Universes without the Weak Force: Astrophysical Processes with Stable Neutrons E. Grohs1, Alex R. Howe2, and Fred C. Adams1;2 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA and 2Department of Astronomy, University of Michigan, Ann Arbor, Michigan 48109, USA (Dated: January 19, 2018) We investigate a class of universes in which the weak interaction is not in operation. We consider how astrophysical processes are altered in the absence of weak forces, including Big Bang Nucle- osynthesis (BBN), galaxy formation, molecular cloud assembly, star formation, and stellar evolution. Without weak interactions, neutrons no longer decay, and the universe emerges from its early epochs with a mixture of protons, neutrons, deuterium, and helium. The baryon-to-photon ratio must be smaller than the canonical value in our universe to allow free nucleons to survive the BBN epoch without being incorporated into heavier nuclei. At later times, the free neutrons readily combine with protons to make deuterium in sufficiently dense parts of the interstellar medium, and provide a power source before they are incorporated into stars. Almost all of the neutrons are incorporated into deuterium nuclei before stars are formed. As a result, stellar evolution proceeds primarily through strong interactions, with deuterium first burning into helium, and then helium fusing into carbon. Low-mass deuterium-burning stars can be long-lived, and higher mass stars can synthesize the heavier elements necessary for life. Although somewhat different from our own, such universes remain potentially habitable. Keywords: big bang nucleosynthesis, galaxy formation, stellar nucleosynthesis, multiverse, habitability I. INTRODUCTION interactions, core-collapse supernova will fail to explode and will simply collapse to a degenerate remnant, thereby The fundamental constants that describe the laws of hampering the dispersal of heavy elements. physics appear to have arbitrary values that cannot be These effects would appear to compromise the habit- explained by current theory. One possible | and partial ability of universes where the weak force is significantly | explanation is that other universes exist in which the weaker than in our own. However, this standard argu- fundamental constants have different values, so that they ment has been challenged with the concept of a \weak- are drawn from an as-yet-unknown probability distribu- less universe" [9], namely, a universe without any weak tion. Many authors have argued that significant changes interaction at all. Neutrons would be stable in such a in these constants could render the universe uninhabit- universe, and would therefore most likely have an equal able to life as we know it, and as a result our universe ap- abundance to protons. A universe with the same baryon pears to be “fine-tuned” for life [1{5]. On the other hand, density as ours would convert virtually all baryons to recent work suggests that when multiple constants are al- helium during BBN, leaving behind no free protons (no lowed to vary, large regions of the parameter space that hydrogen to make water). However, if the baryon den- result in habitable universes can be found [6{8]. This sity is lower (more properly the baryon-to-photon ratio paper continues the exploration of alternate possibilities η), significant amounts of protons and deuterium can sur- for the fundamental constants with a focus on the weak vive the BBN epoch [9] and would be available later for force. deuterium burning in stars (which takes place through The strength of the weak interaction is a fundamen- the strong interaction). Note that stars in such a weak- tal part of the standard model of particle physics and less universe can also produce heavier elements by strong represents one parameter that could vary from region reactions. Although core-collapse supernova might not to region. The weak interaction governs the rate of ra- function, at least not in the same manner as in our uni- dioactive decay, the rate of conversion of hydrogen into verse, these heavy elements could still be dispersed by + helium via the p(p; νee )D stage of the pp-chain in low- Type Ia supernova and classical novae, allowing the pos- arXiv:1801.06081v1 [astro-ph.GA] 17 Jan 2018 mass stars, and the cross section for neutrino interac- sibility of planet formation and life. tions. The latter two effects are crucial to determin- The opposite case, where the weak interaction is sig- ing whether or not a universe can produce life. If the nificantly stronger than in our universe, would resemble weak force is too weak, or absent altogether, long-lived our universe more closely. A stronger weak interaction stars fueled by weak reactions could not exist. In the ab- increases the rate of radioactive decay, most notably the sence of weak interactions, helium can still be synthesized neutron lifetime, but it does not affect the stability of through strong interactions during Big Bang Nucleosyn- stable nuclei, which is governed primarily by the strong thesis (BBN), as free neutrons are present, but helium interaction. If the neutron lifetime is less than 30 sec- production is suppressed in stellar interiors (which do onds, BBN is suppressed because most neutrons decay not have neutrons). Once synthesized, helium can later before BBN begins. However, this complication is not fuse into heavier elements via the triple alpha process an impediment because stars in this all-hydrogen uni- in sufficiently massive stars. However, without neutrino verse will be more efficient at converting hydrogen to he- 2 lium. In addition, core-collapse supernovae will be more Iron peak elements in the ISM will capture an excess of efficient at dispersing heavy elements due to the larger free neutrons, allowing stars to form with a small excess neutrino interaction cross sections. The primary concern of protons, which can then form oxygen via the reaction would be the shortened lifetimes of these more efficient 12C(2p; γ)14O. Similar reactions may lead to a deficit of stars. (Note that if the weak interaction is strong enough nitrogen and an excess of neon compared with our uni- to approach the strength of the electromagnetic interac- verse, and likewise, the lack of core-collapse supernovae tion, non-linear effects will likely render these concerns will likely lead to a deficit of non-alpha-process elements. moot.) However, the effect on the chemical evolution of the weak- In this paper, we update and expand upon this idea less universe is neither negligible nor dominant, and the of a weakless universe in Refs. [10{12], and in particu- necessary elements for both planet formation and organic lar Ref. [9]. An important parameter in this problem is chemistry will still be present, implying that such a uni- the baryon-to-photon ratio η, which impacts the compo- verse could still be hospitable to life. sition of the universe after BBN. For the value in our The organization of this paper is as follows. Section II universe, BBN with an equal amount of neutrons and details the outcome of BBN in universes with a range of protons would result in a composition where the 4He η and neutron-to-proton ratios. We examine the impact abundance is greater than 90%. The high abundance of weakless physics on: galaxy formation in Sec. III; the of 4He yields short-lived stars and is problematic for the ISM in Sec. IV; and stellar evolution in Sec. V. Section development of life. For a judicious choice of η, how- VI contains our study of the habitability of the weakless ever, BBN can result in a richer composition with large universe. We summarize and discuss our results in Sec. fractions of deuterium, free protons, and free neutrons. VII. Throughout this paper, we use cgs units with the We determine the range of η for which weakless universes exception of BBN in Sec. II. We use natural units in Sec. could support life, using models of galaxy formation, star II to be consistent with the BBN literature. formation, and subsequent stellar evolution. One crucial issue not addressed in the original proposal II. BIG BANG NUCLEOSYNTHESIS [9] is the abundance of free neutrons left over from BBN, which is comparable to the abundance of free protons. These neutrons can capture onto protons at zero tem- A. Standard versus weakless BBN perature, forming deuterium via the n(p; γ)D reaction. As a result, nuclear fusion can occur in the interstellar In this section, we give a brief overview of the role the medium and could potentially halt the collapse of a gas weak interaction plays in Standard BBN (SBBN) and cloud. This paper considers the effects of neutron cap- then discuss the modifications to SBBN in a weakless ture reactions on four scales of formation: [A] from the universe. We will use the ratio of neutrons to protons intergalactic medium down to the size scale of galaxies; (denoted the n=p ratio) extensively throughout this work [B] from the neutral interstellar medium (ISM) to the nn formation of giant molecular clouds; [C] from the cloud n=p : (1) ≡ n to molecular cloud cores { the sites of individual star p formation events; and finally [D] from the cloud cores Note that the number densities ni in Eq. (1) are the to- to the production of protostars themselves. Neutron fu- tal particle number densities (free particles and nucleons sion becomes significant during the latter stages of this bound in nuclei) and not solely the free particle number hierarchy, and most of the free neutrons are processed densities. Reference [13] showed that n=p would evolve into deuterium before the onset of stellar nuclear burn- due to six weak reactions during primordial nucleosyn- ing. Although gas cooling is delayed, these processes do thesis.