Supersymmetric quantum mechanics for Bianchi class A models

Abstract

In this work we present cosmological quantum solutions for all Bianchi Class A cosmological models obtained by means of supersymmetric quantum mechanics . We are able to write one general expression for all bosonic components occuring in the Grassmann expansion of the wave function of the Universe for this class of models. These solutions are obtained by means of a more general ansatz for the so-called master equations.

Variable equation of state for Bianchi type-VI0 dark energy models

“…Though Bianchi type-I universe is the prime candidate for studying the possible effects of an anisotropy in the early universe on present-day observations, there are few other models (for example, B-VI 0 ), which describe an anisotropic space-time and generate particular interest among physicists (Weaver 2000; Ibáñez et al 1995;Socorro and Medina 2000;Radinschi 2001). Pradhan and Bali (2008) and Bali et al (2008) have studied B-VI 0 space-time in connection with massive strings.…”

Time-dependent toroidal compactification proposals and the Bianchi type II model: Classical and quantum solutions

“…When we compare this solution with the general solution found using separation of variables, we obtain that this corresponds to the asymptotic behavior of this solution, that in some way corresponds to the lowest-order WKB approximation [27,34], which is shown in the Figure 1, where the picks of the plot follow the classical trajectory β + = − √ 3β − − |Ω|, which corresponds at zero phase in the probability amplitude in both solutions; in other words, this wave function (52) has translational symmetry along the last trajectory mentioned. Also is presented a shifting to the wave function in the β − axe in the −∞ direction, how is shown in the graphics to the probability density |Θ| 2 in both sectors (full anisotropy and lowest-order WKB approximation).…”

“…In order to have the best candidates for quantum solutions become those that have a damping behavior with respect to the scale factor, represented in our model with the Ω parameter, in this way we dropped in the full solution the modified Bessel function I ν (z) and the term e S in the Bohm's solution. We obtain the relation between these both physical solutions in the asymptotic behavior to the modified Bessel function for large argument, (40) and it is compared with the Bohm's solutions, (52), who us indicate that is the lowest-order WKB approximation how is indicate in the literature [27,34]. The unnormalized probability density which is shown in the Figure 1, show that the picks of the plot follow the classical trajectory β + = − √ 3β − − |Ω|, which corresponds at zero phase in the probability amplitude in both solutions; in other words, this wave function (52) has translational symmetry along the last trajectory mentioned.…”

Scalar potentials with multi-scalar fields from quantum cosmology and supersymmetric quantum mechanics

“…The exact quantum solutions to the Wheeler-DeWitt equation were found using the Bohmian scheme [16] alternative method to test the obtained family of potentials for the inflation era, such tools restricted the potentials even further and only to an exponential behavior. This method was also used to obtain the SUSY quantum solution for all Bianchi class A Models [31]. Also this class of solutions appears in the excellent books by Moniz [34], where the author present the review of solutions in quantum and supersymmetric cosmology for some cosmological models, including the Bianchi Class A cosmological models, until 2009 year.…”