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

Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 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 ω m and n s have an unquantified dependence on the late universe model.  On the other hand, constraints are quoted on parameters such as spatial curvature or H 0, to which the CMB has no direct sensitivity.  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 ω m and n s have an unquantified dependence on the late universe model.  On the other hand, constraints are quoted on parameters such as spatial curvature or H 0, to which the CMB has no direct sensitivity.

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

Confronting theory with observations workshop, NBIA, Copenhagen, August 18, Angular size  The angular size is given by D A = L/θ.  In the flat sky approximation, this reduces to.  Taking the Einstein-de Sitter model as comparison, we have, where.  The angular size is given by D A = 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, Independence  With large scales excluded, the CMB is sensitive to spatial curvature and expansion history only via D A.  Assuming a FRW model, we have, which can be inverted to obtain.  With large scales excluded, the CMB is sensitive to spatial curvature and expansion history only via D A.  Assuming a FRW model, we have, which can be inverted to obtain.

Confronting theory with observations workshop, NBIA, Copenhagen, August 18, 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 =  We do not take into account gravity waves, vectors or neutrino masses.  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 =  We do not take into account gravity waves, vectors or neutrino masses.

Confronting theory with observations workshop, NBIA, Copenhagen, August 18, Varying the cut  Fitting ΛCDM to ACBAR and WMAP5, we get (τ = 0)  From l min = 2 to l min = 40, the errors on ω b and ω c grow by 28% and on n s by 57%, while the means shift by 1%, 4% and 1%.  Fitting ΛCDM to ACBAR and WMAP5, we get (τ = 0)  From l min = 2 to l min = 40, the errors on ω b and ω c grow by 28% and on n s by 57%, while the means shift by 1%, 4% and 1%.

Confronting theory with observations workshop, NBIA, Copenhagen, August 18, A systematic shift  As l min increases, ω b and n s go down, while ω c and Ω Λ 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 l min = 100.  As l min increases, ω b and n s go down, while ω c and Ω Λ 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 l min = 100.

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

Confronting theory with observations workshop, NBIA, Copenhagen, August 18, Shifted results  We fix the cut at l min = 40, corresponding to z ≾ 60.  The mean values change more than the error bars.  The angle θ A = r s /D A is stable and determined to 0.3%.  We fix the cut at l min = 40, corresponding to z ≾ 60.  The mean values change more than the error bars.  The angle θ A = r s /D A is stable and determined to 0.3%.

Confronting theory with observations workshop, NBIA, Copenhagen, August 18, Summary  The values of ω b, ω c, n s and θ A are determined by the CMB to a precision of 3%, 6%, 2% and 0.3%.  However, a systematic shift affects all parameters except θ A.  The small-angle CMB sky prefers different values of ω b, ω c, n s than the full dataset.  It would be interesting to analyse BAO in the same model-independent spirit.  The values of ω b, ω c, n s and θ A are determined by the CMB to a precision of 3%, 6%, 2% and 0.3%.  However, a systematic shift affects all parameters except θ A.  The small-angle CMB sky prefers different values of ω b, ω c, n s than the full dataset.  It would be interesting to analyse BAO in the same model-independent spirit.