TY - JOUR

T1 - General formulation of cosmological perturbations in scalar-tensor dark energy coupled to dark matter

AU - Kase, Ryotaro

AU - Tsujikawa, Shinji

N1 - Funding Information:
RK is supported by the Grant-in-Aid for Young Scientists B of the JSPS No. 17K14297. ST is supported by the Grant-in-Aid for Scientific Research Fund of the JSPS No. 19K03854 and MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas "Cosmic Acceleration"(No. 15H05890).
Publisher Copyright:
© 2020 IOP Publishing Ltd and Sissa Medialab.

PY - 2020/11

Y1 - 2020/11

N2 - For a scalar field φ coupled to cold dark matter (CDM), we provide a general framework for studying the background and perturbation dynamics on the isotropic cosmological background. The dark energy sector is described by a Horndeski Lagrangian with the speed of gravitational waves equivalent to that of light, whereas CDM is dealt as a perfect fluid characterized by the number density nc and four-velocity ucμ. For a very general interacting Lagrangian f(nc, φ, X, Z), where f depends on nc, φ, X=-μ φ μ φ/2, and Z=ucμμ φ, we derive the full linear perturbation equations of motion without fixing any gauge conditions. To realize a vanishing CDM sound speed for the successful structure formation, the interacting function needs to be of the form f=-f1(φ, X, Z)nc+f2(φ, X, Z). Employing a quasi-static approximation for the modes deep inside the sound horizon, we obtain analytic formulas for the effective gravitational couplings of CDM and baryon density perturbations as well as gravitational and weak lensing potentials. We apply our general formulas to several interacting theories and show that, in many cases, the CDM gravitational coupling around the quasi de-Sitter background can be smaller than the Newton constant G due to a momentum transfer induced by the Z-dependence in f2.

AB - For a scalar field φ coupled to cold dark matter (CDM), we provide a general framework for studying the background and perturbation dynamics on the isotropic cosmological background. The dark energy sector is described by a Horndeski Lagrangian with the speed of gravitational waves equivalent to that of light, whereas CDM is dealt as a perfect fluid characterized by the number density nc and four-velocity ucμ. For a very general interacting Lagrangian f(nc, φ, X, Z), where f depends on nc, φ, X=-μ φ μ φ/2, and Z=ucμμ φ, we derive the full linear perturbation equations of motion without fixing any gauge conditions. To realize a vanishing CDM sound speed for the successful structure formation, the interacting function needs to be of the form f=-f1(φ, X, Z)nc+f2(φ, X, Z). Employing a quasi-static approximation for the modes deep inside the sound horizon, we obtain analytic formulas for the effective gravitational couplings of CDM and baryon density perturbations as well as gravitational and weak lensing potentials. We apply our general formulas to several interacting theories and show that, in many cases, the CDM gravitational coupling around the quasi de-Sitter background can be smaller than the Newton constant G due to a momentum transfer induced by the Z-dependence in f2.

KW - dark energy theory

KW - modified gravity

UR - http://www.scopus.com/inward/record.url?scp=85096488955&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85096488955&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2020/11/032

DO - 10.1088/1475-7516/2020/11/032

M3 - Article

AN - SCOPUS:85096488955

VL - 2020

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

SN - 1475-7516

IS - 11

M1 - 032

ER -