2014 # 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 corr…

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“…• (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:…”

confidence: 99%

“…• (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:…”

confidence: 99%

“…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.…”

confidence: 95%

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

confidence: 99%

“…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.…”

mentioning

confidence: 99%