Primordial perturbations and precision cosmology from the Cosmic Microwave Background

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Primordial perturbations and precision cosmology
from the Cosmic Microwave Background

• Antony Lewis
• CITA, University of Toronto

http//cosmologist.info
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Outline

• Introduction and current data
• Parameter estimation
• General primordial perturbations
• Current constraints
• CMB Polarization E and B modes
• Future constraints
• Complications E/B mixing CMB lensing

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Theory
Observations
Source NASA/WMAP Science Team
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Evolution of the universe
Opaque
Transparent
Hu White, Sci. Am., 290 44 (2004)
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Perturbation evolutionCMB monopole source till
380 000 yrs (last scattering), linear in
conformal timescale invariant primordial
adiabatic scalar spectrum
photon/baryon plasma dark matter, neutrinos
Characteristic scales sound wave travel
distance diffusion damping length
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CMB temperature power spectrumPrimordial
perturbations later physics
diffusion damping
acoustic oscillations
primordial powerspectrum
Hu White, Sci. Am., 290 44 (2004)
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(almost) uniform 2.726K blackbody
Dipole (local motion)
O(10-5) perturbations (galaxy)
Observations the microwave sky today
Source NASA/WMAP Science Team
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CMB observation history
numerous balloon and ground based observations
Source NASA/WMAP Science Team
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WMAP other CMB data
Redhead et al astro-ph/0402359
Galaxy surveys, galaxy weak lensing, Hubble
Space Telescope, supernovae, etc...
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What can we learn from the CMB?

• Initial conditionsWhat types of perturbations,
  power spectra, distribution function (Gaussian?)
  gt learn about inflation or alternatives.
• What and how much stuffMatter densities (Ob,
  Ocdm) neutrino mass
• Geometry and topologyglobal curvature OK of
  universe topology
• EvolutionExpansion rate as function of time
  reionization- Hubble constant H0 dark energy
  evolution w pressure/density
• AstrophysicsS-Z effect (clusters), foregrounds,
  etc.

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CMB Cl and statistics

• Theory Linear physics Gaussian primordial
  fluctuations

Theory prediction
- variance (average over all possible sky
realizations)
linearized GR Boltzmann equations
Initial conditions cosmological parameters
Cl
CAMB http//camb.info
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• Observations only one sky

Use estimator for variance
Cosmic Variance
WMAP low l
Assume alm gaussian
- inverse gamma distribution( noise, sky cut,
etc).
l
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Parameter Estimation

• Can compute P( ? data) P( Cl(?) clobs)
  
• Often want marginalized constraints. e.g.

• BUT Large n integrals very hard to compute!
• If we instead sample from P( ? data) then it
  is easy

Can easily learn everything we need from set of
samples
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Markov Chain Monte Carlo sampling

• Metropolis-Hastings algorithm
• Number density of samples proportional to
  probability density
• At its best scales linearly with number of
  parameters(as opposed to exponentially for brute
  integration)

CosmoMC code at http//cosmologist.info/cosmomc
Lewis, Bridle astro-ph/0205436
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CMB data alonecolor optical depth
Samples in6D parameterspace
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Plot number density of samples as function of
parameters
e.g. CMBgalaxy lensing BBN prior
Contaldi, Hoekstra, Lewis astro-ph/0302435
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Primordial Perturbationsfluid at redshift lt 109

• Photons
• Nearly massless neutrinosFree-streaming (no
  scattering) after neutrino decoupling at z 109
• Baryons electronstightly coupled to photons by
  Thomson scattering
• Dark MatterAssume cold. Coupled only via
  gravity.
• Dark energyprobably negligible early on

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Perturbations O(10-5)

• Linear evolution
• Fourier k mode evolves independently
• Scalar, vector, tensor modes evolve
  independently
• Various linearly independent solutions

Scalar modes Density perturbations, potential
flows
Vector modes Vortical perturbations
Tensor modes Anisotropic space distortions
gravitational waves
http//www.astro.cf.ac.uk/schools/6thFC2002/GravWa
ves/sld009.htm
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General regular linear primordial perturbation
-isocurvature-
irregular modes, neutrino n-pole modes,
n-Tensor modes Rebhan and Schwarz
gr-qc/9403032 other possible components, e.g.
defects, magnetic fields, exotic stuff
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Adiabatic modesWhat is the primordial power
spectrum?
Parameters are primordial power spectrum bins
P(ki) cosmological parameters
On most scales P(k) 2.3 x 10-9 Close to scale
invariant
Bridle, Lewis, Weller, Efstathiou
astro-ph/0302306
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Matter isocurvature modes

• Possible in two-field inflation models, e.g.
  curvaton scenario
• Curvaton model gives adiabatic correlated CDM
  or baryon isocurvature, no tensors
• CDM, baryon isocurvature indistinguishable
  differ only by cancelling matter mode

CDM baryon (CDM-baryon)
Constrain B ratio of matter isocurvature to
adiabatic ns power law spectrum tiltNo
evidence, though still allowed.Not very well
constrained. Gordon, Lewis astro-ph/0212248
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General isocurvature models

• General mixtures currently poorly constrained

Bucher et al astro-ph/0401417
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Primordial Gravitational Waves(tensor modes)

• Well motivated by some inflationary models-
  Amplitude measures inflaton potential at horizon
  crossing- distinguish models of inflation
• Observation would rule out other models -
  ekpyrotic scenario predicts exponentially small
  amplitude - small also in many models of
  inflation, esp. two field e.g. curvaton
• Weakly constrained from CMB temperature
  anisotropy

- cosmic variance limited to 10 - degenerate
with other parameters (tilt, reionization, etc)
Look at CMB polarization B-mode smoking gun
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CMB Polarization
Generated during last scattering (and
reionization) by Thomson scattering of
anisotropic photon distribution
Hu astro-ph/9706147
Observe Stokes parameters
-
-
Q
U
Rank 2 trace free symmetric tensor
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E and B polarization
gradient modesE polarization
curl modes B polarization
e.g.
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Why polarization?

• E polarization from scalar, vector and tensor
  modes (constrain parameters, break
  degeneracies, reionization)
• B polarization only from vector and tensor modes
  (curl grad 0) non-linear scalars

smoking gun for primordial vector and tensor
modes
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CMB polarization from primordial gravitational
waves (tensors)
Tensor B-mode
Tensor E-mode
Adiabatic E-mode
Weak lensing
Planck noise(optimistic)

• Amplitude of tensors unknown
• Clear signal from B modes there are none from
  scalar modes
• Tensor B is always small compared to adiabatic E

Seljak, Zaldarriaga astro-ph/9609169
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Regular vector mode neutrino vorticity mode
logical possibility but unmotivated (contrived).
Spectrum unknown.
B-modes
Similar to gravitational wave spectrum on large
scales distinctive small scale
Lewis astro-ph/0403583
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Other B-modes?

• Topological defects

Seljak, Pen, Turok astro-ph/9704231
Non-Gaussian signals
global defects
10 local strings frombrane inflation
r0.1
lensing
Pogosian, Tye, Wasserman, Wyman hep-th/0304188
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• Primordial inhomogeneous magnetic fields -
  Lorentz force on Baryons - Anisotropic stress
  sources vector and tensor metric perturbations

e.g. Inhomogeneous field B 3x10-9 G, spectral
index n -2.9
Tensor amplitude uncertain. Non-Gaussian
signal.
tensor
vector
Lewis, astro-ph/0406096. Subramanian, Seshadri,
Barrow, astro-ph/0303014
Observable amplitudes probably already ruled out
by cluster field observations
Banerjee and Jedamzik astro-ph/0410032
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Complications

• E/B mixing
• Lensing of the CMB

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Partial sky E/B separation problem
Pure E
Pure B
Inversion non-trivial with boundaries
Likely important as reionization signal same
scale as galactic cut
Use set of E/B/mixed harmonics that are
orthogonal and complete over the observed
section of the sphere. Project onto the pure B
modes to extract B. (Nearly) pure B modes do
exist Lewis, Challinor, Turok astro-ph/0106536
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Underlying B-modes
Part-sky mix with scalar E
Observation
Separation method
Recovered B modesmap of gravity waves
Lewis astro-ph/0305545
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Weak lensing of the CMB
Last scattering surface
Inhomogeneous universe - photons deflected
Observer
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Lensing potential and deflection angles
LensPix sky simulation code http//cosmologist.in
fo/lenspix
Lensing effect can be largely subtracted if only
scalar modes lensing present, but approximate
and complicated (especially posterior
statistics). Hirata, Seljak astro-ph/0306354,
Okamoto, Hu astro-ph/0301031
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Lensed CMB power spectra
Few on temperature 10 on TE/EE
polarization New lensed BB signal
How to calculate it accurately?
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Series expansion method?
Doesnt converge (though works surprisingly well
given this plot!)
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Accurate lensed Cl calculation correlation
function method
Need non-perturbative term account for sky
curvature Challinor and Lewis 2005
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Comparison with lowest order harmonic and flat
results
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Planck (2007) parameter constraint simulation
(neglect non-Gaussianity of lensed field BB
noise dominated so no effect on parameters)
Important effect, but using lensed CMB power
spectrum gets right answer
Lewis 2005
LensPix lensed sky simulation codehttp//cosmolog
ist.info/lenspix
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Conclusions

• CMB contains lots of useful information!-
  primordial perturbations well understood
  physics (cosmological parameters)
• Precision cosmology- sampling methods used to
  constrain many parameters with full posterior
  distribution
• Currently no evidence for any deviations from
  standard near scale-invariant purely adiabatic
  primordial spectrum
• Large scale B-mode polarization from primordial
  gravitational waves - energy scale of
  inflation - rule out most ekpyrotic and pure
  curvaton/ inhomogeneous reheating models and
  others
• Small scale B-modes - Strong signal from any
  vector vorticity modes, strong magnetic fields,
  topological defects
• Weak lensing of CMB - B-modes potentially
  confuse primordial signals- Using lensed CMB
  power spectra good enough for precision parameter
  estimation with Planck
• Foregrounds, systematics, etc, may make things
  much more complicated!

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arXiv paper discussion and comments