Noether symmetry for non-minimally coupled fermion fields

Abstract

Abstract. A cosmological model where a fermion field is non-minimally coupled with the gravitational field is studied. By applying Noether symmetry the possible functions for the potential density of the fermion field and for the coupling are determined. Cosmological solutions are found showing that the non-minimally coupled fermion field behaves as an inflaton describing an accelerated inflationary scenario, whereas the minimally coupled fermion field describes a decelerated period, behaving as a standard matter field.PACS numbers: 98.80.Cq, 95.35.+d ‡ Dedicated to Professor Luis P. Chimento on the occasion of his sixtieth birthday.

Nonlinear spinor fields in Bianchi type-VI0 spacetime

“…are among the most studied ones, though some other models of dark energy are also proposed. After some remarkable works by different authors [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], showing the important role of spinor field in the evolution of the Universe, it has been extensively used to model the dark energy. This success is directly related to its ability to answer some fundamental questions of modern cosmology: (i) Problem of initial singularity and its possible elimination [22][23][24][25][26][35][36][37][38]; (ii) problem of isotropization [24,25,27,36,39] and (iii) late time acceleration of the Universe [28-30, 32, 35-38, 40, 41].…”

Analysis of the nonminimally coupled scalar field in the Palatini formalism by the Noether symmetry approach

“…The purpose of this paper is to analyse the dynamics of this field in the Palatini formalism [1][2][3] through the Noether symmetry approach [4][5][6][7][8][9][10][11]. The most fundamental aspect to be noted in the Palatini formalism is the independence, a priori, between the metric tensor and affine connection, which are in fact independent geometric variables [1].…”

Noether gauge symmetry for f(R) gravity in Palatini formalism

“…There are two kinds of Noether symmetry approach for cosmological studies in the literature : The first one is the so-called Noether symmetry approach in which the Lie derivative of a given Lagrangian vanishes, (Capozziello and de Ritis 1993;de Ritis et al 1990;Demianski et al 1 Sanyal and Modak 2001;Camci and Kucukakca 2007;Souza and Kremer 2008) and the second one is the so-called Noether gauge symmetry (NGS) approach Hussain et al 2011 We note that the Noether symmetry approach without gauge term allows one to choose the potential dynamically in the scalar-tensor gravity theory (Sanyal et al 2003), and very recently, the explicit form of the function f (R) (Capozziello and de Felice 2008;Vakili 2008). For this form of f (R), cosmological solutions of FRW metric can describe the accelerated period of the universe.…”