QCD-scale modified-gravity universe

A possible gluon-condensate-induced modified-gravity model with f(R) ∝ ∣R∣^1/2 has been suggested previously. Here, a simplified version is presented using the constant flat-spacetime equilibrium value of the QCD gluon condensate and a single pressureless matter component (cold dark matter, CDM). The resulting dynamical equations of a spatially-flat and homogeneous Robertson-Walker universe are solved numerically. This simple empirical model allows, in fact, for a careful treatment of the boundary conditions and does not require a further scaling analysis as the original model did. Reliable predictions are obtained for several observable quantities of the homogeneous model universe. In addition, the estimator E_G, proposed by Zhang et al. to search for deviations from standard Einstein gravity, is calculated for linear sub-horizon matter-density perturbations. The QCD-scale modified-gravity prediction for E_G(z) differs from that of the ΛCDM model by about ±10% depending on the redshift z.