Classical and quantum exact solutions for the anisotropic Bianchi type I in multi-scalar field cosmology with an exponential potential driven inflation

Abstract

The anisotropic Bianchi type I in multi-scalar field cosmology is studied with a particular potential of the form $\mathrm{V}={\mathrm{V}}_0{\mathrm{e}}^{-\left[{\lambda }_1{\varphi }_1+\cdots +{\lambda }_{\mathrm{n}}{\varphi }_{\mathrm{n}}\right]},$ which emerges as a condition between the time derivatives of their corresponding momenta. Using the Hamiltonian formalism for the inflation epoch with a quintessence framework we find the exact solutions for the Einstein-Klein-Gordon (EKG) system with different scenarios specified by the parameter ${\lambda }^2={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\lambda }_{\mathrm{i}}^2$. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables and suitable ansatz.

12 pages, 1 table. currently under review. arXiv admin note: substantial text overlap with arXiv:1811.11565

References in corpus (5)

• Theory of cosmological perturbations in an anisotropic universe
• Predictions from an anisotropic inflationary era
• Stability of multi-field cosmological solutions
• Effect of reheating on predictions following multiple-field inflation
• Bianchi type I model with two interacting scalar fields