Abstract
We present, for the first time, the quantization process for the Einstein-aether scalar field cosmology. We consider a cosmological theory proposed as a Lorentz violating inflationary model, where the aether and scalar fields interact through the assumption that the aether action constants are ultra-local functions of the scalar field. For this specific theory there is a valid minisuperspace description which we use to quantize. For a particular relation between the two free functions entering the reduced Lagrangian the solution to the Wheeler–DeWitt equation as also the generic classical solution are presented for any given arbitrary potential function.
Highlights
Scalar fields play a prominent role in modern cosmology
In this work we realize this idea for the case of a spatially flat FLRW universe and a scalar field with arbitrary potential and we present, for the first time, the quantization of the Einsteinaether scalar field cosmology; we derive the generic algebraic classical solution to the field equations
We lastly proceed with the presentation of the classical solution for the gravitational field equations for arbitrary potential
Summary
Scalar fields play a prominent role in modern cosmology. The main mechanism for the description of the inflation is based on the domination of a scalar field potential, known as inflaton [6]. One can contemplate a non-trivial coupling of the scalar to the aether field by allowing the coefficients of its kinetic action to be functions of the scalar field [24] Such a theory has been proposed before as an alternative inflationary model which provides two periods of inflation [25]. 2, we define the cosmological model that we focus on in this work; it is the Einstein-aether scalar field cosmology in a homogeneous and isotropic geometric background space where only quadratic terms of the derivatives exist in the Action Integral. The latter property is essential for enabling a minisuperspace description of the gravitational field equations.
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