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Observational constraints on primordial perturbations Antony Lewis CITA, Toronto http://cosmologist.info

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Primordial fluid at redshift < 10 9 Photons Nearly massless neutrinos Free-streaming (no scattering) after neutrino decoupling at z ~ 10 9 Baryons tightly coupled to photons by Thomson scattering Dark Matter Assume cold. Coupled only via gravity. Dark energy probably negligible early on Perturbations O(10 -5 ) => linear evolution Scalar, vector, tensor modes evolve independently Each Fourier k mode evolves independently

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General perturbation Scalar Adiabatic (observed) Matter density Cancelling matter density (unobservable) Neutrino density (contrived) Neutrino velocity (very contrived) Vector Neutrino vorticity (very contrived) Tensor Gravitational waves + 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… General regular linear primordial perturbation

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Irregular (decaying) modes Generally ~ a -1, a -2 or a -1/2 E.g. decaying vector modes unobservable at late times unless ridiculously large early on Adiabatic decay ~ a -1/2 after neutrino decoupling. possibly observable if generated around or after neutrino decoupling Otherwise have to be very large (non-linear?) at early times Amendola, Finelli: astro-ph/0411273

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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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Constraints from data Can compute P( {ө} | data) using e.g. assumption of Gaussianity of CMB field and priors on parameters Often want marginalized constraints. e.g. BUT: Large n-integrals very hard to compute! If we instead sample from P( {ө} | data) then it is easy: Use Markov Chain Monte Carlo to sample

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MCMC sampling for parameter estimation Number density of samples proportional to probability density At its best scales linearly with number of parameters (as opposed to exponentially for brute integration) For CMB: P( {ө} | data) ~ P(C l (ө)|data) Theoretical C l numerically computed using linearised GR + Boltzmann equations (CAMB) CosmoMC code at http://cosmologist.info/cosmomc Lewis, Bridle: astro-ph/0205436http://cosmologist.info/cosmomc

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Bridle, Lewis, Weller, Efstathiou: astro-ph/0302306 Adiabatic modes What is the primordial power spectrum? Reconstruct in bins by sampling posterior using MCMC with current data On most scales P(k) ~ 2.3 x 10 -9 Close to scale invariant

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WMAP TT power spectrum at low l data from http://lambda.gsfc.nasa.gov/http://lambda.gsfc.nasa.gov/ compared to theoretical power law model (mean over realizations)

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Low quadrupole Indication of less power on very large scales? Any physical model cannot give sharper cut in power than a step function with zero power for k< k c k cut model favoured by data, but only by ~1 sigma No physical model will be favoured by the data by any more than this e.g. Contaldi et al: astro-ph/0303636 Allowing for foreground uncertainties etc, evidence is even weaker 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 Constrain B = ratio of matter isocurvature to adiabatic No 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 Polarization can break degeneracies Bucher et al. astro-ph/0012141

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The future: CMB Polarization Stokes Parameters - - QU Q -Q, U -U under 90 degree rotation Spin-2 field Q + i U or Rank 2 trace free symmetric tensor θ sqrt(Q 2 + U 2 ) θ = ½ tan -1 U/Q

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E and B polarization Trace free gradient: E polarization Curl: B polarization e.g.

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

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Primordial Gravitational Waves 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 - significant power only at l<100, 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 from primordial gravitational waves (tensors) Adiabatic E-mode Tensor B-mode Tensor E-mode Planck noise (optimistic) Weak lensing 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. Lewis: astro-ph/0403583 Similar to gravitational wave spectrum on large scales: distinctive small scale B-modes

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Pogosian, Tye, Wasserman, Wyman: hep-th/0304188 Topological defects Seljak, Pen, Turok: astro-ph/9704231 10% local strings from brane inflation: lensing r=0.1 global defects: Other B-modes? Non-Gaussian signals

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Conclusions Currently only very weak evidence for any deviations from standard near scale-invariant purely adiabatic primordial spectrum Precision E polarization - Much improved constraints on isocurvature modes Large scale Gaussian B-mode CMB 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, lensing, etc)

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http://CosmoCoffee.info arXiv paper discussion and comments

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Cosmic Microwave Background Theory Antony Lewis CITA, University of Toronto

Cosmic Microwave Background Theory Antony Lewis CITA, University of Toronto

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