Reconstruction in the Horndeski theory within the scope of the Bianchi I cosmology

Abstract

In this paper, [R. K. Muharlyamov and T. N. Pankratyeva, Eur. Phys. J. Plus 136, 590 (2021)] we have proposed a reconstruction method for the kinetic gravity braiding theory in the framework of the flat Friedman–Robertson–Walker spacetime. Here, we develop this method in the Bianchi I spacetime model for a subclass of the Horndeski theory: [Formula: see text], [Formula: see text], [Formula: see text]. The Hubble parameter [Formula: see text] and the canonical kinetic term [Formula: see text] are set a priori. The choice of the function [Formula: see text] determines the anisotropic properties of the Universe. This makes it possible to provide believable anisotropy. The presented method allows for a realistic model of the Universe to simply reconstruct some scalar field theory. Reconstruction example is given for anisotropic model of a post-inflationary transition to the radiation-dominated phase. The model is investigated for the absence ghosts and Laplacian instabilities.