Abstract
We determine exact and analytic solutions of the gravitational field equations in Einstein–aether scalar model field with a Bianchi I background space. In particular, we consider nonlinear interactions of the scalar field with the aether field. For the model under consideration we can write the field equations by using the minisuperspace description. The point-like Lagrangian of the field equations depends on three unknown functions. We derive conservation laws for the field equations for specific forms of the unknown functions such that the field equations are Liouville integrable. Furthermore, we study the evolution of the field equations and the evolution of the anisotropies by determining the equilibrium points and analyzing their stability.
Highlights
According to the cosmological principle, the universe is homogeneous and isotropic in large scales
In the following we are interested on the exact solutions of Bianchi I spacetimes in Einstein–aether theory with a scalar field interacting with the aether field
We apply the same procedure as before, where we find that the reduced dynamical system admits linear conservation laws for the following sets of the unknown functions {F (ζ ) = F0, U (ζ ) = U0}, F (ζ ) = F0e−F1ζ, U (ζ ) = 0 and
Summary
According to the cosmological principle, the universe is homogeneous and isotropic in large scales. Exact and analytic solutions of isotropic and homogeneous spacetimes in Einstein–aether scalar field cosmology are presented in [56,65,66,67]. In the following we are interested on the exact solutions of Bianchi I spacetimes in Einstein–aether theory with a scalar field interacting with the aether field. From such analysis we can extract information for the evolution of the field equations and for the main phases of the cosmological history For this analysis one can apply linearization around equilibrium points, monotonic principle [68], the invariant manifold theorem [69,70,71,72,73], the center manifold theorem [69,70,71,74], and normal forms theory [69,70,71].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
