Scalar field, nonminimal coupling, and cosmology

Abstract

We study the dynamics of a flat Friedmann-Robertson-Walker universe filled with a self-interacting scalar field nonminimally coupled to the gravitational field. Dynamical equations for the system can be derived from a pointlike Lagrangian. For this system an additional Nother symmetry exists provided that the coupling constant 6 is equal to 0 or i. When l= $ the scalar potential has to be constant. In this case we obtain an exact solution. We also analyze the behavior of the scalar field when S f 0, i .Most of the considered solutions are unphysical but there exists a very interesting case in which the effective cosmological constant is rapidly changing, which might lead to inflation.

Unified cosmology with scalar–tensor theory of gravity

“…Over the decades, Noether symmetry has been found to play important roles in explaining the cosmic evolution [24][25][26][27][28][29][30][31][32]. However, for a non-minimally coupled scalar-tensor theory of gravity, a metric independent conserved current is admissible directly from the field equations in general, which is not realized from Noether symmetry [33][34][35][36].…”

Scale factor dualities in anisotropic cosmologies

“…In that paper the existence of point symmetries in the cosmological field equations was considered. A point symmetry of a set of coupled differential equations may be identified by defining a vector field [38,42,43] X ≡ X n ∂ ∂q n + dX n dt When a cosmological constant is present, it can be shown that point symmetries only exist in the field equations of the Brans-Dicke theory and, moreover, that such symmetries arise in types I, II, VI 0 and VII 0 , but not for the types VIII and IX [41]. It is interesting that the same class A types admit duality symmetries and this suggests that these dualities may be related to the point symmetries.…”

Tomographic representation of minisuperspace quantum cosmology and noether symmetries

“…In particular, it has been shown that symmetries can play an important role to select viable cosmological models [18][19][20][21]. In the framework of the so-called Noether Symmetry Approach [21][22][23] it is possible, in principle, to find out cyclic variables related to conserved quantities and then to reduce cosmological dynamics.…”