lensing effect can be largely subtracted if only scalar modes + lensing present, but approximate and complicated (especially posterior statistics). Hirata, Seljak: astro-ph/0306354, Okamoto, Hu: astro-ph/0301031

36. Lensed CMB power spectra Few % on temperature 10% on TE/EE polarization New lensed BB signal How to calculate it accurately?

37. Series expansion method? Doesn’t converge (though works surprisingly well given this plot!)

38. Accurate lensed Cl calculation: correlation function method Need non-perturbative term; account for sky curvatureChallinor and Lewis 2005

39. Comparison with lowest order harmonic and flat results

40. Planck (2007+) parameter constraint simulation(neglect non-Gaussianity of lensed field; BB noise dominated so no effect on parameters) Important effect, but using lensed CMB power spectrum gets ‘right’ answer LensPix lensed sky simulation code:http://cosmologist.info/lenspix Lewis 2005

41. Conclusions • CMB contains lots of useful information!- primordial perturbations + well understood physics (cosmological parameters) • Precision cosmology- sampling methods used to constrain many parameters with full posterior distribution • Currently no evidence for any deviations from standard near scale-invariant purely adiabatic primordial spectrum • Large scale B-mode polarization from primordial gravitational waves: - energy scale of inflation - rule out most ekpyrotic and pure curvaton/ inhomogeneous reheating models and others • Small scale B-modes - Strong signal from any vector vorticity modes, strong magnetic fields, topological defects • Weak lensing of CMB :- B-modes potentially confuse primordial signals- Using lensed CMB power spectra good enough for precision parameter estimation with Planck • Foregrounds, systematics, etc, may make things much more complicated!

42. http://CosmoCoffee.info arXiv paper discussion and comments