Prof. David Alonso

Abstract:

Context. Computing the matter power spectrum, P(k), as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used.

Aims. We aim to construct an efficient, differentiable, interpretable, symbolic emulator for the redshift zero linear matter power spectrum which achieves sub-percent level accuracy. We also wish to obtain a simple analytic expression to convert A_s to σ₈ given the other cosmological parameters.

Methods. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and σ₈. We learn the ratio between an existing low-accuracy fitting function for P(k) and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation.

Results. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2% between k = 9 × 10⁻³ − 9 h Mpc⁻¹ and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than CAMB and 36 times faster than the neural network based matter power spectrum emulator BACCO. We also provide a simple analytic approximation for σ₈ with a similar accuracy, with a root mean squared fractional error of just 0.1% when evaluated across the same range of cosmologies. This function is easily invertible to obtain A_s as a function of σ₈ and the other cosmological parameters, if preferred.

Conclusions. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.

Abstract:

We make use of the Gaia-unWISE quasar catalogue, Quaia, to constrain the growth history out to high redshifts from the clustering of quasars and their cross-correlation with maps of the Cosmic Microwave Background (CMB) lensing convergence. Considering three tomographic bins, centred at redshifts z̅i = [0.69, 1.59, 2.72], we reconstruct the evolution of the amplitude of matter fluctuations σ 8(z) over the last ∼ 12 billion years of cosmic history. In particular, we make one of the highest-redshift measurements of σ 8 (σ 8(z = 2.72) = 0.22 ± 0.06), finding it to be in good agreement (at the ∼ 1σ level) with the value predicted by ΛCDM using CMB data from Planck. We also used the data to study the evolution of the linear quasar bias for this sample, finding values similar to those of other quasar samples, although with a less steep evolution at high redshifts. Finally, we study the potential impact of foreground contamination in the CMB lensing maps and, although we find evidence of contamination in cross-correlations at z ∼ 1.7 we are not able to clearly pinpoint its origin as being Galactic or extragalactic. Nevertheless, we determine that the impact of this contamination on our results is negligible.

Abstract:

Context. The upcoming Simons Observatory Small Aperture Telescopes aim at achieving a constraint on the primordial tensor-to-scalar ratio r at the level of σ (r = 0)≤0.003, observing the polarized CMB in the presence of partial sky coverage, cosmic variance, inhomogeneous non-white noise, and Galactic foregrounds. Aims. We present three different analysis pipelines able to constrain r given the latest available instrument performance, and compare their predictions on a set of sky simulations that allow us to explore a number of Galactic foreground models and elements of instrumental noise, relevant for the Simons Observatory. Methods. The three pipelines employ different combinations of parametric and non-parametric component separation at the map and power spectrum levels, and use B-mode purification to estimate the CMB B-mode power spectrum. We applied them to a common set of simulated realistic frequency maps, and compared and validated them with focus on their ability to extract robust constraints on the tensor-to-scalar ratio r. We evaluated their performance in terms of bias and statistical uncertainty on this parameter. Results. In most of the scenarios the three methodologies achieve similar performance. Nevertheless, several simulations with complex foreground signals lead to a > 2σ bias on r if analyzed with the default versions of these pipelines, highlighting the need for more sophisticated pipeline components that marginalize over foreground residuals. We show two such extensions, using power-spectrum-based and map-based methods, that are able to fully reduce the bias on r below the statistical uncertainties in all foreground models explored, at a moderate cost in terms of σ (r).