The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions

TL;DR

This paper derives the most general form of the Horndeski Lagrangian that admits cosmological scaling solutions, which could help address the coincidence problem by making the matter-dark energy ratio independent of initial conditions.

Contribution

It identifies the general form of the coupled Horndeski Lagrangian that allows for cosmological scaling solutions, independent of specific model details.

Findings

Horndeski Lagrangian equals scalar field pressure in FRW metric

Derived the most general Lagrangian form for scaling solutions

Scaling solutions can explain the matter-dark energy ratio stability

Abstract

We consider the general scalar field Horndeski Lagrangian coupled to matter. Within this class of models, we present two results that are independent of the particular form of the model. First, we show that in a Friedmann-Robertson-Walker metric the Horndeski Lagrangian coincides with the pressure of the scalar field. Second, we employ the previous result to identify the most general form of the Lagrangian that allows for cosmological scaling solutions, i.e. solutions where the ratio of matter to field density and the equation of state remain constant. Scaling solutions of this kind may help solving the coincidence problem since in this case the presently observed ratio of matter to dark energy does not depend on initial conditions, but rather on the theoretical parameters.