Mimicking the cosmological constant: Constant curvature spherical solutions in a nonminimally coupled model

The purpose of this study is to describe a perfect fluid matter distribution that leads to a constant curvature region, thanks to the effect of a nonminimal coupling. This distribution exhibits a density profile within the range found in the interstellar medium and an adequate matching of the metric components at its boundary. By identifying this constant curvature with the value of the cosmological constant and superimposing the spherical distributions arising from different matter sources throughout the universe, one is able to mimic a large-scale homogeneous cosmological constant solution.

Figure 1

Main: scaled solution ${\theta }_0(x)/{\theta }_0(0)$ for $ϵ=\lambda =0$. Inset: ratio $Q_{\lambda }$ for $\lambda ={10}^{-3}$ (full line), ${10}^{-2}$ (dashed line) and ${10}^{-1}$ (dotted line).

Figure 2

Comparison of the metric coefficients $e^{2\nu }$ (full line) and $e^{2\sigma }$ (dashed line) derived from the $ϵ=0$ solution (black line) and the usual GR interior solution (grey line).