Conformal structure of FLRW cosmology: spinorial representation and the so (2, 3) algebra of observables

• Published in: The journal of high energy physics Vol. 2020; no. 3
• Main Authors: Achour, Jibril Ben, Livine, Etera R.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V; Springer
• Subjects: Algebra; Classical and Quantum Gravitation; Cosmology; Elementary Particles; General Relativity and Quantum Cosmology; Geometric transformation; High energy physics; High Energy Physics - Theory; Invariance; Kinematics; Lie groups; Mathematical Physics; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity; Relativity Theory; Representations; Scalars; String Theory; Classical Theories of Gravity; Global Symmetries; Conformal and W Symmetry
• ISSN: 1126-6708; 1029-8479
• DOI: 10.1007/JHEP03(2020)067

A bstract It was recently shown that the homogeneous and isotropic cosmology of a massless scalar field coupled to general relativity exhibits a new hidden conformal invariance under Mobius transformation of the proper time, additionally to the invariance under time-reparamterization. The resulting Noether charges form a sl 2 ℝ Lie algebra, which encapsulates the whole kinematics and dynamics of the geometry. This allows to map FLRW cosmology onto conformal mechanics and formulate quantum cosmology in CFT 1 terms. Here, we show that this conformal structure is embedded in a larger so (3, 2) algebra of observables, which allows to present all the Dirac observables for the whole gravity plus matter sectors in a unified picture. Not only this allows one to quantize the system and its whole algebra of observables as a single irreducible representation of so (3, 2), but this also gives access to a scalar field operator ϕ ̂ opening the door to the inclusion of non-trivial potentials for the scalar field. As such, this extended conformal structure might allow to perform a group quantization of inflationary cosmological backgrounds.