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Abstract
In quarticorder 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})/(^{2p})□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 wφ=−1−2pH˙/(3H^{2}). The scaling solution, which corresponds to p=1, is the unique case in which all the terms in the field density ρφ and the pressure Pφ obey the scaling relation ρφ∝Pφ∝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.
Original language  English 

Pages (fromto)  167175 
Number of pages  9 
Journal  Physical Letters B 
Volume  790 
Early online date  17 Jan 2019 
DOIs  
Publication status  Published  10 Mar 2019 
Keywords
 grqc
 astroph.CO
 hepph
 hepth
 RCUK
 STFC
 ST/N000668/1
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Frusciante, N. (Creator), Kase, R. (Creator), Koyama, K. (Creator), Tsujikawa, S. (Creator) & Vernieri, D. (Creator), Elsevier BV, 5 Jan 2019
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