Noether symmetry approach in phantom quintessence cosmology

Abstract

In the framework of phantom quintessence cosmology, we use the Noether Symmetry Approach to obtain general exact solutions for the cosmological equations. This result is achieved by the quintessential (phantom) potential determined by the existence of the symmetry itself. A comparison between the theoretical model and observations is worked out. In particular, we use type Ia supernovae and large-scale structure parameters determined from the 2-degree Field Galaxy Redshift Survey and from the Wide part of the VIMOS-VLT Deep Survey ). It turns out that the model is compatible with the presently available observational data. Moreover we extend the approach to include radiation. We show that it is compatible with data derived from recombination and it seems that quintessence do not affect nucleosynthesis results

Dynamical analysis in scalar field cosmology

“…The latter implies that in the configuration space (minisuperspace), the first integrals are considered as "selection rules" for scalar field potentials and coupling functions in the case of modified gravity theories. The above features have inspired many authors to propose the admittance of a Noether (point or dynamical) symmetry by the field equations as a selection rule for dark-energy models, including those of modified gravity [8][9][10][11][12][13][14][15][16][17][18][19].…”

f ( R )-gravity from Killing tensors

“…On the other hand, Noether point symmetries have been introduced as a selection rule for the determination of the functional form of the potential in scalar field cosmology in [40]. Since then that method has been applied in various cosmological models and new solutions have been found (for instance see [41][42][43][44][45][46][47][48][49][50] and references cited therein). In [51] Noether symmetries were applied in the scalar field cosmological scenario as a geometric selection rule for the determination of the functional form of the potential.…”

Bianchi type I cosmology in generalized Saez–Ballester theory via Noether gauge symmetry

“…This approach gives a power-law evolutionary form of scale factor which is consistent with the astrophysical observations. Moreover the evolution of state-parameter obtained in such an approach also gives a phantom crossing behavior of dark energy [12]. The Noether symmetry approach has been applied to Bianchi cosmological models in literature: Capozziello et al [13] investigated the Bianchi universes via Noether symmetries.…”