Five Degrees on Loan: Alpher and Herman's Relic Temperature, Repriced

In 1948 Ralph Alpher and Robert Herman announced that the hot early universe should still be glowing today at about 5 degrees above absolute zero. Seventeen years later the glow was found, at 2.7255 degrees, and the 5 became one of the most celebrated predictions in cosmology. This paper does not grade the glow, the hot beginning, or the men. It grades one number's paperwork. The estimate runs on a single cube root: the present temperature is the buildup temperature, about a billion degrees, times the cube root of the ratio of two densities — the density of matter today divided by the density of matter when the elements began to form. Neither density was measured. The present density, about 10⁻³⁰ grams per cubic centimetre, is stated in the group's papers as a given; it is never derived in them. The early density comes from a neutron-capture fit that the group's own papers printed in three different versions within a year. Run the one formula on the group's three printed early densities and it answers 7.94 K, 19.26 K, and 5.93 K. Only the third is ever quoted. Replace the assumed present density with the modern measured baryon density and the famous answer moves to 4.40 K; replace it with the modern total matter density and it moves to 8.25 K. Run the paper's second assumed input — its matter-to-radiation ratio, which corresponds to a baryon-to-photon ratio 152 times smaller than the measured one — at today's density, and the same machinery predicts 14.54 K. The 5 K figure is exactly as derived as its two inputs, and its inputs were loans. Grade: TWO ASSUMED INPUTS, ONE CUBE ROOT — PRICED, STILL GLOWING. This paper stands outside my work on the vacuum catastrophe; quantum gravity stands not solved in my books, and nothing here moves it. Keywords: cosmic microwave background; Alpher; Herman; Gamow; big bang nucleosynthesis; assumed step; census.