On consistency conditions for strong SRRT inflation in two-field cosmological models

TL;DR

This paper investigates the geometric PDE conditions necessary for strong SRRT inflation in two-field cosmological models, providing methods to determine scalar field metrics from potentials and analyzing solutions near critical points.

Contribution

It introduces a geometric PDE framework for strong SRRT inflation, linking scalar metrics and potentials, and analyzes solution behavior near critical points using PDE theory.

Findings

Derived a geometric PDE relating scalar metric and potential.

Simplified the PDE in conformal coordinates for analysis.

Analyzed solution behavior near critical points of the potential.

Abstract

We discuss the strong version of the consistency conditions for SRRT inflation in general two-field cosmological models. In the fiducial case, this condition is a geometric PDE which relates the scalar field metric and scalar potential of such models. When supplemented by appropriate boundary conditions, this equation determines the scalar field metric in terms of the scalar potential or the other way around, thereby selecting "fiducial" models for strong SRRT inflation. When the scalar potential is given, the equation can be simplified by fixing the conformal class of the scalar field metric, in which case it locally becomes an equation for the conformal factor of that metric when written in isothermal coordinates. We analyze this equation with standard methods of PDE theory, discuss its quasilinearization near a non-degenerate critical point of the scalar potential and extract natural asymptotic conditions for its solutions near such points.