Matter density perturbations and effective gravitational constant in modified gravity models of dark energy

By S. Tsujikawa. 2007

259 citations recorded by the source corpus.

We derive the equation of matter density perturbations on subhorizon scales for a general Lagrangian density $f(R,\ensuremath{\phi},X)$ that is a function of a Ricci scalar $R$, a scalar field $\ensuremath{\phi}$, and a kinetic term $X=\ensuremath{-}(\ensuremath{\nabla}\ensuremath{\phi}{)}^{2}/2$. This is useful to constrain modified gravity dark energy models from observations of large-scale structure and weak lensing. We obtain the solutions for the matter perturbation ${\ensuremath{\delta}}_{m}$ as well as the gravitational potential $\ensuremath{\Phi}$ for some analytically solvable models. In an $f(R)$ dark energy model with the Lagrangian density $f(R)=\ensuremath{\alpha}{R}^{1+m}\ensuremath{-}\ensuremath{\Lambda}$, the growth rates of perturbations exhibit notable differences from those in the standard Einstein gravity unless $m$ is very close to 0. In scalar-tensor models with the Lagrangian density $f=F(\ensuremath{\phi})R+2p(\ensuremath{\phi},X)$, we relate the models with coupled dark energy scenarios in the Einstein frame and reproduce the equations of perturbations known in the current literature by making a conformal transformation. We also estimate the evolution of perturbations in both Jordan and Einstein frames when the energy fraction of dark energy is constant during the matter-dominated epoch.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5808699ddd8366399bfaf3874b39571684929e69

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Citations in the corpus

Modified Gravity and Cosmology (2011, unknown): “For studies on this subject the reader is referred to [1180, 629, 122, 377, 1219, 1226, 1043, 1220, 519, 1221, 914, 940].”
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Growth factor in $f(T)$ gravity (2010, background): “In f(R) or scalar-tensor gravity, one can get an analogous equation for fractional matter perturbation δm with a redefinition of Newton’s constant in the short wave-length limit [25].”
Evolution of the f σ 8 tension with the Planck 15 / Λ CDM determination and implications for modified gravity theories (2018, background): “[38] Shinji Tsujikawa, “Matter density perturbations and ef-”
f(R) Theories (2010, background): “This was further extended to scalar-tensor theories [93, 171, 586] and f (R) gravity [586, 597].”
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