Exact solution of the Einstein–Skyrme model in a Kantowski–Sachs spacetime

Abstract

We consider a Skyrme fluid with a constant radial profile in locally rotational Kantowski-Sachs spacetime. The Skyrme fluid is an anisotropic fluid with zero heat flux and with an equation of state parameter wS that |ws| ≤ 1 3. From the Einstein field equations we define the Wheeler-DeWitt equation. For the last equation we perform a Lie symmetry classification and we determine the invariant solutions for the wavefunction of the model. Moreover from the Lie symmetries of the Wheeler-DeWitt equation we construct Noetherian conservation laws for the field equations which we use in order to write the solution in closed form. We show that all pf the cosmological parameters are expressed in terms of the scale factor of the two dimensional sphere of the Kantowski-Sachs spacetime. Finally from the application of Noether's theorem for the Wheeler-DeWitt equation we derive conservation laws for the wavefunction of the universe.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

Cosmological Einstein-Skyrme solutions with nonvanishing topological charge

“…(32a) is an ODE for u(t) that can be directly solved. If Λ > 0, (26) implies ρ ∼ ρ 0 e (ω/2)t for t → ∞. In this limit, Eq.…”

“…In order to examine the stability properties of the static Einstein universe around the isotropic solutions (26) and (27), let us consider the critical points for the field equations (12a)-(12c). The critical points of the Hamiltonian (19) are given by the conditions ∂V ef f ∂a = 0 and…”

“…Regular particle-like configurations [22] and dynamical properties of the system have also been investigated numerically [23]. Even in the sector with vanishing topological charge the cosmological consequences of the Skyrme model are quite interesting [24][25][26].…”

Dynamical system analysis of Einstein–Skyrme model in a Kantowski–Sachs spacetime

“…Further, for line-element (5), the modified field equation (3) is expressed in terms of the parameters, {A, B} (reference [5]),…”

“…On the other hand for variable radial profile both anisotropic Bianchi I and KS model have been investigated only numerically and for the existence of the solutions there should be restrictions both on the cosmological constant as well as on the Skyrme coupling. Recently, Paliathanasis et al [5] have considered this Skyrme model in KS space-time for studying quantum cosmology. Formulating the Whealer-Dewitt equation, they have performed the Lie symmetry classification and have obtained the invariant solutions for the wave function.…”