2018/02/26 by James E. Lidsey, Lidsey, James E. · 1 voice · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1802.09186
openalex publication_date 2018/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The cosmological field equations sourced by a self-interacting scalar field are dynamically equivalent to a closed system of equations obtained by applying the moment method to non-linear Schrödinger equations possessing an underlying non-relativistic conformal SL(2,ℝ) symmetry. We consider the one-dimensional, quintic Schrödinger equation relevant to strongly repulsive, dilute Bose gases. The action of the diffeomorphism group on the space of Schrödinger operators generates an harmonic trapping potential that can be identified with the kinetic energy of the cosmological scalar field. Inflationary cosmologies are represented by points on the orbit of the de Sitter solution, which is the quotient manifold \rm Diff(ℝ)/SL(2,ℝ). Key roles are played by the Schwarzian derivative of the diffeomorphism and the Ermakov-Pinney equation. The underlying SL(2,ℝ) symmetry results in a first integral constraint which ensures energy-momentum conservation. When the analysis is restricted to the universal cover group of diffeomorphisms on the circle, the generation of a rolling scalar field can be understood in terms of the Virasoro coadjoint action. The corresponding symplectic two-form and Hamiltonian generator of the coadjoint orbit are determined by the scalar field kinetic energy.