Eur. Phys. J. C (2012) 72: 2219
https://doi.org/10.1140/epjc/s10052-012-2219-3

Regular Article - Theoretical Physics

Higgs boson, renormalization group, and naturalness in cosmology

¹ Theory Department, Lebedev Physics Institute, Leninsky Prospect 53, Moscow, 119991, Russia
² Dipartimento di Fisica ed Astronomia and INFN, via Irnerio 46, 40126, Bologna, Italy
³ L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, 119334, Russia
⁴ Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937, Köln, Germany
⁵ University of Nottingham, University Park, Nottingham, NG7 2RD, UK

^* e-mail: barvin@td.lpi.ru

Received: 4 September 2012
Revised: 16 October 2012
Published online: 9 November 2012

Abstract

We consider the renormalization group improvement in the theory of the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. At the one-loop level with the running of constants taken into account, it leads to a range of the Higgs mass that is entirely determined by the lower WMAP bound on the cosmic microwave background (CMB) spectral index. We find that the SM phenomenology is sensitive to current cosmological data, which suggests to perform more precise CMB measurements as a SM test complementary to the LHC program. By using the concept of a field-dependent cutoff, we show the naturalness of the gradient and curvature expansion in this model within the conventional perturbation theory range of the SM. We also discuss the relation of these results to two-loop calculations and the limitations of the latter caused by parametrization and gauge dependence problems.