TY - JOUR

T1 - Tracker and scaling solutions in DHOST theories

AU - Frusciante, Noemi

AU - Kase, Ryotaro

AU - Koyama, Kazuya

AU - Tsujikawa, Shinji

AU - Vernieri, Daniele

N1 - Funding Information:
ST thanks warm hospitalities during his stay in University of Portsmouth at which a part of this work was done. The research of NF is supported by Fundação para a Ciência e a Tecnologia (FCT) through national funds (UID/FIS/04434/2013), by FEDER through COMPETE2020 (POCI-01-0145-FEDER-007672) and by FCT project “DarkRipple – Spacetime ripples in the dark gravitational Universe” with ref. number PTDC/FIS-OUT/29048/2017. RK is supported by the Grant-in-Aid for Young Scientists B of the JSPS No. 17K14297. KK is supported by the UK STFC grant ST/N000668/1 and the European Research Council under the European Union's Horizon 2020 programme (grant agreement No. 646702 “CosTesGrav”). ST is supported by the Grant-in-Aid for Scientific Research Fund of the JSPS No. 16K05359 and MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Cosmic Acceleration” (No. 15H05890). DV acknowledges financial support from the FCT Project No. UID/FIS/00099/2013.
Funding Information:
ST thanks warm hospitalities during his stay in University of Portsmouth at which a part of this work was done. The research of NF is supported by Fundação para a Ciência e a Tecnologia (FCT) through national funds ( UID/FIS/04434/2013 ), by FEDER through COMPETE2020 ( POCI-01-0145-FEDER-007672 ) and by FCT project “DarkRipple – Spacetime ripples in the dark gravitational Universe” with ref. number PTDC/FIS-OUT/29048/2017 . RK is supported by the Grant-in-Aid for Young Scientists B of the JSPS No. 17K14297 . KK is supported by the UK STFC grant ST/N000668/1 and the European Research Council under the European Union's Horizon 2020 programme (grant agreement No. 646702 “CosTesGrav”). ST is supported by the Grant-in-Aid for Scientific Research Fund of the JSPS No. 16K05359 and MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Cosmic Acceleration” (No. 15H05890 ). DV acknowledges financial support from the FCT Project No. UID/FIS/00099/2013 .
Publisher Copyright:
© 2019 The Author(s)

PY - 2019/3/10

Y1 - 2019/3/10

N2 - In quadratic-order degenerate higher-order scalar–tensor (DHOST) theories compatible with gravitational-wave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by ϕ˙/Hp=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 cubic-order Horndeski Lagrangian L=c2X−c3X(p−1)/(2p)□ϕ where c2,c3 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˙/(3H2). 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∝H2. Extending the analysis to the coupled DHOST theories with the field-dependent coupling Q(ϕ) between the scalar field and matter, we show that the scaling solution exists for Q(ϕ)=1/(μ1ϕ+μ2), where μ1 and μ2 are constants. For the constant Q, i.e., μ1=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 late-time cosmic acceleration preceded by the scaling ϕ-matter-dominated epoch.

AB - In quadratic-order degenerate higher-order scalar–tensor (DHOST) theories compatible with gravitational-wave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by ϕ˙/Hp=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 cubic-order Horndeski Lagrangian L=c2X−c3X(p−1)/(2p)□ϕ where c2,c3 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˙/(3H2). 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∝H2. Extending the analysis to the coupled DHOST theories with the field-dependent coupling Q(ϕ) between the scalar field and matter, we show that the scaling solution exists for Q(ϕ)=1/(μ1ϕ+μ2), where μ1 and μ2 are constants. For the constant Q, i.e., μ1=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 late-time cosmic acceleration preceded by the scaling ϕ-matter-dominated epoch.

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U2 - 10.1016/j.physletb.2019.01.009

DO - 10.1016/j.physletb.2019.01.009

M3 - Article

AN - SCOPUS:85060326230

SN - 0370-2693

VL - 790

SP - 167

EP - 175

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

ER -