Detecting the tensor-to-scalar ratio with the pure pseudospectrum reconstruction of B -mode

The B-mode of polarized anisotropies of the cosmic microwave background is a unique and nearly direct probe of primordial inflation, as it can constrain the amplitude of the primordial gravity waves. However, its detection and precise measurement is made difficult by a minute amplitude of the signal and the fact that the signal has to be discerned from many contributions of noncosmological origin and reliably estimated in the presence of numerous sources of statistical uncertainties. Among these last effects, the E-to-B leakage, arising as a result of partial sky coverage, has been found to play a key and potentially fundamental role in determining the possible statistical significance with which the primordial B-mode signal can be detected. In this work we employ the pure pseudospectrum formalism devised to minimize the effects of the leakage on the variance of power spectrum estimates and discuss the limits on the tensor-to-scalar ratio, r, that could be realistically set by current and forthcoming measurements of the B-mode angular power spectrum. We compare those with the results obtained using other approaches: naive mode counting, minimum-variance quadratic estimators, and revisiting the question of optimizing the sky coverage of small-scale, suborbital experiments in order to maximize the statistical significance of the detection of r. We show that the optimal sky coverage is largely insensitive to the adopted approach at least for reasonably compact sky patches. We find, however, that the mode counting overestimates the detection significance by a factor ∼1.17 as compared to the lossless maximum variance approach and by a factor ∼1.25 as compared to the lossy pure pseudospectrum estimator. In a second time, we consider more realistic experimental configurations. With a pure pseudospectrum reconstruction of B-modes and considering only statistical uncertainties, we find that a detection of r ∼ 0.11, r ∼ 0.0051, and r ∼ 0.0026 at 99% confidence level is within the reach of current suborbital experiments, future arrays of ground-based telescopes, and a satellite mission, respectively. This means that an array of telescopes could be sufficient to discriminate between largeand small-field models of inflation, even if the E-to-B leakage is consistently included but accounted for in the analysis. However, a satellite mission will be required to distinguish between different small-field models depending on the number of e-folds.