157 research outputs found
Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions
In this paper, we present a complete Noether Symmetry analysis in the
framework of scalar-tensor cosmology. Specifically, we consider a non-minimally
coupled scalar field action embedded in the FLRW spacetime and provide a full
set of Noether symmetries for related minisuperspaces. The presence of
symmetries implies that the dynamical system becomes integrable and then we can
compute cosmological analytical solutions for specific functional forms of
coupling and potential functions selected by the Noether Approach.Comment: 9 pages, accepted for publication by Phys. Rev.
Generalizing the autonomous Kepler Ermakov system in a Riemannian space
We generalize the two dimensional autonomous Hamiltonian Kepler Ermakov
dynamical system to three dimensions using the sl(2,R) invariance of Noether
symmetries and determine all three dimensional autonomous Hamiltonian Kepler
Ermakov dynamical systems which are Liouville integrable via Noether
symmetries. Subsequently we generalize the autonomous Kepler Ermakov system in
a Riemannian space which admits a gradient homothetic vector by the
requirements (a) that it admits a first integral (the Riemannian Ermakov
invariant) and (b) it has sl(2,R) invariance. We consider both the
non-Hamiltonian and the Hamiltonian systems. In each case we compute the
Riemannian Ermakov invariant and the equations defining the dynamical system.
We apply the results in General Relativity and determine the autonomous
Hamiltonian Riemannian Kepler Ermakov system in the spatially flat Friedman
Robertson Walker spacetime. We consider a locally rotational symmetric (LRS)
spacetime of class A and discuss two cosmological models. The first
cosmological model consists of a scalar field with exponential potential and a
perfect fluid with a stiff equation of state. The second cosmological model is
the f(R) modified gravity model of {\Lambda}_{bc}CDM. It is shown that in both
applications the gravitational field equations reduce to those of the
generalized autonomous Riemannian Kepler Ermakov dynamical system which is
Liouville integrable via Noether integrals.Comment: Reference [25] update, 21 page
Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries
We determine the autonomous three dimensional Newtonian systems which admit
Lie point symmetries and the three dimensional autonomous Newtonian Hamiltonian
systems, which admit Noether point symmetries. We apply the results in order to
determine the two dimensional Hamiltonian dynamical systems which move in a
space of constant non-vanishing curvature and are integrable via Noether point
symmetries. The derivation of the results is geometric and can be extended
naturally to higher dimensions.Comment: Accepted for publication in Journal of Physics A: Math. and Theor.,13
page
Comment on Ricci Collineations for type B warped space-times
We present two counterexamples to the paper by Carot et al. in Gen. Rel.
Grav. 1997, 29, 1223 and show that the results obtained are correct but not
general.Comment: LaTex, 3 pages, Eq. (9) and reference added, typos corrected; Gen.
Rel. Grav (to appear
New Schwarzschild-like solutions in f(T) gravity through Noether symmetries
Spherically symmetric solutions for f(T) gravity models are derived by the so
called Noether Symmetry Approach. First, we present a full set of Noether
symmetries for some minisuperspace models. Then, we compute analytical
solutions and find that spherically symmetric solutions in f(T) gravity can be
recast in terms of Schwarzschild-like solutions modified by a distortion
function depending on a characteristic radius. The obtained solutions are more
general than those obtained by the usual solution methods.Comment: 10 pages, to appear in Phys. Rev.
Dynamical analysis in scalar field cosmology
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 parameter and the effective dark-energy equation of state parameter for cosmologies containing a combination of perfect fluid and a scalar field whose self-interaction potential is a power of hyperbolic functions. We find solutions explicitly when the perfect fluid is radiation or cold dark matter and determine the effects of nonzero spatial curvature. Using the Planck 2015 data, we determine the evolution of the effective equation of state of the dark energy. Finally, we study the global dynamics using dimensionless variables. We find that if the current cosmological model is Liouville integrable (admits conservation laws) then there is a unique stable point which describes the de-Sitter phase of the universe.AP acknowledges financial support of INFN. JDB acknowledges support from the STFC.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevD.91.12353
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