Tracker and scaling solutions in DHOST theories
Abstract
In quadraticorder degenerate higherorder scalartensor (DHOST) theories compatible with gravitationalwave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by ϕ ˙ /H^{p} = constant , where ϕ ˙ is the time derivative of a scalar field ϕ, H is the Hubble expansion rate, and p is a constant. While the tracker is present up to the cubicorder Horndeski Lagrangian L =c_{2} X c_{3}^{X (p  1) / (2 p)} □ ϕ, where c_{2} ,c_{3} are constants and X is the kinetic energy of ϕ, the DHOST interaction breaks this structure for p ≠ 1. Even in the latter case, however, there exists an approximate tracker solution in the early cosmological epoch with the nearly constant field equation of state w_{ϕ} =  1  2 p H ˙ / (3H^{2}). The scaling solution, which corresponds to p = 1, is the unique case in which all the terms in the field density ρ_{ϕ} and the pressure P_{ϕ} obey the scaling relation ρ_{ϕ} ∝P_{ϕ} ∝H^{2}. Extending the analysis to the coupled DHOST theories with the fielddependent coupling Q (ϕ) between the scalar field and matter, we show that the scaling solution exists for Q (ϕ) = 1 / (μ_{1} ϕ +μ_{2}), where μ_{1} and μ_{2} are constants. For the constant Q, i.e., μ_{1} = 0, we derive fixed points of the dynamical system by using the general Lagrangian with scaling solutions. This result can be applied to the model construction of latetime cosmic acceleration preceded by the scaling ϕmatterdominated epoch.
 Publication:

Physics Letters B
 Pub Date:
 March 2019
 DOI:
 10.1016/j.physletb.2019.01.009
 Bibcode:
 2019PhLB..790..167F