The Equation of State of Novel Double-Field Pure K-Essence for Inflation, Dark Matter and Dark Energy

Abstract

K-essence theories are usually studied in the framework of a single scalar field ϕ. Namely, the Lagrangian of K-essence is the function of the single scalar field ϕ and its covariant derivative. However, in this paper, we explore a double-field pure K-essence, i.e., the corresponding Lagrangian is the function of covariant derivatives of double scalar fields without a dependency on scalar fields themselves. This is why we call it double-field pure K-essence. The novelty of this K-essence is that its Lagrangian contains the quotient term of the kinetic energies from the two scalar fields. This results in the presence of many interesting features; for example, the equation of state can be arbitrarily small and arbitrarily large. In comparison, the range of the equation of state for quintessence is −1 to +1. Interestingly, this novel K-essence can play the role of an inflation field, dark matter, or dark energy by appropriately selecting the expressions of Lagrangian.