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On the detection of the tensor-to-scalar ratio r using the CMB B-modes Agnès Ferté In collaboration with: Julien Peloton, Julien Grain, Radek Stompor Based on: arxiv:2506.06409 CMB B-modes caused by tensor perturbations and lensing of E-modes (Q,U) maps E and B modes power spectra Tensor-to-scalar ratio r CMB B-modes at low-l probe the primordial Universe Lensing B modes: 1st direct detection by Polarbear (arxiv:1403.2369) Primordial B modes: r<0.12 (Bicep2/Keck + Planck) Estimation of B modes power spectrum on a masked sky: the E-to-B leakage Function of the mask 1 % of the sky Standard estimation of B-modes Mode counting variance From Grain et al, 2009 Pure pseudo spectrum method (x2pure code) + optimisation of the window function 1 % of the sky Other methods pure mode counting Smith, 2006 Grain et al, 2009 Ferté et al, 2013 From Ferté et al, 2013 Pure pseudo spectrum method (x2pure code) + optimisation of the window function 71 % of the sky Other methods pure mode counting Smith, 2006 Grain et al, 2009 Ferté et al, 2013 Impact of leakage on the forecasts of CMB B modes detection? • 1st investigation: ideal experiments • 2nd investigation: 3 selected realistic experiments Signal-to-noise ratio computed using Fisher matrix Error on r Covariance matrix computed using: - Mode counting variance = - Pure method = pure estimation + MC simulations 1st approach: ideal small scale experiments 1% r=0.1 Mode-counting variance for optimal sky coverage r = 0.1 Optimal sky fraction 2nd approach: 3 realistic experiments Spec. Sky fraction Noise (muK-arcmin) Beam (arcmin) Small scale Array of telescope Satellite 1% 36% 71% inhomogenesous (average of 5) 1 2 8 3 8 Uncertainties on the power spectrum r = 0.1 Accessible r at 3σ detection Example of satellite xp mode counting pure Small scale xp Telescopes array Satellite mission Mode counting r > 0.038 r > 0.0011 r > 0.0009 Pure method r > 0.11 r > 0.0051 r > 0.0026 Foreground impact on the detection of r Remove the first bin: 2 < l < 20 Example of satellite xp Small scale xp Telescopes array Satellite mission Mode counting r > 0.04 r > 0.0016 r > 0.0013 Pure method r > 0.11 r > 0.0053 r > 0.0028 TO TAKE AWAY • The pure estimation of B modes is awesome • The mode-counting approach is enough to state on optimal sky coverage • The pure method is mandatory to perform realistic forecasts on r detection • Potential future satellite mission: r ≥ 10-3 Stage 4 array of telescope: r ≥ 10-2 Current ground-based or balloon borne: r ≥ 10-1 • Side ‘personal’ note: the CMB TB and EB correlations hold information on fundamental physics (e.g. : parity breaking, birefringence, primordial magnetic field…) From NASA Effect of binning Optimised window functions SNR on r Small scale Array of telescopes