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New CMB (and other) Tests of Inflation, Dark Energy, and other novel physics
Marc Kamionkowski(Caltech)
Johns Hopkins, 23 May 2010
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What you’re about to hear
• Review of standard inflationary scenario– Where we are now– The current paths forward
• Some new CMB tests of inflation (statistical isotropy)
• An explanation for a possible anomaly• Quintessence and cosmological birefringence
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Isotropy problem: Why is the Universe so smooth?
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I. Inflation:
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The mechanism: Vacuum energyassociated with new ultra-high-energyphysics (e.g., grand unification, strings,supersymmetry, extra dimensions….)
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Inflation prediction #1:The Universe is flat
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The Geometry of the Universe
Warped spacetime acts as lens:
“flat” “open” “closed”(MK, Spergel, Sugiyama 1994)
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Map of CMB (Boomerang 2000)
Sizes of hot/cold spotsUniverse is flat
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More quantitatively
wavenumber l~1/θ
Four
ier a
mpl
itude
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Inflation prediction #2: Primordialdensity perturbations
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Inflation predicts matter power spectrum
with
i.e.,
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ns=1ns<1
ns>1
P(k)
k
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WMAP:
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WHATNEXT???
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INFLATION
GEOMETRY SMOOTHNESS STRUCTUREFORMATION
What is Einfl?
STOCHASTIC GRAVITATIONAL WAVEBACKGROUND with amplitude Einfl
2
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transparentopaque
Transparent to gravitational waves
10-38 sec
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Detection of gravitational waves with 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 (Slosar,Hirata et al.)): |fnl|<100
T/T
Gaussian
Not gaussian
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Inflation doing very well
• Location of first acoustic peak; flat Universe• Nearly scale-invariant spectrum• Adiabatic perturbations• Consistent with Gaussian
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Next steps
• Test whether ns differs from 1• Seek inflationary gravitational-wave
background with CMB polarization either from space, ground, or balloon (cf., Jaffe, MK, Wang 2000; SPIDER, Keck Array, CLASS, PIPER, Planck, CMBPol)
• Seek gravitational waves directly with BBO/DECIGO (e.g., Smith, Cooray, MK, 2006,2008)
• 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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To test….
• Require family of models that violate statistical isotropy and/or homogeneity, with departure from SI/SH parametrized by quantity that can be dialed to zero
• Develop estimators that measure SI/SH-violating parameters from observables
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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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Example: An inflationary model(Ackerman, Carroll, Wise, 2007)
• Spontaneous breaking of Lorentz symmetry during inflation produces nonzero vector field; 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…..e.g.,
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Smallest detectable quadrupole anisotropy
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Can also look with galaxy surveys (Ando,MK, PRL 2008)
• Probe on distance scales ~10-100 Mpc, where δ~1, and evolution of density perturbations becomes nonlinear
• Anisotropy in primordial power may get altered• Have shown that amplitude of primordial power
quadrupole suppressed, but by <7%, in quasilinear regime
• Pullen-Hirata have now found (with SDSS) strong constraints to power quadrupole
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Other weird inflation: bumps in the inflaton potential (Pahud, MK, Liddle 2008)
• Suppose inflaton potential:
WMAP:
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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 WMAP1 and WMAP3
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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 may get variation in P(k) across Universe
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Problem:
• If ϕ varies, then V(ϕ) varies large-scale density fluctuation, which is constrained to be very small by CMB quadrupole/octupole (Erickcek, MK, Carroll, arXiv:0806.0377; Erickcek, Carroll, MK, arXiv:0808.1570)
• Real problem: 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: 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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More recent development!
• 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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III. Cosmological Birefringence(Lue, Wang, MK 1999; MK 2008; Gluscevic, MK, Cooray, 2009; MK 2010)
•Is physics responsible for inflation or cosmic acceleration 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 quintessence field Φ(t) couples to electromagnetism through:
WMAP/BOOMERanG/QUaD searches: α<few degrees (Feng et al., astro-ph/0601095; Komatsu et al. 2008; Wu et al. 2008)
Time evolution of Φ(t) leads to rotation, by angle α, of CMB polarization as photons propagate from CMB surface of last scatter (Carroll, Field, Jackiw 1998)
Rotation induces EB cross-correlation with same shape as original EE power spectrum (Lue, Wang, MK 1999)
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How to De-Rotate the CMB Polarization (MK, 2008; Gluscevic, MK, Cooray 2009; Yadav et al. 2009)
• But what if rotation angle varies from one point on sky to another?? (e.g., Pospelov and Ritz 2008; Caldwell et al., in preparation)
• Then observed polarization has nothing to do with primordial polarization!!!
• 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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Magic? Get more out than you put in?
• Measure Stokes parameters Qobs and Uobs at each point on sky
• Analysis gives rotation angle α and Qprim and Uprim at each point on sky
• What’s going on?
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Cosmological Birefringence with Radio Sources (MK 2010)
If no CB, then on average, polarizations and position angles of a large number of sources should be 90 deg
If there is CB, there should be amean offset
Data from 100s of sources: rotation < few degrees
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Spatially-varying rotation
• If rotation varies with position on sky:
• Can measure (MK 2010)
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• But even simpler analysis is constraining; variance in α from ~10 sources at z>2 is <few degrees
The best current constraint!
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But can do better with high-resolution intensity-polarization maps (Leahy 1997; Wardle, Pearly, Cohen 1997)
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And even better (MK 2010)
• Use E/B decomposition for polarization• α = (EB/EE)/2 = (IB/IE)/2
Uses full information from polarization-intensity and polarization-polarization correlations to search for rotation
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Finally, cosmological neutrino birefringence! (Ando, MK, Mocioiu 2009)
• What if we have
???
Leads to MSW-like effects in vacuum; novel, and possibly detectable, effects in atmospheric neutrinos and ultra-high-energy neutrinos
• E.g., M* up to 106 GeV may be accessible with UHE neutrinos if DE-induced mixing is in
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Conclusions
• Will soon have new tests of inflation (B modes; non-Gaussianity, etc.) with forthcoming CMB experiments
• But there may be more we can do with CMB, extragalactic sources, neutrinos, etc. to learn about inflation and dark enery
• Implications of anomalies should be explored---window to new physics?
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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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What more?
• Required curvaton “supermode” probably too big to be QM produced---may have to due with curvaton web (Mukhanov-Linde)? Or pre-inflationary remnant?
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Spatial Distribution of the Curvaton Field
0
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The origin of the CMB
Formed 380,000 yrsafter Big Bang, whenT~eV and hydrogenforms
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“Open”(Less matter)
“Flat”(critical density)
“Closed”(more matter)
Cosmological geometry: The shape of spacetime General relativity: Matter warps spacetime
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• We provide straightforward recipe for measuring gLM’s (and evaluating errors) from CMB data• Are minimum-variance estimators:
most sensitive possible
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Resolution:
• Actually, are infinite family of α, Qprim and Uprim
consistent with given Qobs and Uobs
• Analysis assumes primordial pattern is Gaussian and finds α, Qprim and Uprim most consistent with that assumption
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So far….
• There is hemispherical power asymmetry in WMAP
• Cannot be accounted for by single-field slow-roll inflation
• Can be explained by curvaton with large-amplitude long-wavelength fluctuation
• Model constrained by homogeneity predicts fnl>50