The ${}^7\mathrm{Li}$ abundance calculated in BBN with the baryon-to-photon ratio fixed from fits to the CMB power spectrum is inconsistent with the observed lithium abundances on the surface of metal-poor halo stars. Previous cosmological solutions proposed to resolve this ${}^7\mathrm{Li}$ problem include photon cooling (possibly via the Bose-Einstein condensation of a scalar particle) or the decay of a long-lived $X$ particle (possibly the next-to-lightest supersymmetric particle). In this paper we reanalyze these solutions, both separately and in concert. We also introduce the possibility of a primordial magnetic field (PMF) into these models. We constrain the $X$ particles and the PMF parameters by the observed light element abundances using a likelihood analysis to show that the inclusion of all three possibilities leads to an optimum solution to the lithium problem. We deduce allowed ranges for the $X$ particle parameters and energy density in the PMF that can solve ${}^7\mathrm{Li}$ problem.

• Received 28 February 2014

DOI:https://doi.org/10.1103/PhysRevD.90.023001