On inflation with nonminimal coupling
Abstract
A simple realization of inflation consists of adding the following operators to the EinsteinHilbert action: ( ∂ϕ)^{2}, λϕ ^{4}, and ξϕ ^{2} _{ R }, with ξ a large nonminimal coupling. Recently there has been much discussion as to whether such theories make sense quantum mechanically and if the inflaton ϕ can also be the Standard Model Higgs. In this work we answer these questions. Firstly, for a single scalar ϕ, we show that the quantum field theory is well behaved in the pure gravity and kinetic sectors, since the quantum generated corrections are small. However, the theory likely breaks down at m _{Pl} /ξ due to scattering provided by the selfinteracting potential λϕ ^{4}. Secondly, we show that the theory changes for multiple scalars overrightarrow φ with nonminimal coupling ξ overrightarrow φ \cdot overrightarrow φ mathcal{R} , since this introduces qualitatively new interactions which manifestly generate large quantum corrections even in the gravity and kinetic sectors, spoiling the theory for energies ≳ m _{Pl} /ξ. Since the Higgs doublet of the Standard Model includes the Higgs boson and 3 Goldstone bosons, it falls into the latter category and therefore its validity is manifestly spoiled. We show that these conclusions hold in both the Jordan and Einstein frames and describe an intuitive analogy in the form of the pion Lagrangian. We also examine the recent claim that curvaturesquared inflation models fail quantum mechanically. Our work appears to go beyond the recent discussions.
 Publication:

Journal of High Energy Physics
 Pub Date:
 November 2010
 DOI:
 10.1007/JHEP11(2010)023
 arXiv:
 arXiv:1002.2995
 Bibcode:
 2010JHEP...11..023H
 Keywords:

 Higgs Physics;
 Cosmology of Theories beyond the SM;
 Renormalization Group;
 High Energy Physics  Phenomenology;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 14 pages, 2 figures. Version 2: Clarified findings and improved wording. Elaborated important sections and removed an unnecessary section. Added references. Version 3: Updated towards JHEP version. Version 4: Final JHEP version