Exact cosmological solution of a Scalar-Tensor Gravity theory compatible with the $\Lambda CDM$ model

Abstract

We consider the massive scalar-tensor theory in the Jordan frame $F(\Phi )=K^2{\Phi }^2$ and $U(\Phi )=(1/2)m^2{\Phi }^2$, where $F(\Phi )$ corresponds to a constant Brans-Dicke parameter ${\omega }_{BD}=1/4K^2$. The constraint of the Solar System experiments is $K^2<(1/400{)}^2$. For dustlike matter in a spatially flat homogeneous isotropic universe, we reduce the equations of motion to a system of two differential equations of first order which can be exactly solved. We obtain simple and explicit expressions for $\frac{\Phi (z)}{\Phi (0)}$ and $\frac{H(z)}{H_0}$ that depend only on two parameters, $K^2$ and ${\Omega }_{m,0}$. For $K\le 1/400$ the expansion rate $H(z)$ can be practically superposed on the $\Lambda$CDM solution $H_{\Lambda }(z)$, up to high redshift $z$, but the equation of state $w_{DE}(z)$ of the dark energy is not constant: it presents a very slight crossing of the phantom divide line $w=-1$ in the neighborhood of $z=0$ and becomes very slightly positive at high redshifts.

Final version. Minor changes after proof corrections

References in corpus (2)

• Reconstructing Dark Energy
• Approaches to Understanding Cosmic Acceleration

Cited by in corpus (1)

• Constraints on scalar-tensor theories of gravity from observations