Particle theory

Abstract:

We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is reviewed and its main features and shortcomings are discussed. It has been observed recently that line bundle cohomology can be described by dividing the Picard lattice into certain regions in each of which the cohomology dimension is described by a polynomial formula. Based on this structure, we set up a network capable of identifying the regions and their associated polynomials, thereby effectively generating a conjecture for the correct cohomology formula. For complex surfaces, we also set up a network which learns certain rigid divisors which appear in a recently discovered master formula for cohomology dimensions.

Abstract:

We have shown (Colin et al. 2019) that the acceleration of the Hubble expansion rate inferred from Type Ia supernovae is essentially a dipole with 3.9$\sigma$ significance, approximately aligned with the CMB dipole, while its monopole component which may be interpreted as due to a Cosmological Constant (or more generally dark energy) is consistent with zero at 1.4$\sigma$. This is challenged by Rubin & Heitlauf (2019) who assert that we incorrectly assumed the supernova light-curve parameters to be independent of redshift, and erred further in considering their measured redshifts (in the heliocentric frame) rather than transforming them to the CMB frame (in which the universe supposedly looks isotropic). We emphasize that our procedure is justified and that their criticism serves only to highlight the rather "arbitrary corrections" that are made to the data in order to infer isotropic cosmic acceleration. This is a vivid illustration of the 'Cosmological Fitting Problem' faced by observers who live in an inhomogeneous universe but still use the maximally symmetric FLRW cosmolgy to interpret observations.