Cosmography and Large Scale Structure by 𝑓(𝑅)-Gravity: New Results

Figure 6

Density versus 𝑎₁: predictions on the behavior of 𝑎₁. The horizontal black bold line indicates the Newtonian-limit, 𝑎₁→3/4 which we expect to be realized on scales comparable with Solar System. Vertical lines indicate typical approximated values of matter density (without dark matter) for different gravitational structures: Universe (bold dashed) with critical density 𝜌_crit≈10⁻²⁶kg/m³; galaxy clusters (dashed line) with 𝜌_cl≈10⁻²³kg/m³; galaxies (dot-dashed) with 𝜌_gal≈10⁻¹¹kg/m³; sun (dotted) with 𝜌_sun≈10³kg/m³. Arrows and boxes show the predicted trend for 𝑎₁.