Modified Gravity Theories: Distinguishing from ΛCDM Model

The method and probability of distinguishing between the Λ cold dark matter (ΛCDM) model and modified gravity are studied from future observations for the growth rate of cosmic structure (Euclid redshift survey). We compare the mock observational data to the theoretical cosmic growth rate by modified gravity models, including the extended Dvali–Gabadadze–Porrati (DGP) model, kinetic gravity braiding model, and Galileon model. In the original DGP model, the growth rate fσ8 is suppressed in comparison with that in the ΛCDMmodel in the setting of the same value of the today’s energy density of matter Ωm;0, due to suppression of the effective gravitational constant. In the case of the kinetic gravity braiding model and the Galileon model, the growth rate fσ8 is enhanced in comparison with the ΛCDM model in the same value of Ωm;0, due to enhancement of the effective gravitational constant. For the cosmic growth rate data from the future observation (Euclid), the compatible value of Ωm;0 differs according to the model. Furthermore, Ωm;0 can be stringently constrained. Thus, we find the ΛCDM model is distinguishable from modified gravity by combining the growth rate data of Euclid with other observations.