Noether Symmetry Approach Research Articles

Cosmic expansion from boson and fermion fields

This paper consists in analyzing an action that describes boson and fermion fields minimally coupled to the gravity and a common matter field. The self-interaction potentials of the fields are not chosen a priori but from the Noether symmetry approach. The Noether forms of the potentials allow the boson field to play the role of dark energy and matter and the fermion field to behave as standard matter. The constant of motion and the cyclic variable associated with the Noether symmetry allow the complete integration of the field equations, whose solution produces a universe with alternated periods of accelerated and decelerated expansion.

The dark sector from interacting canonical and non-canonical scalar fields

In this work general models with interactions between two canonical scalar fields and between one non-canonical (tachyon type) and one canonical scalar field are investigated. The potentials and couplings to the gravity are selected through the Noether symmetry approach. These general models are employed to describe interactions between dark energy and dark matter, with the fields being constrained by the astronomical data. The cosmological solutions of some cases are compared with the observed evolution of the late Universe.

The Noether symmetry approach in a ‘cosmic triad’ vector field scenario

To realize the accelerations in the early and late periods of our universe, we need to specify potentials for the dominant fields. In this paper, by using the Noether symmetry approach, we try to find suitable potentials in the ‘cosmic triad’ vector field scenario. Because the equation of state parameter of dark energy has been constrained in the range of −1.21 ⩽ ω ⩽ −0.89 by observations, we derive the Noether conditions for the vector field in quintessence, phantom and quintom models, respectively. In the first two cases, constant potential solutions have been obtained. What is more, a fast decaying point-like solution with power-law potential is also found for the vector field in the quintessence model. For the quintom case, we find an interesting constraint on the field potentials, where C and are constants related to the Noether symmetry.

Noether symmetry approach in multiple scalar fields scenario

In this Letter, we find suitable potentials in the multiple scalar fields scenario by using the Noether symmetry approach. We discussed three models with multiple scalar fields: N-quintessence with positive kinetic terms, N-phantom with negative kinetic terms and N-quintom with both positive and negative kinetic terms. In the N-quintessence case, the exponential potential which could be derived from several theoretic models is obtained from the Noether conditions. In the N-phantom case, the potential V02(1−cos(3N2ϕmpl)), which could be derived from the Pseudo Nambu–Goldstone boson model, is chosen as the Noether conditions required. In the N-quintom case, we derive a relation DVϕq′=−D˜Vϕp′ between the potential forms for the quintessence-like fields and the phantom-like fields by using the Noether symmetry.

Noether symmetric minisuperspace model of f(R) cosmology

AbstractWe study the metric f(R) cosmology using Noether symmetry approach by utilizing the behavior of the corresponding Lagrangian under infinitesimal generators of the desired symmetry. The existence of Noether symmetry of the cosmological f(R) minisuperspace helps us to find out the form of f(R) function for which such symmetry exist. It is shown that the resulting form for f(R) yields a power law expansion for the cosmic scale factor. We also show that in the corresponding Noether symmetric quantum model, the solutions to the Wheeler‐DeWitt equation can be expressed as a superposition of states of the form eiS. It is shown that in terms of such wavefunctions the classical trajectories can be recovered.

Noether symmetric minisuperspace model of f(R) cosmology

We study the metric $f(R)$ cosmology using Noether symmetry approach by utilizing the behavior of the corresponding Lagrangian under infinitesimal generators of the desired symmetry. The existence of Noether symmetry of the cosmological $f(R)$ minisuperspace helps us to find out the form of $f(R)$ function for which such symmetry exist. It is shown that the resulting form for $f(R)$ yields a power law expansion for the cosmic scale factor. We also show that in the corresponding Noether symmetric quantum model, the solutions to the Wheeler-DeWitt equation can be expressed as a superposition of states of the form $e^{iS}$. It is shown that in terms of such wavefunctions the classical trajectories can be recovered.

Noether symmetry approach in phantom quintessence cosmology

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.

Noether symmetric [formula omitted] quantum cosmology and its classical correlations

We quantize a flat FRW cosmology in the context of the f(R) gravity by Noether symmetry approach. We explicitly calculate the form of f(R) for which such symmetries exist. It is shown that the existence of a Noether symmetry yields a general solution of the Wheeler–DeWitt equation where can be expressed as a superposition of states of the form eiS. In terms of Hartle criterion, this type of wave function exhibits classical correlations, i.e. the emergent of classical universe is expected due to the oscillating behavior of the solutions of Wheeler–DeWitt equation. According to this interpretation we also provide the Noether symmetric classical solutions of our f(R) cosmological model.

Palatini [formula omitted] cosmology and Noether symmetry

We study Palatini f(R) cosmology using Noether symmetry approach for the matter-dominated universe. In order to construct a point-like Lagrangian in the flat FRW space–time, we use the dynamical equivalence between f(R) gravity and scalar–tensor theories. The existence of Noether symmetry of the cosmological f(R) Lagrangian helps us to find out the form of f(R) and the exact solutions for cosmic scale factor. We show that this symmetry always exist for f(R)∼Rn and the Noether constant is a function of the Newton's gravitational constant and the current matter content of the universe.

Scalar–tensor cosmology with [formula omitted] curvature correction by Noether symmetry

We discuss scalar–tensor cosmology with an extra R−1 correction by the Noether symmetry approach. The existence of such a symmetry selects the forms of the coupling ω(φ), of the potential V(φ) and allows to obtain physically interesting exact cosmological solutions.

NOETHER SYMMETRY APPROACH TO SCALAR-FIELD-DOMINATED COSMOLOGY WITH DYNAMICALLY EVOLVING G AND Λ

This paper studies the cosmological equations for a scalar field φ in the framework of a quantum gravity modified Einstein–Hilbert Lagrangian where G and Λ are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Λ = Λ(G) and the potential V = V(φ) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling.

Spherically symmetric solutions in f(R) gravity via the Noether symmetry approach

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether symmetry approach. A general formalism in the metric framework is developed considering a point-like f(R) Lagrangian where spherical symmetry is required. Examples of exact solutions are given.

Noether symmetry approach in pure gravity with variable G and Λ

We find exact cosmological solutions when the Newton parameter and the cosmological term dynamically evolve in a renormalization-group improved Hamiltonian approach. In our derivation we use the Noether symmetry approach, leading to an interesting variable transformation which yields exact and general integration of the cosmological equations. The functional dependence of Λ on G is determined by the method itself, therefore generalizing previous results on symmetry principles in cosmology. We find new functional relations between Λ and G, jointly with power-law inflation for pure gravity.

Noether symmetry approach in matter-dominated cosmology with variable G and Λ

In the framework of renormalization-group improved cosmologies, we use the Noether symmetry approach to get exact and general integration of the matter-dominated cosmological equations. This is performed by using an expression of Λ = Λ (G) determined by the method itself. We also work out a comparison between such a model and the concordance ΛCDM model as to the magnitude–redshift relationship, hence showing that no appreciable differences occur.

Noether Symmetry Study in General Scalar Tensor Theory

We present the gravitational coupling function and potential function in a General Scalar Tensor Theory from Noether symmetry approach. Some exact cosmological solutions are presented in the spatially flat, homogeneous and isotropic background. The solutions are exponentially expanding without any graceful exit from inflation. Also the solutions asymptotically reduce to Einstein's theory with finite value of the coupling function supporting the earlier claim of Santiago et al. Further it is shown that in a particular case the effective Newtonian constant is determined by the effective potential of the scalar field.

Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach

Higher-order corrections of Einstein-Hilbert action of general relativity can be recovered by imposing the existence of a Noether symmetry to a class of theories of gravity where Ricci scalar R and its d'Alembertian $\Box R$ are present. In several cases, it is possible to get exact cosmological solutions or, at least, to simplify dynamics by recovering constants of motion. The main result is that a Noether vector seems to rule the presence of higher-order corrections of gravitaty.

Nonminimal coupling and cosmic no-hair theorem

We give (sufficient) conditions for the extension of the cosmic no-hair conjecture to nonminimally coupled scalar-tensor theories in which the coupling is not given a priori. Furthermore, in a Friedman-Robertson-Walker spacetime, we get exact solutions for such theories using the so-called Noether symmetry approach. The results are interesting because we obtain behaviours able to avoid the initial singularity.