The evolution of the Friedmann universe in pure Lovelock gravity is identical to the four dimensional universe in general relativity for a barotropic fluid

It is demonstrated that the general relativistic four dimensional perfect fluid cosmology is entirely equivalent to the universe in pure Lovelock gravity within a specific dimensional spectrum. For a particular dimensional spectrum, it is shown that there is no qualitative nor quantitative difference between four dimensional general relativity and any order of the pure Lovelock gravity theory in the context of a barotropic perfect fluid-filled universe. They are one and the same. The dynamics and evolution of the Friedmann–Lemaître–Robertson–Walker (FLRW) universe are discussed in the pure Lovelock class of gravity theories. It is demonstrated that an equation of state imposed on the pure Lovelock field equations for the FLRW spacetime, in a particular critical dimensional spectrum, yields a system that is entirely equivalent to the four dimensional general relativistic universe. This is to say that the dynamical evolution of the conventional perfect fluid-filled four dimensional universe in general relativity, is entirely equivalent to that of any order of the pure subclass of Lovelock gravity. Thus, a specific dimensional spectrum implies no deviation from general relativity.