Instabilities in Horndeski Yang-Mills inflation

Jose Beltran Jimenez (1) , Lavinia Heisenberg , Ryotaro Kase , Ryo Namba , Shinji Tsujikawa

1 CPT - Centre de Physique Théorique - UMR 7332

A non-Abelian SU(2) gauge field with a nonminimal Horndeski coupling to gravity gives rise to a de Sitter solution followed by a graceful exit to a radiation-dominated epoch. In this Horndeski-Yang-Mills (HYM) theory we derive the second-order action for tensor perturbations on the homogeneous and isotropic quasi–de Sitter background. We find that the presence of the Horndeski nonminimal coupling to the gauge field inevitably introduces ghost instabilities in the tensor sector during inflation. Moreover, we also find Laplacian instabilities for the tensor perturbations deep inside the Hubble radius during inflation. Thus, we conclude that the HYM theory does not provide a consistent inflationary framework due to the presence of ghosts and Laplacian instabilities.

Mots clés: perturbation: tensor; coupling: nonminimal; background: de Sitter; stability; inflation; gauge field theory; Yang-Mills; ghost; gravitation; nonabelian; SU(2)

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Astrophysique [astro-ph]; Relativité Générale et Cosmologie Quantique [gr-qc]

Jose Beltran Jimenez, Lavinia Heisenberg, Ryotaro Kase, Ryo Namba, Shinji Tsujikawa. Instabilities in Horndeski Yang-Mills inflation. Physical Review D, 2017, 95 (6), pp.063533. ⟨10.1103/PhysRevD.95.063533⟩. ⟨hal-01554553⟩