General Relativity and Gravitation (2019) 51:109 https://doi.org/10.1007/s10714-019-2588-0 RESEARCH ARTICLE Detailed qualitative dynamical analysis of a cosmological Higgs field Carlos R. Fadragas 1 · Rolando Cardenas 1 · Mariano Rodriguez Ricard 2 · Ailier Rivero-Acosta 1,3 · Adrian Linares-Rodriguez 1 Received: 6 March 2019 / Accepted: 16 August 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract A scalar cosmological Higgs field is expected to exist in our universe in order to create inertial mass. Some results obtained at LHC suggest that this idea must be reconsid- ered. The cosmological effects of scalar fields have been proposed as a mechanism to drive the evolution of the universe in various scenarios. In this paper we investigate, from the dynamical systems perspective, the evolution of a Universe consisting of a matter component ρ together with a scalar field φ exhibiting a quartic polynomial self-interacting potential. We consider an homogeneous and isotropic flat Friedmann– Robertson–Walker metric. Center Manifold Theory is employed to investigate the dynamics near a non-hyperbolic critical point. We prove that there are two possible late time attractors corresponding to stable de Sitter solutions. Keywords Cosmological Higgs field · Stability dynamical analysis · Center manifold theory 1 Introduction A scalar cosmological Higgs field (CHF) is expected to exist in our universe in order to create inertial mass [1]. Recently, some results obtained at LHC suggest that this idea must be reconsidered [2,3]. However, the well known hierarchy problem might appear to make known scalar fields inappropriate for a cosmological setting [4]. A dynamical solution of a decaying scalar field was suggested in [5], allowing a large scalar field in the early universe to evolve into the small scalar field seen today. Besides, B Ailier Rivero-Acosta ailierrivero@mail.com 1 Laboratorio de Ciencia Planetaria, Departamento de Física, Universidad Central de Las Villas, Santa Clara, Cuba 2 Facultad de Matemática y Computación, Universidad de La Habana, Havana, Cuba 3 División de Ciencias e Ingenierías, Universidad de Guanajuato, León, Guanajuato, Mexico 0123456789().: V,-vol 123