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Cosmological Time-Dependent Quark Masses and Big Bang Nucleosynthesis

There has been considerable interest [1] in the use of big bang nucleosynthesis (BBN) to constrain any possible time variation of fundamental physical constants in the early universe. A time dependence of fundamental constants in an expanding universe can be a generic result [2] of theories unifying gravity and other interactions. It can be argued [3] that BBN is much more sensitive to variations in the averaged quark mass, i.e., mq ≡ (mu + md)/2, than other physical parameters such as variations in the fine structure constant. Hence, mq may be the best parameter to search for evidence of time variation of fundamental constants. We reinvestigate the constraints from BBN on a possible time-dependent quark mass [4]. The limits on such quark-mass variations are particularly sensitive to the adopted observational abundance constraints. Hence, we have adopted updated light-element abundances and uncertainties deduced from observations. Changing mq affects nuclear reaction rates through the dependence of the rates on nuclear binding energies and the reaction Q values. Resonant reactions of BBN were treated slightly differently than those in the previous study [1]. There are two important resonant reactions: 3He(d, p)4He and 3H(d, n)4He. We adopt an analytic reaction rate for variable nuclear binding energy [5]. For the 3He(d, p)4He reaction, the resonance is an excited state of the compound nucleus 5Li*. For the 3H(d, n)4He reaction the compound nucleus is 5He*. The resonance energies are related to the excitation energy in the compound nucleus and the net binding energies of the reactants. We point out that there is a consistency check on the δmq sensitivity of the forward 3He(d, p)4He reaction from the reverse 4He(p, d)3He reaction [4]. As a test on the robustness of the constraint on δmq /mq we include the variations in the resonance energy based on the parameters in this reverse channel. In Fig. 1 we show primordial abundances as a function of variations in the quark mass δmq /mq for a fixed value of baryon-to-photon ratio η = 6.23 × 10−10 from WMAP 7 data for model ΛCDM+SZ+lens. The revised constraints on 7Li and 4He do not confirm a concordance best fit for a positive value of δmq /mq = 0.016 ± 0.005 [1]. Rather, the optimum concordance level is for much smaller values consistent with δmq /mq = 0. Combining limits from all nuclides (except 3He), we deduce conservative concordance limits of −0.005 <~ δmq /mq <~ 0.007. Since 4He and D abundances mainly determine the concordance region, we present analytic formulas for the dependence of the 4He and D abundances with quark mass [4]. 6Li production in standard BBN occurs via the 4He(d, γ)6Li reaction, and some consequence of a varying quark mass on its abundance exists. Nevertheless, we show that effects of a varying quark mass on the resonant 4He(d, γ)6Li reaction can be safely neglected [4]. Cosmological Time-Dependent Quark Masses and Big Bang Nucleosynthesis