STOchastic LAttice Simulation of hybrid inflation

TL;DR

This paper uses lattice simulations to analyze the spatial structure of curvature perturbations in hybrid inflation models, revealing how topological defects evolve and connect during inflation, with implications for early universe physics.

Contribution

It introduces the stochastic lattice simulation code {STOLAS} to study topological defect structures and curvature perturbations in hybrid inflation, highlighting the reconnection of defects and their topological signatures.

Findings

Topological defects reconnect into finer structures during inflation.

PDFs show an upper bound in the Cubic case, affecting PBH formation.

Euler characteristic reveals global structures linked to defect types.

Abstract

We investigate the spatial profile of the curvature perturbation generated in multi-waterfall hybrid inflation models, which are known to produce various topological defects. Using the lattice simulation code \acl{STOLAS}, based on the stochastic formalism of inflation, we analyse six cases by varying the number of waterfall fields $n$ and the functional form of the inflaton potential (``Quadratic'' and ``Cubic'' cases). Our statistical analysis shows that the \acp{PDF} and power spectra are broadly consistent with the so-called stochastic-$\delta N$ algorithm. The ``Cubic'' case also exhibits a characteristic upper bound in the \ac{PDF}, as discovered in our previous work, that suppresses \acl{PBH} formation while potentially affecting halo formation. Furthermore, we employ the Euler characteristic as a topological diagnostic tool to identify the structures of the waterfall fields as well as the curvature perturbation. We find that the topological defects, such as domain walls ($n=1$), cosmic strings ($n=2$), and monopoles ($n=3$), are reconnected during inflation into finer structures by the stochastic noise, making their correlation lengths much smaller than the Hubble scale at the critical point of the waterfall phase transition counterintuitively. The Euler characteristic also implies global structures of the curvature perturbation for $n=1$, though we do not conclude if they are due to the domain wall, because neither the strings ($n=2$) nor monopoles ($n=3$) leave such structures. The global structures of the curvature perturbation will provide a novel probe for the physics of the early universe.