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Gaussianity, Flatness, Tilt, Running, and Gravity Waves: WMAP and Some Future Prospects

Gaussianity, Flatness, Tilt, Running, and Gravity Waves: WMAP and Some Future Prospects. Eiichiro Komatsu University of Texas at Austin July 11, 2007. Cosmology and Strings: 6 Numbers. Successful early-universe models must produce: The universe that is nearly flat, |  K |<O(0.02)

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Gaussianity, Flatness, Tilt, Running, and Gravity Waves: WMAP and Some Future Prospects

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  1. Gaussianity, Flatness, Tilt, Running, and Gravity Waves: WMAP and Some Future Prospects Eiichiro Komatsu University of Texas at Austin July 11, 2007

  2. Cosmology and Strings: 6 Numbers • Successful early-universe models must produce: • The universe that is nearly flat, |K|<O(0.02) • The primordial fluctuations that are • Nearly Gaussian, |fNL|<O(100) • Nearly scale invariant, |ns-1|<O(0.05), |dns/dlnk|<O(0.05) • Nearly adiabatic, |S/R|<O(0.2)

  3. Cosmology and Strings: 6 Numbers • A “generous” theory would make cosmologists very happy by producing detectable primordial gravity waves (r>0.01)… • But, this is not a requirement yet. • Currently, r<O(0.5)

  4. How Flat is our Universe? • The peak positions of CMB anisotropy measured by WMAP 3yr data gave: K = 1m = 0.3040 + 0.4067 CMB alone cannot constrain curvature.

  5. +H0 from HST +BAO from LRGs Flatness: WMAP+ • The current best combination is WMAP+BAO extracted from LRGs in SDSS. • CMB and BAO are absolute distance indicators. • SNs measure only relative distances. +SNs from “Gold” +SNs from SNLS +P(k) from SDSS +P(k) from 2dFGRS

  6. We Need Absolute Distance Indicators to Constrain K • The angular diameter distance DA(z) is related to the luminosity distance DL(z) by • DL(z)=(1+z)2 DA(z) • When curvature  is smaller than the comoving distance (z), DA(z) may be expanded in Taylor series as • DA(z) ~ (z)+ (z)/6, where (z)=c*int(dz/Hubble) • Therefore,  nearly cancels in a relative distance between objects that are not greatly separated. • Relative distances between supernovae are less sensitive to curvature. • Relative distances between CMB (at z=1090) and BAO (at z=0.35 for LRGs) are more sensitive to curvature.

  7. WMAP 3yr Results: 2% Flatness • WMAP3+HST: 0.048<K<0.020 (95%) • Note that the HST result, H0=728 km/s/Mpc, is also an absolute distance measurement, so it can be as good as BAO in terms of constraining curvature. However, the distance error from HST (8%) is bigger than the error from BAO (3%). A room for improvement. • WMAP3+SNs: 0.035<K<0.013 • WMAP3+BAO: 0.032<K<0.008 • This is, in a way, a test of inflation to 2% level.

  8. 0.1% Flatness in Future? • Planck CMB data + future BAO data at z=3 (from the planned galaxy surveys e.g., HETDEX, WFMOS, BOSS) would yield ~0.1% determination of flatness. • Knox, PRD 73, 023503 (2006) • Therefore, flatness would offer 0.1% test of inflation in 5-10 years.

  9. Gaussianity vs Flatness • So, we are generally happy that geometry of our observable Universe is flat. • Geometry of our Universe is consistent with being flat to ~2% accuracy at 95% CL. • What do we know about Gaussianity? • Let’s take a usual model, F=FL+fNLFL2 • FL~10-5 is the linear curvature perturbation in the matter era • WMAP 3yr: 54<fNL<114 (95% CL) • One can improve on this by ~15%, see Creminelli et al. • Therefore,  is consistent with being Gaussian to ~100(10-5)2/(10-5)=0.1%accuracy at 95% CL. • The Truth: Inflation is supported more by Gaussianity than by flatness.

  10. How Would fNL Modify PDF? • One-point PDF is not very useful for measuring primordial NG. We need something better: • Bispectrum: • 54<fNL<114 • Trispectrum: • N/A (yet) • Minkowski functionals: • 70<fNL<91

  11. Gaussianity vs Flatness: Future • Flatness will never beat Gaussianity. • In 5-10 years, we will know flatness to 0.1% level. • In 5-10 years, we will know Gaussianity to 0.01% level (fNL~10), or even to 0.005% level (fNL~5), at 95% CL. • However, a real potential in Gaussianity test is that we might detect something at this level (multi-field, curvaton, DBI, ghost cond., new ekpyrotic…) • Or, we might detect curvature first? • Is 0.1% curvature interesting/motivated?

  12. Confusion about fNL (1): Sign • What is fNL that is actually measured by WMAP? • When we expand  as =L+fNLL2,  is Bardeen’scurvature perturbation (metric space-space), H, in the matter dominated era. • Let’s get this stright:  is not Newtonian potential (metric time-time) • Newtonian potential is . (There is a minus sign!) • In the SW limit, temperature anisotropy is T/T=(1/3). • A positive fNL resultes in a negative skewness of T. • It is useful to remember that fNL positive = Temperature skewed negative (more cold spots) = Matter density skewed positive (more objects)

  13. Confusion about fNL (2): Primordial vs Matter Era • In terms of the primordial curvature perturbation in the comoving gauge, R, Bardeen’s curvature perturbation in the matter era is given by L=+(3/5)RL at the linear level (notice the plus sign). • Therefore, R=RL+(3/5)fNLRL2 • There is another popular quantity, =+R. (Bardeen, Steinhardt & Turner (1983); Notice the plus sign.) • =L+(3/5)fNLL2  R=RL(3/5)fNLRL2  R=RLfNLRL2  =L(3/5)fNLL2

  14. FAQ: Why Care About Matter Era? • A. Because that’s what we measure. • It is important to remember that fNL receives three contributions: • Non-linearity in inflaton fluctuations,  • Falk, Rangarajan & Srendnicki (1993) • Maldacena (2003) • Non-linearity in - relation • Salopek & Bond (1990; 1991) • Matarrese et al. (2nd order PT) • N papers; gradient-expansion papers • Non-linearity in T/T- relation • Pyne & Carroll (1996); Mollerach & Matarrese (1997)

  15. g=1 • f • in slow-roll  g(+mpl-1f) • g~O(1/) • f • in slow-roll  mpl-1g( +mpl-1f) • g=1/3 • f • for Sachs-Wolfe T/T~ gT(+f) T/T~gT[L+(f+gf+ggf)L2] fNL ~ f+ gf+ ggfin slow-roll Komatsu, astro-ph/0206039

  16. 3 Ways to Get Larger Non-Gaussianity from Early Universe fNL ~ f+ gf+ ggf • Break slow-roll: ff • Features in V() • Kofman, Blumenthal, Hodges & Primack (1991); Wang & Kamionkowski (2000); Komatsu et al. (2003); Chen, Easther & Lim (2007) • DBI inflation • Chen, Huang, Kachru & Shiu (2004) • Ekpyrotic model, old and new

  17. 3 Ways to Get Larger Non-Gaussianity from Early Universe fNL ~ f+ gf+ ggf 2. Amplify field interactions (without breaking scale invariance): f • Often done by non-canonical kinetic terms • Ghost inflation • Arkani-Hamed, Creminelli, Mukohyama & Zaldarriaga (2004) • DBI Inflation • Chen, Huang, Kachru & Shiu (2004)

  18. 3 Ways to Get Larger Non-Gaussianity from Early Universe fNL ~ f+ gf+ ggf 3. Suppress the perturbation conversion factor, gg • Generate curvature perturbations from isocurvature (entropy) fluctuations with an efficiency given by g. • Linde & Mukhanov (1997); Lyth & Wands (2002) • Curvaton predicts gcurvaton which can be arbitrarily small • Lyth, Ungarelli & Wands (2002) • New Ekpyrotic model?

  19. Confusion about fNL (3): Maldacena Effect • Maldacena’s celebrated non-Gaussianity paper (Maldacena 2003) uses the sign convention that is minus of that in Komatsu & Spergel (2001): • fNL(Maldacena) = fNL(Komatsu&Spergel) • The result: cosmologists and high-energy physicists have often been using different sign conventions. • It is always useful to ask ourselves, “do we get more cold spots in CMB for fNL>0?” • If yes, it’s Komatsu&Spergel convention. • If no, it’s Maldacena convention.

  20. Positive fNL = More Cold Spots Simulated temperature maps from fNL=0 fNL=100 fNL=5000 fNL=1000

  21. Gaussianity Tests: Future Prospects • The current status: fNL<102 (95%) from WMAP • Komatsu et al. (2003); Spergel et al. (2006); Creminelli et al. (2006) • Planck (temperature + polarization): fNL<6 (95%) • Yadav, Komatsu & Wandelt (2007) • High-z galaxy survey (e.g., ADEPT): fNL<7 (95%) • Sefusatti & Komatsu (2007) • CMB and LSS are independent. By combining these two constraints, we get fNL<4.5 (95%). This is currently the best constraint that we can possibly achieve in the foreseeable future (~10 years)

  22. Tilt, ns • A constraint from WMAP 3yr results: 0.074 < ns1 < 0.010 (95%) • Or, ns=0.9580.016 (68%) • 2.6 hint of ns<1. • However, it must be always remembered that this constraint assumes zero gravity waves, r=0. • “tensor-to-scalar ratio”, r = hGW2/2 • CMB power spectrum from GWs is proportional to r.

  23. nsr Degeneracy: ns=0.9580.120r

  24. Let’s Understand ns-r Degeneracy

  25. Model Power Spectra Scalar T Tensor T (prop to r) Scalar E Tensor E (prop to r) Tensor B (prop to r)

  26. ns: Tilting Spectrum ns>1: Need more power on large angular scales, more gravity waves

  27. ns: Tilting Spectrum ns<1: Need less power on large angular scales, less gravity waves

  28. ns: 3yr Highlight • When no gravity waves exist… • 1yr Result (WMAP only fit) • ns=0.990.04 • 3yr Result (WMAP only fit) • ns=0.9580.016 • Where did this dramatic improvement come from?

  29. ns- Degeneracy: Finally Broken 1 Year WMAP Parameter Degeneracy Line from Temperature Data Alone 1 Year WMAP + other CMB 3 Year WMAP Polarization Data Nailed Tau

  30. Polarization From Reionization • CMB was emitted at z~1100. • Some fraction of CMB was re-scattered in a reionized universe. • Photons scatterd away from our line of sight -> temperature damping • Photons scattered into our line of sight -> polarized light e- e- e- e- e- e- IONIZED z=1100, t～1 e- e- e- e- e- NEUTRAL First-star formation z～11, t～0.1 REIONIZED e- e- e- e- z=0

  31. Temperature Damping, and Polarization Generation e-2 “Reionization Bump” 2

  32. Running Index, dns/dlnk • Constraints from WMAP 3yr: • dns/dlnk = 0.0550.031 (w/o GWs) • dns/dlnk = 0.0850.043 (w GWs) • No strong evidence for scale dependent ns, yet. Note that slow-roll inflation models usually predict dns/dlnk~O(0.001). • We need to go beyond CMB to constrain this better: we need good measurements of P(k) at small scales. • E.g., when clustering data of Lyman-alpha clouds are included, dns/dlnk = 0.0150.012 (Slosar, McDonald & Seljak 2007; w/o GWs)

  33. Tilt and Running: Future • The future lies in the large-scale structure data. • CMB becomes unusable for precision cosmology at small spatial scales due to the Silk damping and secondary anisotropy. • CMB is limited to k~0.2 Mpc1 • The large-scale structure data can extend the spatial dynamic range by an order of magnitude, up to k~2 Mpc1. (10x better than CMB) • ns1 = O(0.001) and dns/dlnk = O(0.001) are within our reach (Takada, Komatsu & Futamase 2006)

  34. Primordial Gravity Waves • 3yr limits from WMAP only (95%): • r<0.65 (no running ns) • r<1.1 (with running ns) • The constraint is still dominated entirely by the temperature data. • With polarization data only, the constraint is r<2.2 (95%; with or without running)

  35. Primordial Gravity Waves: Future • B-mode polarization is the only way to go. • If CMB polarization can’t see it, no direct detection experiments (even BBO) will see it. • WMAP 3 years (2006): r < 2.2 (B-mode 95%) • WMAP 8 years (2009): r ~ 0.3 • WMAP 12 years (2013): r ~ 0.2 • Planck 1.5 years (launch 2008; results >2010): r ~ 0.05 • CMBPol/EPIC (20xx): r~0.01

  36. Pulsar timing CMB anisotropy WGW(k) LISA LIGO ~k-2 k Entered the horizon during MD RD Speaking of Primordial Gravity Waves… Usual Cartoon Picture

  37. Numerical Solution: Traditional Flat?

  38. Primordial Gravity Waves as a “Time Machine” in Minkowski spacetime in FRW spacetime Cosmological Redshift Therefore, the gravity wave spectrum is sensitive to the entire history of cosmic expansion after inflation.

  39. Watanabe & Komatsu (2006) Improving Calculations • Change in the background expansion law • Relativistic Degrees of Freedom: g*(T) • Radiation Content of the Early Universe • Neutrino physics • Neutrino Damping(J. Stewart 1972, Rebhan & Schwarz 1994, Weinberg 2004, Dicus & Repko 2005 ) • Collisionless Damping due to Anisotropic Stress

  40. Relativistic Degrees of Freedom: g*(T) In the early universe, WGW MD RD k RD g*(T) T, k

  41. Relativistic Degrees of Freedom: g*(T) Particle Contents: rest mass photon 0 neutrinos 0 e-, e+ .51 MeV muon 106 MeV pions 140 MeV gluon 0 u quark 5 MeV d quark 9 MeV s quark 110 MeV c quark 1.3 GeV tauon 1.8 GeV b quark 4.4 GeV W bosons 80 GeV Z boson 91 GeV Higgs boson 114 GeV t quark 174 GeV QGP P.T. ~180MeV e-,e+ ann. ~510keV SUSY ? ~1TeV

  42. Collisionless damping of tensor modes by anisotropic stress due to neutrino free-streaming Deviation from equilibrium distribution of n couples with GWs though gravity. Asymptotic solution: 35.5% less!

  43. Watanabe & Komatsu (2006) The Most Accurate Spectrum of GW in the Standard Model of Particle Physics Old Result

  44. Features in the Spectrum

  45. Cosmological Events and Sensitivities Cosmological events Detector sensitivities CMB ~10-18 Hz WMAPWGW0 < 10-11 PlanckWGW0 < 10-13 Pulsar timing ~10-8 Hz WGW0< 10-8 LISA ~10-2 Hz WGW0 < 10-11 DECIGO/BBO ~ 0.1 Hz WGW0 < ? Adv. LIGO ~102 Hz WGW0< 10-10 Matter-radiation equality e+e- annihilation Neutrino decoupling QGP phase transition ElectroWeak P.T. SUSY breaking Reheating (1014 GeV) GUT scale (1016 GeV) Planck scale (1019 GeV)

  46. Summary • WMAP is doing fine. • We continue to improve on the accuracy of 6 key parameters for cosmology vs strings: • Flatness • Gaussianity • Tilt • Running • Gravity waves • Adiabaticity (which I have not talked about) • FYI: Improved calculations of the primordial gravity wave spectrum. • A straight, featureless line is obsolete!

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