Studies in the Big Bang Nucleosynthesis of Lithium Isotopes

There has been a lingering puzzle in that the $^6$Li abundance observed in metal poor halo stars appears to exhibit a plateau as a function of metallicity similar to that for $^7$Li. This suggests a possible big bang origin for $^6$Li. However, becauuse the radiative capture of a deutron by and alpha particle during the big bang is suppressed, it is difficult to explain this observed $^6$Li abundance. At the same time the observed $^7$Li abundance is below that expected from BBN. In this talk we summarize a variety of approaches by which we have attempted to explain this observation. Among the possibilities are uncertainties in the stellar astrophysics of lithium isotope detection, galactic chemical evolution, effects from a massive charged or uncharged unstable relic supersymmetric particle present during BBN, or a time variation of fundamental constants. We show that it is possible, but difficult, to obtain a simultaneous solution to both the problems of underproduction of $^6$Li and overproduction of $^7$Li in a single paradigm.