N. Dimakis

Lie point and variational symmetries in minisuperspace Einstein gravity

We consider the application of the theory of symmetries of coupled ordinary differential equations to the case of reparametrization invariant Lagrangians quadratic in the velocities; such Lagrangians encompass all minisuperspace models. We find that, in order to acquire the maximum number of possibly existing symmetry generators, one must (a) consider the lapse N(t) among the degrees of freedom and (b) allow the action of the generator on the Lagrangian and/or the equations of motion to produce a multiple of the constraint, rather than strictly zero. The result of this necessary modification of the standard theory (concerning regular systems) is that the Lie point symmetries of the equations of motion are exactly the variational symmetries (containing the time reparametrization symmetry) plus the well known scaling symmetry. These variational symmetries are seen to be the simultaneous conformal Killing fields of both the metric and the potential, thus coinciding with the conditional symmetries defined in phase space. In a parametrization of the lapse for which the potential becomes constant, the generators of the aforementioned symmetries become the Killing fields of the scaled supermetric and its homothetic field, respectively.

Noether analysis of Scalar-Tensor Cosmology

A scalar--tensor theory of gravity, containing an arbitrary coupling function

Minisuperspace canonical quantization of the Reissner-Nordström black hole via conditional symmetries

F(\phi)

Noether symmetries and stability of ideal gas solutions in Galileon cosmology

and a general potential

General Analytic Solutions of Scalar Field Cosmology with Arbitrary Potential

V(\phi)

Integrability and chemical potential in the (3 + 1)-dimensional Skyrme model

, is considered in the context of a spatially flat FLRW model. The use of reparametrization invariance enables a particular lapse parametrization in which the mini--superspace metric completely specifies the dynamics of the system. A requirement of existence of the maximal possible number of autonomous integrals of motion is imposed. This leads to a flat mini--superspace metric realized by a particular relation between the coupling function and the potential. The space of solutions is completely described in terms of the three autonomous integrals of motion constructed by the Killing fields of the mini--supermetric and an additional rheonomous emanating from the homothetic field. The solutions contain the arbitrary function which remains after the imposition of the relation between

Variational contact symmetries of constrained Lagrangians

F(\phi)

(Compactified) black branes in four dimensional

and

f(R)

V(\phi)

-gravity

. To exemplify the use of the general results, we select some particular cases and study their physical implications through an effective energy--momentum tensor, which tends out to be that of a perfect fluid.