Closing the Cosmographic Hierarchy: Dynamical Attractors from Inflation to Reheating

TL;DR

This paper introduces a potential-independent framework for cosmological dynamics, revealing inflation as a natural attractor and describing reheating through an extended autonomous system.

Contribution

It develops a novel, potential-independent cosmographic approach that unifies inflation and reheating dynamics without slow-roll assumptions.

Findings

Inflationary solutions are natural attractors in the dynamical system.

Reheating is characterized by an effective equation of state within the extended system.

The radiation-dominated phase emerges as the late-time attractor.

Abstract

We develop a potential-independent cosmographic framework, in which cosmographic parameters are promoted to dynamical variables within a closed autonomous system. Although the cosmographic hierarchy is formally infinite, we achieve closure by mapping potential slow-roll parameters onto the kinematic phase space within General Relativity with a minimally coupled scalar field. Within this framework, we perform a stability analysis and show that inflationary (quasi-de Sitter) solutions arise as natural attractors, while stiff-fluid configurations act as repellers without invoking the slow-roll approximation. To describe the transition to standard Big Bang evolution, we extend the system to include a radiation component and a phenomenological decay term. This leads to a generalized, potential-independent description of reheating characterized by an effective equation of state $w_{\rm eff}$. We demonstrate that the radiation-dominated phase is the late-time attractor of the extended system. These results provide a unified kinematical description of the expansion history from inflation through reheating, bridging cosmography and scalar field dynamics.