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 EG, 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 EG(z) differs from that of the ΛCDM model by about ±10% depending on the redshift z.