Cosmic Inflation and Genetic Algorithms

Abstract

Large classes of standard single‐field slow‐roll inflationary models consistent with the required number of e‐folds, the current bounds on the spectral index of scalar perturbations, the tensor‐to‐scalar ratio, and the scale of inflation can be efficiently constructed using genetic algorithms. The setup is modular and can be easily adapted to include further phenomenological constraints. A semi‐comprehensive search for sextic polynomial potentials results in ∼scriptOfalse(300,000false)$\sim \mathcal {O}(300,000)$ viable models for inflation. The analysis of this dataset reveals a preference for models with a tensor‐to‐scalar ratio in the range 0.0001≤r≤0.0004$0.0001\le r\le 0.0004$. We also consider potentials that involve cosine and exponential terms. In the last part we explore more complex methods of search relying on reinforcement learning and genetic programming. While reinforcement learning proves more difficult to use in this context, the genetic programming approach has the potential to uncover a multitude of viable inflationary models with new functional forms.

String Cosmology: from the Early Universe to Today

“…The large multitude of IIB vacua implies that optimisation strategies are important. Modern computational tools are promising in this direction (see [220,221,222,223,224]).…”

Ising Machines for Diophantine Problems in Physics

“…In particular it will be interesting to employ them in the string theory landscape context, and compare them to the genetic algorithmic and machine learning techniques that have been studied in Refs. [6, 69–86].…”

“…(For example the study of monad bundle constructions in Ref. [6] involved a complicated set of constraints that prevented it being extended to consider the full set of phenomenological constraints of the Standard Model, including for example the correct Yukawa couplings, because the search space is too large, indeed comparable to some of the larger parameter spaces that we will consider here.) Indeed determining precisely which complexity class a problem falls into is itself an important question.…”

Root bundles: Applications to F-theory Standard Models

“…Motivated by the progress made in using machine learning techniques for applications in String Theory [1,35,63] (see also [92]), recent studies have utilized machine learning techniques in an attempt to overcome this limitation. For instance, the work in [17] investigated the complex structure dependency of line bundle cohomologies in a systematic way.…”

“…These insights were put on a sound theoretical foundation by use of Brill-Noether theory [32]. 1 These insights led to a quantitative study of jumps in charged matter vector pairs as a function of the complex structure moduli of the matter curve C R .…”