### Abstract

We investigate a dark energy scenario in which a canonical scalar field ϕ is coupled to the four velocity u_{c} ^{μ} of cold dark matter (CDM) through a derivative interaction u_{c} ^{μ}∂_{μ}ϕ. The coupling is described by an interacting Lagrangian f(X,Z), where f depends on X=−∂^{μ}ϕ∂_{μ}ϕ/2 and Z=u_{c} ^{μ}∂_{μ}ϕ. We derive stability conditions of linear scalar perturbations for the wavelength deep inside the Hubble radius and show that the effective CDM sound speed is close to 0 as in the standard uncoupled case, while the scalar-field propagation speed is affected by the interacting term f. Under a quasi-static approximation, we also obtain a general expression of the effective gravitational coupling felt by the CDM perturbation. We study the late-time cosmological dynamics for the coupling f∝X^{(2−m)/2}Z^{m} and show that the gravitational coupling weaker than the Newton constant can be naturally realized for m>0 on scales relevant to the growth of large-scale structures. This allows the possibility for alleviating the tension of σ_{8} between low- and high-redshift measurements.

Original language | English |
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Article number | 135400 |

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

Volume | 804 |

DOIs | |

Publication status | Published - 2020 May 10 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics