2015 # Dynamical analysis in scalar field cosmology

**Abstract:** We give a general method to find exact cosmological solutions for scalar-field dark energy in the presence of perfect fluids. We use the existence of invariant transformations for the Wheeler De Witt (WdW) equation. We show that the existence of a point transformation under which the WdW equation is invariant is equivalent to the existence of conservation laws for the field equations, which indicates the existence of analytical solutions. We extend previous work by providing exact solutions for the Hubble para…

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“…This means that the theory provides us with a cosmological constant term, a dust term and a stiff fluid, equivalently with that of the minimally coupled scalar field [60].…”

confidence: 99%

“…This means that the theory provides us with a cosmological constant term, a dust term and a stiff fluid, equivalently with that of the minimally coupled scalar field [60].…”

confidence: 99%

“…Recently the same analysis has been performed and for a general perfect fluid with nonzero equation of state parameter [57], whereas for some locally rotational spacetimes the Noether point symmetry classification of f (R)-cosmology can be found in [60]. Some other f (R)-models with closed-form solutions can be found in [61], while the application of point transformations in f (R)-gravity in static spherically symmetric spacetimes can be found in [62,63] Another geometric selection rule which is based upon the group invariant transformations of the Wheeler-DeWitt equations was introduced in [64]. It has been shown that the existence of a Lie point symmetry for the WheelerDeWitt equation is equivalent with the existence of a Noetherian conservation law for the classical field equations.…”

confidence: 99%

“…Furthermore, following the method which was established in [19] for scalar field cosmology with a matter source, we determine Noetherian conservation laws for the field equations. The existence of the new conservation laws implies that the field equations are Liouville integrable and with the method of separation of variables we write the analytical solution of the model.…”

confidence: 99%