Professor Pedro Ferreira

Abstract:

There is tentative evidence for a mismatch between the rest frames of matter and the cosmic microwave background, the “quasar dipole anomaly.” We consider such a dipole in tilted anisotropic models, for a range of scenarios and sources: spatial curvature, cosmic heat flux, large scale electromagnetic fields, and a Khronon field. Crucially, we determine the ancillary effects on other cosmological observables in each of these models, and we show that, apart from the case of the Khronon field, it is unlikely that one can obtain a dipole with the amplitude that is being observed unless one considers additional exotica.

Abstract:

Abstract The galaxy luminosity and stellar mass function (LF, SMF), and halo mass function (HMF), are fundamental quantities in astrophysics and crucial inputs to a range of astrophysical and cosmological analyses. They are typically parametrised by fitting functions that have been chosen ‘by eye’ to match observed or simulated data. We apply symbolic regression—specifically the Exhaustive Symbolic Regression (ESR) algorithm—to automate the search for optimal LF, SMF and HMF functional forms. ESR scores all functions up to a maximum complexity composed of a user-defined basis set of operators using the description length, an approximation to the Bayesian evidence that balances accuracy with complexity. We find many functions that outperform the Schechter and double Schechter functions for the LF and SMF, and that outperform all investigated literature functions (that outperform the Press–Schechter, Warren, Tinker, Sheth–Tormen and Jenkins) for the HMF. By additionally imposing ‘physicality checks’ on functions’ extrapolation and integration properties, we identify the optimal, low-complexity functional forms in terms of accuracy, simplicity and behaviour beyond the data range. As well as providing drop-in replacements for literature LF, SMF and HMF fitting functions, and identifying robust behaviour across well-fitting functions, we present a framework with which symbolic regression may be used to automate the discovery of optimal functions for any astrophysical dataset.