Two scalar field cosmology: Conservation laws and exact solutions

Abstract

We consider the two scalar field cosmology in a FRW spatially flat spacetime where the scalar fields interact both in the kinetic part and the potential. We apply the Noether point symmetries in order to define the interaction of the scalar fields. We use the point symmetries in order to write the field equations in the normal coordinates and we find that the Lagrangian of the field equations which admits at least three Noether point symmetries describes linear Newtonian systems. Furthermore, by using the corresponding conservation laws we find exact solutions of the field equations. Finally, we generalize our results to the case of N scalar fields interacting both in their potential and their kinematic part in a flat FRW background.Comment: 17 pages, to be published in Phys. Rev.

Dynamically Generated Inflationary ΛCDM

“…• (i) U eff (u) (37) has an almost flat region for large positive u: U eff (u) 2Λ 0 for large u. This almost flat region correspond to "early" universe' inflationary evolution with energy scale 2Λ 0 as it will be evident from the autonomous dynamical system analysis of the cosmological dynamics in Section 4; • (ii) U eff (u) (37) has has a stable minimum for a small finite value u = u * : ∂U eff ∂u = 0 for u ≡ u * , where:…”

Closed-form solutions of the Wheeler–DeWitt equation in a scalar-vector field cosmological model by Lie symmetries

“…where we can see that R (2) = 0, when f (φ) is given by (28), and there does not exist any function f (φ), where R (2) = const = 0. Recall that all two dimensional spaces are Einstein spaces and conformally flat.…”

“…Hence we conclude that the WDW Eq. (19) can admits Lie symmetries, if and only if, f (φ) is given by (28).…”

“…Numerous applications of Noether's theorem 1 in general relativity and cosmology are those concerned with the following form of action [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] …”

Quantum cosmology for non-minimally coupled scalar field in FLRW space–time: A symmetry analysis

“…So cosmologists have been trying for dynamical dark energy models having a variable equation of state (with negative energy) [23] to accommodate the observational evidences. In the present work, the dynamical dark energy is chosen as a non-minimally coupled scalar field having self interacting potential [24]- [30]. The evolution equations of the present cosmological model are highly non-linear and coupled second order differential equations.…”