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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

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is the universe homogeneous and isotropic


Is the Universe homogeneous and isotropic?

Marc Kamionkowski


Tsvi-fest, 17 December 2009

what you re about to hear
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 spotsUniverse is flat

(MK, Spergel, Sugiyama, 1994)


Density field:

  • fractional density perturbation:
  • Power spectrum P(k):
  • Inflation predicts
  • With
  • And








inflationary gravitational waves and cmb polarization
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
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):




next steps
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
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
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
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,




how to measure g lm
How to measure gLM

Lots of equations…..

iii rotation of cmb polarization lue wang mk 1999 mk 2008 gluscevic mk cooray 2009
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
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
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
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
  • 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)



explaining the power asymmetry
Explaining the power asymmetry
  • Postulate long-wavelength curvaton fluctuation Δσ
  • Keep inflaton smooth

This is now the


model parameters
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
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


Upper limitfrom CMBhomogeneityconstraint

Lower limitfrom fnl<100


new developments
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
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

  • 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?