Encoding the scaling of the cosmological variables with the Euler Beta function

We study the scaling exponents for the expanding isotropic flat cosmological models. The dimension of space, the equation of state of the cosmic fluid and the scaling exponent for a physical variable are related by the Euler Beta function that controls the singular behavior of the global integrals. We encounter dual cosmological scenarios using the properties of the Beta function. For the entropy density integral we reproduce the Fischler-Susskind holographic bound.