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

Abstract

For a scalar field $\varphi$ 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 $n_c$ and four-velocity $u_c^{\mu }$. For a very general interacting Lagrangian $f(n_c,\varphi ,X,Z)$, where $f$ depends on $n_c$, $\varphi$, $X=-{\partial }^{\mu }\varphi {\partial }_{\mu }\varphi /2$, and $Z=u_c^{\mu }{\partial }_{\mu }\varphi$, 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 $f=-f_1(\varphi ,X,Z)n_c+f_2(\varphi ,X,Z)$. 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 $f_2$.

26 pages, 1 figure, published version

References in corpus (28)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Dynamics of dark energy
• Cosmology and the Fate of Dilatation Symmetry
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A
• Beyond the Cosmological Standard Model
• Covariant Galileon
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Healthy theories beyond Horndeski
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• Measuring the dark side (with weak lensing)
• Large-scale instability in interacting dark energy and dark matter fluids
• Indications of a late-time interaction in the dark sector
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Consequences of dark matter-dark energy interaction on cosmological parameters derived from SNIa data
• Probing the interaction between dark matter and dark energy in the presence of massive neutrinos
• Effective Field Theory of Cosmic Acceleration: constraining dark energy with CMB data
• The Parameterized Post-Friedmannian Framework for Interacting Dark Energy Theories
• Do we have any hope of detecting scattering between dark energy and baryons through cosmology?
• Interacting quintessence from a variational approach Part II: derivative couplings
• Interacting quintessence from a variational approach Part I: algebraic couplings
• Understanding the suppression of structure formation from dark matter$\unicode{x2013}$dark energy momentum coupling
• Scalar-Fluid interacting dark energy: cosmological dynamics beyond the exponential potential
• On cosmological signatures of baryons-dark energy elastic couplings
• Suppressed cosmic growth in coupled vector-tensor theories

Cited by in corpus (23)

• Late time interacting cosmologies and the Hubble constant tension
• Probing elastic interactions in the dark sector and the role of $S_8$
• Stability of scalar perturbations in scalar-torsion $f(T,\varphi )$ gravity theories in the presence of a matter fluid
• Velocity-dependent interacting dark energy and dark matter with a Lagrangian description of perfect fluids
• Stealth dark energy in scordatura DHOST theory
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Cosmological perturbations in the interacting dark sector: Mapping fields and fluids
• J-PAS: forecasts on interacting vacuum energy models
• KiDS-1000 Cosmology: machine learning -- accelerated constraints on Interacting Dark Energy with COSMOPOWER
• IDECAMB: an implementation of interacting dark energy cosmology in CAMB
• Cosmic sign-reversal: non-parametric reconstruction of interacting dark energy with DESI DR2
• Measuring dark energy with expansion and growth
• The 6x2pt method: supernova velocities meet multiple tracers
• Observational constraints on interactions between dark energy and dark matter with momentum and energy transfers
• Effective field theory of coupled dark energy and dark matter
• Cosmological perturbations for ultra-light axion-like particles in a state of Bose-Einstein condensate
• Vainshtein screening in Horndeski theories nonminimally and kinetically coupled to ordinary matter
• Constraints on Multicomponent Dark Energy from Cosmological Observations
• Cosmological dynamical systems of non-minimally coupled fluids and scalar fields
• Revisiting observational constraints on coupled exponential quintessence with energy and momentum transfers: degeneracy with massive neutrinos
• Dynamical analysis of $k$-essence cosmology in the light of Supernova Ia observations
• $G_3$ -- interacting scalar tensor dark energy
• On the road to percent accuracy VI: the nonlinear power spectrum for interacting dark energy with baryonic feedback and massive neutrinos