locally flat metric in cosmology

a freely-falling observer perceives the metric as being locally Minkowskian, because by a choice of coordinates any metric \(g_{\mu\nu}\) can be made locally constant and equal to \(\eta_{\mu\nu}\), where only second derivatives can not be made to vanish: at the same time this sets the scale at which the locally Minkowskian approximation is valid. could you estimate what this scale is for a cosmological fundamental observer?