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Analysing the CMB in a model-independent manner

Analysing the CMB in a model-independent manner. Syksy Räsänen University of Helsinki. JCAP08(2010)023, arXiv:1003.0810 (M. Vonlanthen, SR and R. Durrer). Model-dependence.

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Analysing the CMB in a model-independent manner

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  1. Analysing the CMBin a model-independent manner Syksy Räsänen University of Helsinki JCAP08(2010)023,arXiv:1003.0810 (M. Vonlanthen, SR and R. Durrer) Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  2. Model-dependence • Usually in CMB analysis, a specific model is assumed for both the early and the late universe, and their physics is not disentangled. • Limits on early parameters such as ωm and ns have an unquantified dependence on the late universe model. • On the other hand, constraints are quoted on parameters such as spatial curvature or H0, to which the CMB has no direct sensitivity. Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  3. Physics probed by the CMB • The observed CMB anisotropies depend on • 1) The pattern set at decoupling and • 2) The processing between decoupling and today. • The initial pattern is given by well understood atomic and gravitational physics at last scattering (and the seeds of structure). • Late evolution involves reionisation, as well as poorly understood physics of late universe (dark energy, modified gravity, non-linearities). • We keep 1) fixed, and remain agnostic about 2). Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  4. The CMB parameters • Keeping general relativity, atomic physics and CDM fixed, the decoupling pattern is set by • 1) the baryon density ωb, • 2) the CDM density ωc and, • 3) the primordial spectral index ns and amplitude A. • Late evolution changes • 1) the overall amplitude, • 2) the angular size, and • 3) the subhorizon pattern ⇒ Marginalise ⇒ Parametrise ⇒ Cut Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  5. Angular size • The angular size is given by DA = L/θ. • In the flat sky approximation, this reduces to . • Taking the Einstein-de Sitter model as comparison, we have , where . ⇒ ⇒ Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  6. Independence • With large scales excluded, the CMB is sensitive to spatial curvature and expansion history only via DA. • Assuming a FRW model, we have , which can be inverted to obtain . Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  7. Cutting large scales • Causal physics can change the correlation properties on subhorizon scales. • The effects (ISW, RS, SZ, lensing, ...) are model-dependent. • The physics at late times is unknown, so we drop low multipoles. • From FRW+linear models of reionisation and the ISW effect, we know that we should cut to at least l =20-40. • We do not take into account gravity waves, vectors or neutrino masses. Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  8. Varying the cut • Fitting ΛCDM to ACBAR and WMAP5, we get (τ = 0) • From lmin= 2 to lmin= 40, the errors on ωb and ωc grow by 28% and on ns by 57%, while the means shift by 1%, 4% and 1%. Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  9. A systematic shift • As lmin increases, ωb and ns go down, while ωc and ΩΛ go up. • In terms of the new error bars, the effect is less than 2σ, in terms of the old error bars, it is more than 5σ, at lmin= 100. Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  10. Large angle amplitude • The shift corresponds to increasing low multipole power: Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  11. Shifted results • We fix the cut at lmin= 40, corresponding to z ≾60. • The mean values change more than the error bars. • The angle θA = rs/DA is stable and determined to 0.3%. Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

  12. Summary • The values of ωb, ωc, ns and θA are determined by the CMB to a precision of 3%, 6%, 2% and 0.3%. • However, a systematic shift affects all parameters except θA. • The small-angle CMB sky prefers different values of ωb, ωc, ns than the full dataset. • It would be interesting to analyse BAO in the same model-independent spirit. Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 2010

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