Lunar Laser Ranging constraints on nonminimally coupled dark energy and standard sirens

Understand

In dark energy models where a scalar field $\phi$ is coupled to the Ricci scalar $R$ of the form $e^{-2Q (\phi-\phi_0)/M_{\rm pl}}R$, where $Q$ is a coupling constant, $\phi_0$ is today's value of $\phi$, and $M_{\rm pl}$ is the reduced Planck mass, we study how the recent Lunar Laser Ranging (LLR) experiment places constraints on the nonminimal coupling from the time variation of gravitational coupling.

• Besides a potential of the light scalar responsible for cosmic acceleration, we take a cubic Galileon term into account to suppress fifth forces in over-density regions of the Universe.
• Even if the scalar-matter interaction is screened by the Vainshtein mechanism, the time variation of gravitational coupling induced by the cosmological background field $\phi$ survives in the solar system.
• For a small Galileon coupling constant $\beta_3$, there exists a kinetically driven $\phi$-matter-dominated-epoch ($\phi$MDE) prior to cosmic acceleration.