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##### Is the Universe homogeneous and isotropic?

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**Statistically**Is the Universe homogeneous and isotropic? Marc Kamionkowski (Caltech) Tsvi-fest, 17 December 2009**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)**Map of CMB**Sizes of hot/cold spotsUniverse is flat (MK, Spergel, Sugiyama, 1994)**Density field:**• fractional density perturbation: • Power spectrum P(k): • Inflation predicts • With • And i.e.,**ns<1**P(k) ns=1 ns>1 k**Inflationary gravitational waves and CMB polarization**“E modes” “B modes” 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 (MK, Kosowsky, Stebbins 1996; Seljak, Zaldarriaga 1996)**And one final prediction: gaussianity**• Gravitational potential (e.g., Verde, Wang,Heavens, MK, 2000) with fNL<1 (e.g., Wang & MK, 2000) Forecast that fNL as small as ~5 detectable by forthcoming Planck satellite Gaussian field**Not gaussian**Current constraints (WMAP5,SDSS): |fnl|<100 Gaussian T/T**Next steps**• Test whether ns differs from 1 • Seek inflationary gravitational-wave background • Search for non-Gaussianity**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!!**Statistical isotropy**• Consider models withand • Most generally,with L=2,4,6,… (Note: cannot get dipole from SI violation!!)**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,**Statisticallyisotropic**Apowerquadrupole**How to measure gLM**Lots of equations…..**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**Rotation of CMB Polarization**• E.g., suppose electromagnetic energy density has additional term (depending on quintessence field Φ(t)): 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) WMAP/BOOMERanG/QUaD searches: α<few degrees**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**IV. Hemispherical Power Asymmetry from Inflation(Erickcek,**MK, Carroll, 2008; Erickek, Carroll, MK, 2008; Erickcek, Hirata, MK, 2009) Eriksenet al. found >3σ evidence forpower asymmetry in WMAP**Recall: Violation of statistical isotropy cannot produce**power dipole. • Must therefore be violation of statistical homogeneity • …..need spatial modulation of power….**Can it be due to a large-scale inflaton mode?**• P(k) ~ V3/2/V’, with V(ϕ) evaluated at valuewhen k exited horizon during inflation • If there is a large-scale fluctuation in ϕ, then might expect variation in P(k) across Universe**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)**Solution**• Add second scalar field (curvaton); energy density generated by one and perturbations generated by other (or both by some combination) Curvaton Inflaton**Explaining the power asymmetry**• Postulate long-wavelength curvaton fluctuation Δσ • Keep inflaton smooth This is now the curvaton!**Model parameters**• R=ρσ/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**Model prediction: non-Gaussianity**• Mapping from curvaton to density perturbation nonlinear • Predicts non-Gaussianity, with fnl = 5 ξ2 / (4R) • Current constraint fnl < 100 constrains R-ξ parameter space • Asymmetry A requires some nonzero fnl**50<fnl<100**Upper limitfrom CMBhomogeneityconstraint Lower limitfrom fnl<100 12<fnl<100**New Developments!**• SDSS quasar distribution/clustering restricts asymmetry to be small on smaller distance scales (Hirata 2009)**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)**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**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?