Professor Pedro Ferreira

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 Our emulator will be usable long after the codes on which numerical approximations are built become outdated.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:

Inflation is a highly favored theory for the early Universe. It is compatible with current observations of the cosmic microwave background and large scale structure and is a driver in the quest to detect primordial gravitational waves. It is also, given the current quality of the data, highly underdetermined with a large number of candidate implementations. We use a new method in symbolic regression to generate all possible simple scalar field potentials for one of two possible basis sets of operators. Treating these as single-field, slow-roll inflationary models we then score them with an information-theoretic metric ("minimum description length") that quantifies their efficiency in compressing the information in current data. We explore two possible priors on the parameter space of potentials, one related to the functions' structural complexity and one that uses a Katz back-off language model to prefer functions that may be theoretically motivated. This enables us to identify the inflaton potentials that optimally balance simplicity with accuracy at explaining current data, which may subsequently find theoretical motivation. Our exploratory study opens the door to extraction of fundamental physics directly from data, and may be augmented with more refined theoretical priors in the quest for a complete understanding of the early Universe.

Abstract:

Context. The cosmological surveys that are planned for the current decade will provide us with unparalleled observations of the distribution of galaxies on cosmic scales, by means of which we can probe the underlying large-scale structure (LSS) of the Universe. This will allow us to test the concordance cosmological model and its extensions. However, precision pushes us to high levels of accuracy in the theoretical modelling of the LSS observables, so that no biases are introduced into the estimation of the cosmological parameters. In particular, effects such as redshift-space distortions (RSD) can become relevant in the computation of harmonic-space power spectra even for the clustering of the photometrically selected galaxies, as has previously been shown in literature. Aims. In this work, we investigate the contribution of linear RSD, as formulated in the Limber approximation by a previous work, in forecast cosmological analyses with the photometric galaxy sample of the Euclid survey. We aim to assess their impact and to quantify the bias on the measurement of cosmological parameters that would be caused if this effect were neglected. Methods. We performed this task by producing mock power spectra for photometric galaxy clustering and weak lensing, as is expected to be obtained from the Euclid survey. We then used a Markov chain Monte Carlo approach to obtain the posterior distributions of cosmological parameters from these simulated observations. Results. When the linear RSD is neglected, significant biases are caused when galaxy correlations are used alone and when they are combined with cosmic shear in the so-called 3 × 2 pt approach. These biases can be equivalent to as much as 5σ when an underlying ΛCDM cosmology is assumed. When the cosmological model is extended to include the equation-of-state parameters of dark energy, the extension parameters can be shifted by more than 1σ.