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Is the Universe homogeneous and isotropic?
Marc Kamionkowski(Caltech)
Tsvi-fest, 17 December 2009
Statistically
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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)
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Inflaton potential
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Map of CMB
Sizes of hot/cold spotsUniverse is flat (MK, Spergel, Sugiyama, 1994)
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Primordial density perturbations
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Density field:
fractional density perturbation:
Power spectrum P(k):
Inflation predicts
With
And
i.e.,
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ns=1ns<1
ns>1
P(k)
k
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Inflationary gravitational waves and CMB polarization
Temperature map:
Polarization Map:
Density perturbations have no handedness”so they cannot produce a polarization with a curlGravitational waves do have a handedness, so theycan (and do) produce a curl
“E modes”“B modes”
(MK, Kosowsky, Stebbins 1996; Seljak, Zaldarriaga 1996)
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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
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Current constraints (WMAP5,SDSS): |fnl|<100
T/T
Gaussian
Not gaussian
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Next steps
• Test whether ns differs from 1• Seek inflationary gravitational-wave
background• Search for non-Gaussianity
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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!!
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Statistical isotropy
• Consider models with
and
• Most generally,
with L=2,4,6,…
(Note: cannot get dipole from SI violation!!)
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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,
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Statisticallyisotropic
A powerquadrupole
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How to measure gLM
Lots of equations…..
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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
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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)
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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
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IV. Hemispherical Power Asymmetry from Inflation(Erickcek, MK, Carroll, 2008; Erickek, Carroll, MK, 2008; Erickcek, Hirata, MK,
2009)
Eriksen et al. found >3σ evidence forpower asymmetry in WMAP
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Isotropic power
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A power dipole
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• Recall: Violation of statistical isotropy cannot produce power dipole.
• Must therefore be violation of statistical homogeneity
• …..need spatial modulation of power….
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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
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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)
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Solution• Add second scalar field (curvaton); energy
density generated by one and perturbations generated by other (or both by some combination)
Curvaton Inflaton
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Explaining the power asymmetry
• Postulate long-wavelength curvaton fluctuation Δσ
• Keep inflaton smooth
This is now the curvaton!
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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
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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
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Upper limitfrom CMBhomogeneityconstraint
Lower limitfrom fnl<100
50<fnl<100
12<fnl<100
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New Developments!
• SDSS quasar distribution/clustering restricts asymmetry to be small on smaller distance scales (Hirata 2009)
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• 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)
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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
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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?