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Observational Constraints on Primordial Perturbations in Cosmology

This article discusses the observational constraints on primordial perturbations in the early universe, covering topics such as primordial fluid, dark matter, scalar-vector-tensor modes, irregular modes, constraints from data analysis, matter isocurvature modes, and primordial gravitational waves. It explores the advancements in observational techniques, such as sampling posterior using Markov Chain Monte Carlo (MCMC), and the potential of future developments in CMB polarization studies to uncover valuable insights into the early universe.

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Observational Constraints on Primordial Perturbations in Cosmology

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

  2. Primordial fluid at redshift < 109 • Photons • Nearly massless neutrinosFree-streaming (no scattering) after neutrino decoupling at z ~ 109 • Baryonstightly coupled to photons by Thomson scattering • Dark MatterAssume cold. Coupled only via gravity. • Dark energyprobably negligible early on • Perturbations O(10-5) => linear evolution • Scalar, vector, tensor modes evolve independently • Each Fourier k mode evolves independently

  3. General regular linear primordial perturbation + 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…

  4. 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

  5. WMAP + other CMB data Redhead et al: astro-ph/0402359 + Galaxy surveys, galaxy weak lensing, Hubble Space Telescope, supernovae, etc...

  6. 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

  7. 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(Cl(ө)|data)Theoretical Cl numerically computed using linearised GR + Boltzmann equations(CAMB) CosmoMC code athttp://cosmologist.info/cosmomcLewis, Bridle:astro-ph/0205436

  8. Adiabatic modesWhat 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 Bridle, Lewis, Weller, Efstathiou: astro-ph/0302306

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

  10. Low quadrupoleIndication 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< kc • k cut model favoured by data, but only by ~1 sigma • No physical model will be favoured by the data by any more than thise.g. Contaldi et al:astro-ph/0303636 • Allowing for foreground uncertainties etc, evidence is even weaker astro-ph/0302306

  11. 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 adiabaticNo evidence, though still allowed.Not very well constrained. Gordon, Lewis:astro-ph/0212248

  12. General isocurvature models • General mixtures currently poorly constrained Bucher et al: astro-ph/0401417 Polarization can break degeneracies Bucher et al. astro-ph/0012141

  13. The future: CMB PolarizationStokes’ Parameters - - Q U Q → -Q, U → -U under 90 degree rotation Spin-2 field Q + i Uor Rank 2 trace free symmetric tensor θ θ = ½ tan-1 U/Q sqrt(Q2 + U2)

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

  15. 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

  16. 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

  17. 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

  18. 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

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

  20. 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)

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

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