There are reasons to think so, if one connects theory for a variety of phenomena.

First there was a novel explanation for metabolism scaling by a 3/4 power of mass (Kleiber’s Law). That explanation emerged beginning in 2008 based on an animal’s circulatory system scaling by a 4/3 exponent of circulatory system volume. Metabolism scales by an inverse exponent, by a 3/4 power to maintain animal body temperature. In effect the entropy of the circulatory system is 4/3 the entropy of tissue supplied by the circulatory system.

The same 4/3 scaling of entropy occurs in an intermediate step of Stefan’s Law (1879); the derivation was worked out by Boltzmann but the most accessible derivation is that of Planck in his text book on heat. Since Stefan’s Law applies to black body radiation and the universe can be considered in the large as a black body cavity, the involvement of Stefan’s Law is, at least, intriguing.

In 1859 and 1860, Rudolf Clausius gave a demonstration in connection with the kinetics of gas molecules that in effect says that lengths stretch by 4/3 in stationary three dimensional space compared to four dimensional space with motion. If Clausius’s derivation is modified to apply to photons instead of gas molecules, then 3 dim space itself would stretch by 4/3 relative to 4 dim space consisting of 3 dim space + light motion.

In 1926, Lewis Fry Richardson measured that wind eddies scale by 4/3, an observation similar to that of Clausius in 1859 and 1860. In 1941, Andrei Kolmogorov provided mathematical derivations.

In 2000 or so, the fractal envelope of Brownian motion was determined using sophisticated mathematics (stochastic Lowner evolution) to be 4/3.

Common mathematics appears to connect all of the foregoing. That suggests that the 4/3 ratio arises, for comparable circumstances, as a universal law.

In other words, by connecting different phenomena that all relate to 4/3 scaling, one can infer a general law.

Since 4/3 scaling appears to be a general law, it should not be surprising if it applies at a cosmological scale.

It is therefore intriguing that the ratio of energy densities for Omega_r / Omega_M for r radiation and M matter, has been measured at about 0.70 / 0.30. This is very close to the ratio of cosmological energy densities that would result from 4/3 scaling for energy E: E/ (1)^3 : E / (4/3)^3 = 4^3 / 3^3 = 0.7033 / 0.2967. In fact the survey of type 1A supernova by Betoule et al in 2014 measured Omega_M as 0.295 which is exceptionally close indeed to what theory suggests.

It is moreover interesting that the 1998 observations inferred that type 1A supernovae were about 10 to 15% farther away than expected based on luminosity about 3/4 as bright as would be expected for a flat universe. But 3/4 luminosity is equivalent to being 4/3 as far away if two reference frames, one 3 dim and the other 4 dim, are assumed consistent with 4/3 scaling. The 10% to 15% estimates were based on the implicit assumption that looking out into the universe looks out on a single 3 dim space, not two reference frames of 3 and 4 dim.

So. Do the dots connect?