Weak cosmic growth in coupled dark energy with a Lagrangian formulation. (arXiv:1911.02179v1 [gr-qc])

Weak cosmic growth in coupled dark energy with a Lagrangian formulation. (arXiv:1911.02179v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Kase_R/0/1/0/all/0/1">Ryotaro Kase</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Tsujikawa_S/0/1/0/all/0/1">Shinji Tsujikawa</a>

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 $u_{c}^{mu} partial_{mu} phi$. The
coupling is described by an interacting Lagrangian $f(X, Z)$, where $f$ depends
on $X=-partial^{mu} phi partial_{mu} phi/2$ and $Z=u_{c}^{mu}
partial_{mu} phi$. 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 $f propto X^{(2-n)/2}Z^n$ and
show that the gravitational coupling weaker than the Newton constant can be
naturally realized for $n>0$ 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.

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 $u_{c}^{mu} partial_{mu} phi$. The
coupling is described by an interacting Lagrangian $f(X, Z)$, where $f$ depends
on $X=-partial^{mu} phi partial_{mu} phi/2$ and $Z=u_{c}^{mu}
partial_{mu} phi$. 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 $f propto X^{(2-n)/2}Z^n$ and
show that the gravitational coupling weaker than the Newton constant can be
naturally realized for $n>0$ 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.

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