Towards scaling cosmological solutions with full coupled Horndeski Lagrangian: the KGB model

TL;DR

This paper explores the most general scalar-tensor Lagrangian within the Horndeski class that admits cosmological scaling solutions, aiming to address the coincidence problem by analyzing the conditions for such solutions.

Contribution

It identifies the most general form of the KGB Lagrangian allowing for cosmological scaling solutions and demonstrates the impossibility of uniting matter era and scaling attractor in a single solution.

Findings

Derived the general Lagrangian form for scaling solutions.

Showed that matter era and scaling attractor cannot coexist in a single solution.

Extended previous results within the Horndeski class.

Abstract

We study a general scalar field Lagrangian coupled with matter and linear in $\Box\phi$ (also called KGB model). Within this class of models, we find 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. Extending previous results we find that it is impossible to join in a single solution a matter era and the scaling attractor. This is an additional step towards finding the most general scaling Lagrangian within the Horndeski class, i.e. general scalar-tensor models with second order equations of motion.