Binding the diproton in stars: anthropic limits on the strength of gravity

We calculate the properties and investigate the stability of stars that burn via strong (and electromagnetic) interactions, and compare their properties with those that, as in our Universe, include a rate-limiting weak interaction. It has been suggested that, if the diproton were bound, stars would burn ∼1018 times brighter and faster via strong interactions, resulting in a universe that would fail to support life. By considering the representative case of a star in our Universe with initially equal numbers of protons and deuterons, we find that stable, “strong-burning” stars adjust their central densities and temperatures to have familiar surface temperatures, luminosities and lifetimes. There is no “diproton disaster”. In addition, strong-burning stars are stable in a much larger region of the parameter space of fundamental constants, specifically the strength of electromagnetism and gravity. The strongest anthropic bound on stars in such universes is not their stability, as is the case for stars limited by the weak interaction, but rather their lifetime. Regardless of the strength of electromagnetism, all stars burn out in mere millions of years unless the gravitational coupling constant is extremely small, αG≲ 10−30.