Cosmological Models containing both Radiation and Matter

Abstract

JACOBS¹ has recently compared two types of cosmological models which change from a radiation-like model for early time to a matter-like model for recent time. The radiation in these models is in thermal equilibrium with the matter and the photons, neutrons and electrons are not treated separately (as they are, for example, in ref. 2). In a flat space (k = 0), the function R(t) of the line element changes from being like At^½ for early time to being like At^2/3 for recent time. The two models Jacobs discusses will here be called model I and model II. R(t) is given in model I by where and in model II by where β is a constant³. Here the density and pressure are where ρ_r and ρ_m are the density of radiation and matter, respectively, p_r is the pressure of radiation, the pressure of matter is put equal to zero, a is Stefan's constant and T is the radiation temperature. Also, for a Hubble parameter we define and so that the conservation equation gives E_m and E_r were first defined by Davidson⁴ and are the total net rate of transfer of radiation energy per unit volume into matter energy and vice versa. A zero subscript denotes the present epoch. The present value of T is of the order of 3° K from the measurement of the isotropic microwave background first found by Penzias and Wilson⁵ and Roll and Wilkinson⁶. This is believed by many to be a remnant of the initial “big-bang” or “fireball”.