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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

- 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)

Inflaton potential

Map of CMB

Sizes of hot/cold spotsUniverse is flat

(MK, Spergel, Sugiyama, 1994)

Primordialdensity perturbations

- Density field:
- fractional density perturbation:
- Power spectrum P(k):
- Inflation predicts
- With
- And

i.e.,

ns<1

P(k)

ns=1

ns>1

k

“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)

- 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

- Test whether ns differs from 1
- Seek inflationary gravitational-wave background
- Search for non-Gaussianity

- 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!!

- Consider models withand
- Most generally,with L=2,4,6,… (Note: cannot get dipole from SI violation!!)

- Spontaneous breaking of Lorentz symmetry during inflation imprints quadrupole dependence of power on direction:
Then, temperature fluctuations,

Statisticallyisotropic

Apowerquadrupole

Lots of equations…..

- 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

- 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

- 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….

- 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

- 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)

- Add second scalar field (curvaton); energy density generated by one and perturbations generated by other (or both by some combination)

Curvaton

Inflaton

- Postulate long-wavelength curvaton fluctuation Δσ
- Keep inflaton smooth

This is now the

curvaton!

- 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

- 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

- 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)

“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

- 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?