Bianchi type-I cosmology with scalar and spinor fields

Abstract

We consider a system of interacting spinor and scalar fields in a gravitational field given by a Bianchi type-I cosmological model filled with perfect fluid. The interacting term in the Lagrangian is chosen in the form of derivative coupling, i.e., L int = λ 2 ϕ ,α ϕ ,α F, with F being a function of the invariants I an J constructed from bilinear spinor forms S and P. We consider the cases when F is the power or trigonometric functions of its arguments. Self-consistent solutions to the spinor, scalar and BI gravitational field equations are obtained. The problems of initial singularity and asymptotically isotropization process of the initially anisotropic space-time are studied. It is also shown that the introduction of the Cosmological constant (Λ-term) in the Lagrangian generates oscillations of the BI model, which is not the case in absence of Λ term. Unlike the case when spinor field nonlinearity is induced by self-action, in the case in question, wehere nonlinearity is induced by the scalar field, there exist regular solutions even without broken dominant energy condition.

Nonlinear Spinor Fields in Bianchi Type-I Spacetime Reexamined

“…There is widespread consensus among the cosmologists that cosmic microwave background anisotropies in small angular scales have the key to the formation of discrete structure. It was found that the introduction of nonlinear spinor field accelerates the isotropization process of the initially anisotropic Universe [10,11,13].…”

“…However, in cosmology, the role of spinor field was generally considered to be restricted. Only recently, after some remarkable works by different authors [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], showing the important role that spinor fields play on the evolution of the Universe, the situation began to change. This change of attitude is directly related to some fundamental questions of modern cosmology: (i) problem of initial singularity; (ii) problem of isotropization and (iii) late time acceleration of the Universe.…”

“…The main purpose of introducing a nonlinear term in the spinor field Lagrangian is to study the possibility of the elimination of initial singularity. In a number of papers [8][9][10][11][12] it was shown that the introduction of spinor field with a suitable nonlinearity into the system indeed gives rise to singularity-free models of the Universe.…”

Bianchi type I universe with viscous fluid and a term: A qualitative analysis

“…The oscillation takes place around the critical point (H, ε) = (0, (2Λ − κC 2 )/[κ(1 − ζ )]) having the type of cycle under the condition Λ > κC 2 /(1 + ζ ). It was shown in [20,21] that in case of a perfect fluid a positive Λ always invokes oscillations in the model, whereas, in the present model with viscous fluid, it is the case only when Λ obeys (3.20). Unlike the case with radiation where BI admits a singularity-free oscillatory mode of evolution, here, in case of a stiff matter one finds the BI Universe first expands, reaches its maximum and then contracts into a point, thus giving rise to space-time singularity.…”

“…We studied a self-consistent system of the nonlinear spinor and/or scalar fields in a BI spacetime in presence of a perfect fluid and a Λ term [20,21] in order to clarify whether the presence of a singular point an inherent property of the relativistic cosmological models or is it only a consequence of specific simplifying assumptions underlying these models? Recently we have considered a system of nonlinear spinor field in a BI Universe filled with viscous fluid [22].…”