Prof. David Alonso

Abstract:

We present a transfer function-based method to estimate angular power spectra from filtered maps for cosmic microwave background (CMB) surveys. This is especially relevant for experiments targeting the faint primordial gravitational wave signatures in CMB polarisation at large scales, such as the Simons Observatory (SO) small aperture telescopes. While timestreams can be filtered to mitigate the contamination from low-frequency noise, usual methods that calculate the mode coupling at individual multipoles can be challenging for experiments covering large sky areas or reaching few-arcminute resolution. The method we present here, although approximate, is more practical and faster for larger data volumes. We validate it through the use of simulated observations approximating the first year of SO data, going from half-wave plate-modulated timestreams to maps, and using simulations to estimate the mixing of polarisation modes induced by an example of time-domain filtering. We show its performance through an example null test and with an end-to-end pipeline that performs inference on cosmological parameters, including the tensor-to-scalar ratio r. The performance demonstration uses simulated observations at multiple frequency bands. We find that the method can recover unbiased parameters for our simulated noise levels.

Abstract:

The Atacama Cosmology Telescope Data Release 6 (ACT DR6) power spectrum is expected to provide state-of-the-art cosmological constraints, with an associated need for precise error modeling. In this paper we design, and evaluate the performance of, an analytic covariance matrix prescription for the DR6 power spectrum that sufficiently accounts for the complicated ACT map properties. We use recent advances in the literature to handle sharp features in the signal and noise power spectra, and account for the effect of map-level anisotropies on the covariance matrix. In including inhomogeneous survey depth information, the resulting covariance matrix prescription is structurally similar to that used in the Planck Cosmic Microwave Background (CMB) analysis. We quantify the performance of our prescription using comparisons to Monte Carlo simulations, finding better than 3% agreement. This represents an improvement from a simpler, pre-existing prescription, which differs from simulations by ∼ 16%. We develop a new method to correct the analytic covariance matrix using simulations, after which both prescriptions achieve better than 1% agreement. This correction method outperforms a commonly used alternative, where the analytic correlation matrix is assumed to be accurate when correcting the covariance. Beyond its use for ACT, this framework should be applicable for future high resolution CMB experiments including the Simons Observatory (SO).

Abstract:

<jats:p>We present a generalisation of the standard pseudo- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>C</mml:mi><mml:mo>ℓ</mml:mo></mml:msub></mml:math> approach for power spectrum estimation to the case of spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math> fields weighted by a general positive-definite weight matrix that couples the different spin components of the field (e.g.  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi></mml:math> maps in CMB polarisation analyses, or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>γ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>γ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> shear components in weak lensing). Relevant use cases are, for example, data with significantly anisotropic noise properties, or situations in which different masks must be applied to the different field components. The weight matrix map is separated into a spin-0 part, which corresponds to the “mask” in the standard pseudo- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>C</mml:mi><mml:mo>ℓ</mml:mo></mml:msub></mml:math> approach, and a spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mi>s</mml:mi></mml:mrow></mml:math> part sourced solely by the anisotropic elements of the matrix, leading to additional coupling between angular scales and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mi>/</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:math> modes. The general expressions for the mode-coupling coefficients involving the power spectra of these anisotropic weight components are derived and validated. The generalised algorithm is as computationally efficient as the standard approach. We implement the method in the public code NaMaster.</jats:p>