Abstract
The two-loop (order α′) β-function equations, which are equivalent to the equations of motion of α′-corrected string effective action, are considered for anisotropic homogeneous space–times. These equations are solved for all Bianchi-type models in two schemes of effective action, namely R2 and Gauss–Bonnet schemes with zero cosmological constant and then the metric, dilaton and B-field are found at α′ perturbative corrections.
Highlights
The application of low energy, tree-level string effective action for describing the evolution of early universe with a very low coupling, g = e−φ, and curvature is well accepted [1, 2, 3, 4]
In the σ-model context, if one works with the higher order corrections in effective field theory and the equations of motions, it is convenience to transform by the field redefinitions to the Gauss-Bonnet effective action which has no higher than second derivative in its field equations and is free of ghost
The anisotropic homogeneous space-times have been emerged in the context of string cosmology during the search of backgrounds for describing the early universe evolution
Summary
The two-loop β-functions and the possible higher order α′-correction terms to the string effective actions are investigated in [17, 18] These corrections are generically quadratic type terms and give higher order time derivative field equations. The α′-corrected effective action is parametrized by 8 essential coefficients and it is easy to relate it to the Gauss-Bonnet effective action by an appropriate field redefinition and using the leading order equations of motion [17]. In the σ-model context, if one works with the higher order corrections in effective field theory and the equations of motions, it is convenience to transform by the field redefinitions to the Gauss-Bonnet effective action which has no higher than second derivative in its field equations and is free of ghost. Λ is required to be considered for expanding universe at late times
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