Canonical structure of minimal varying $\Lambda$ theories Auteur(s): Alexandrov S., Speziale Simone, Zlosnik Tom (Article) Publié: Classical And Quantum Gravity, vol. 38 p.175011 (2021) Texte intégral en Openaccess : Ref HAL: hal-03197323_v1 Ref Arxiv: 2104.03753 DOI: 10.1088/1361-6382/ac1852 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: Minimal varying $\Lambda$ theories are defined by an action built from the Einstein-Cartan-Holst first order action for gravity with the cosmological constant $\Lambda$ as an independent scalar field, and supplemented by the Euler and Pontryagin densities multiplied by $1/\Lambda$. We identify the canonical structure of these theories which turn out to represent an example of irregular systems. We find five degrees of freedom on generic backgrounds and for generic values of parameters, whereas if the parameters satisfy a certain condition (which includes the most commonly considered Euler case) only three degrees of freedom remain. On de Sitter-like backgrounds the canonical structure changes, and due to an emergent conformal symmetry one degree of freedom drops from the spectrum. We also analyze the self-dual case with an holomorphic action depending only on the self-dual part of the connection. In this case we find two (complex) degrees of freedom, and further discuss the Kodama state, the restriction to de Sitter background and the effect of reality conditions.