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 Mode counting variance Standard estimation of B-modes 1 % of the sky From Grain et al, 2009

Pure pseudo spectrum method (x2pure code) + optimisation of the window function 1 % of the sky pure mode counting Other methods 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 Optimal sky fraction

2nd approach: 3 realistic experiments Spec. Small scale Array of telescope Satellite Sky fraction 1% 36% 71% Noise (muK-arcmin) inhomogenesous (average of 5) 1 2 Beam (arcmin) 8 3 Dire que array de télescopes =study of window functions cause reach a limitation (in the noise)

Uncertainties on the power spectrum

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