# Non-particulate Klein-Gordon modes formed by inflation

## TL;DR

This paper explores the behavior of scalar quantum field modes in an accelerating universe, revealing a transition to non-oscillatory, unstable modes that form a unique quantum state, distinct from traditional particle interpretations.

## Contribution

It introduces a full solution for scalar field modes in an accelerating universe, showing the emergence of non-particulate, unstable modes with a unique quantum representation.

## Key findings

- Unstable modes cease to oscillate and become time-frozen.
- The dark component's energy density remains constant over time.
- The quantum Hilbert space for these modes is uniquely defined.

## Abstract

In a full solution for a scalar quantum field coupled to an accelerating isotropic universe, all constituent non-autonomous modes of elementary excitation cease to oscillate and become unstable at a discrete sequence of times. After canonical quantization the time-frozen Hamiltonian has eigenstates that can be viewed as neither particles nor oscillatory radiation. Under standard canonical quantization, the Hamiltonian has a natural time dependent partitioning into a light component and a dark component. Under equipartition of energy, the energy density of the dark component remains constant. The dark component consists of a finite number of low wave -number repulsive units with time varying force constant. Although these unstable modes have no ground state of minimum energy there exist only finitely many of them and so their quantum Hilbert space representation, by the Stone-von Neumann theorem, is unique up to unitary equivalence. The remaining infinite number of stable modes still have a unique Fock-Cook representation and so overall there is still a preferred physical representation.