The motion of galaxies through the fabric of space-time, according to specific conditions, leads to an expansion in cosmic space and even an acceleration in its expansion. We also find that the properties of this expansion are consistent with the cosmological principle. We can also, according to the conditions of motion, reach the same formula of the Hubble-Lemaître law and the expansion of (FLRW) metric in general relativity, which expresses the expansion of the flat space-time fabric., and thus we get here a paradox in general relativity, where the metric expansion, which expresses the expansion of the flat space-time fabric, is also the one that expresses the motion of galaxies through the fabric of space-time according to specific conditions, This paradox does not represent an error in general relativity's perception of the cosmic model, but it reveals the limitations of general relativity in application, where we find that some of the results that can be obtained from general relativity are unacceptable, such as the motion of galaxies faster than the speed of light, the expansion of wavelengths of light with the expansion of space, the vacuum energy is the only source of dark energy