Weak cosmic growth in coupled dark energy with a Lagrangian formulation

We investigate a dark energy scenario in which a canonical scalar field phi is coupled to the four velocity u(c)(mu) of cold dark matter (CDM) through a derivative interaction u(c)(mu)partial derivative(mu)phi. The coupling is described by an interacting Lagrangian f( X, Z), where fdepends on X = -partial derivative(mu)phi partial derivative(mu)phi/2 and Z = u(c)(mu)partial derivative(mu)phi. 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 proportional to 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 sigma(8) between low- and high-redshift measurements. (c) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).