1. Is the Universe homogeneous and isotropic? Marc Kamionkowski (Caltech) Tsvi-fest, 17 December 2009 Statistically

2. What you’re about to hear I. Review of standard inflationary scenario – Where we are now – The current paths forward II. Some new CMB tests of inflation (statistical isotropy; Pullen & MK, 2007) III. CMB tests of parity violation (Lue, Wang, MK 1999; MK 2008; Gluscevic, Cooray, MK 2009) IV. A new anomaly and possible explanation (Erickcek, MK, Carroll, 2008; Erickcek, Hirata, MK 2009)

3. Inflaton potential

4. Map of CMB Sizes of hot/cold spots  Universe is flat (MK, Spergel, Sugiyama, 1994)

5. Primordial density perturbations

6. Density field: fractional density perturbation: Power spectrum P(k): Inflation predicts With And i.e.,

7. n s =1 n s <1 n s >1 P(k) k

8. Inflationary gravitational waves and CMB polarization Temperature map: Polarization Map: Density perturbations have no handedness” so they cannot produce a polarization with a curl Gravitational waves do have a handedness, so they can (and do) produce a curl “E modes” “B modes” (MK, Kosowsky, Stebbins 1996; Seljak, Zaldarriaga 1996)

10. And one final prediction: gaussianity Gravitational potential (e.g., Verde, Wang, Heavens, MK, 2000) with f NL <1 (e.g., Wang & MK, 2000) Forecast that f NL as small as ~5 detectable by forthcoming Planck satellite Gaussian field

11. Current constraints (WMAP5,SDSS): |f nl |<100  T/T Gaussian Not gaussian

12. Next steps Test whether n s differs from 1 Seek inflationary gravitational-wave background Search for non-Gaussianity

13. II. But is there more? (Pullen,MK, 2007) Inflation predicts Universe statistically isotropic and homogeneous Statistical isotropy: Power spectrum does not depend on direction; i.e., Statistical homogeneity: Power spectrum does not depend on position: These are predictions that can be tested!!

14. Statistical isotropy Consider models with and Most generally, with L=2,4,6,… (Note: cannot get dipole from SI violation!!)

15. E.g., An inflationary model (Ackerman, Carroll, Wise, 2007) Spontaneous breaking of Lorentz symmetry during inflation imprints quadrupole dependence of power on direction: Then, temperature fluctuations,

16. Statistically isotropic A power quadrupole

17. How to measure g LM Lots of equations…..

18. III. Rotation of CMB Polarization (Lue, Wang, MK 1999; MK 2008; Gluscevic, MK, Cooray, 2009) Electroweak interactions are parity violating, and inflation possibly due to unification of fundamental forces. Is physics responsible for primordial perturbations also parity violating? Polarization E and B modes have opposite parity; EB correlation therefore signature of parity violation

20. Rotation of CMB Polarization E.g., suppose electromagnetic energy density has additional term (depending on quintessence field Φ(t)): WMAP/BOOMERanG/QUaD searches: α<few degrees Evolution of Φ(t) leads to rotation, by angle α, of CMB polarization as photons propagate through Universe (Carroll, Field, Jackiw 1998) Rotation induces EB cross-correlation (Lue, Wang, MK 1999)

22. How to De-Rotate the CMB Polarization (MK, 2008; Gluscevic, MK, Cooray 2009) What if rotation angle varies from one point on sky to another?? Then observed polarization has nothing to do with primordial polarization!!! (This would be bad.) We develop technique (with mathematical similarities to SI tests) to measure rotation as function of angle, and thus to infer primordial polarization pattern

24. IV. Hemispherical Power Asymmetry from Inflation (Erickcek, MK, Carroll, 2008; Erickek, Carroll, MK, 2008; Erickcek, Hirata, MK, 2009) Eriksen et al. found >3σ evidence for power asymmetry in WMAP

25. Isotropic power

26. A power dipole

27. Recall: Violation of statistical isotropy cannot produce power dipole. Must therefore be violation of statistical homogeneity …..need spatial modulation of power….

28. Can it be due to a large-scale inflaton mode? P(k) ~ V 3/2 /V’, with V( ϕ ) evaluated at value when k exited horizon during inflation If there is a large-scale fluctuation in ϕ, then might expect variation in P(k) across Universe

29. Problem: If ϕ varies, then V( ϕ ) varies  induce large-scale density fluctuation Must be small (from CMB quadrupole/octupole)  Cannot get large-scale variation in P(k) without violating CMB homogeneity constraint by several orders of magnitude (Erickcek, MK, Carroll, arXiv:0806.0377; Erickcek, Carroll, MK, arXiv:0808.1570) Why? One scalar field (inflaton) controls density perturbations (which we want to vary across Universe) and the total density (which cannot vary)

30. Solution Add second scalar field (curvaton); energy density generated by one and perturbations generated by other (or both by some combination) Curvaton Inflaton

31. Explaining the power asymmetry Postulate long-wavelength curvaton fluctuation Δσ Keep inflaton smooth This is now the curvaton!

32. Model parameters R=ρ σ /ρ : fraction of total energy density from curvaton decay ξ : fraction of total power P(k) due to curvaton Amplitude Δσ and wavelength of long- wavelength fluctuation fixed by amplitude A of power asymmetry R-ξ parameter space constrained by CMB quadrupole/octupole constraint to homogeneity

33. Model prediction: non-Gaussianity Mapping from curvaton to density perturbation nonlinear Predicts non-Gaussianity, with f nl = 5 ξ 2 / (4R) Current constraint f nl < 100 constrains R-ξ parameter space Asymmetry A requires some nonzero f nl

34. Upper limit from CMB homogeneity constraint Lower limit from f nl <100 50<f nl <100 12<f nl <100

35. New Developments! SDSS quasar distribution/clustering restricts asymmetry to be small on smaller distance scales (Hirata 2009)

38. Concordance of small-scale SI with CMB anomaly possible (but just barely), but not easy: Requires isocurvature mode from curvaton decay (Erickcek, Hirata, MK 2009)

39. Evidence for SI violation still tentative, and may be “ugly” Still…… “Frequently nature does not knock with a very loud sound but rather a very soft whisper, and you have to be aware of subtle behavior which may in fact be a sign that there is interesting physics to be had.” ---Douglass Osheroff

40. Conclusions Inflation does extremely well with CMB/LSS data Will soon have new tests (B modes; non- Gaussianity, etc.) with forthcoming CMB experiments But there may be more we can do….. Implications of anomalies should be explored- --window to new physics?