Observational constraints on primordial perturbations

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