Inhomogeneous big bang nucleosynthesis revisited

We reanalyze the allowed parameters for inhomogeneous big bang nucleosynthesis in light of the WMAP constraints on the baryon-to-photon ratio $\eta$ and a recent measurement which has set the neutron lifetime to be $878.5\pm 0.7\pm 0.3\sec$. For a set baryon-to-photon ratio $\eta$ the new lifetime reduces the mass fraction of ${}^4\mathrm{He}$ by 0.0015 but does not significantly change the abundances of other isotopes. This enlarges the region of concordance between ${}^4\mathrm{He}$ and deuterium in the parameter space of $\eta$ and the IBBN distance scale $r_i$. The ${}^7\mathrm{Li}$ abundance can be brought into concordance with observed ${}^4\mathrm{He}$ and deuterium abundances by using depletion factors as high as 9.3. The WMAP constraints, however, severely limit the allowed comoving ($T=100\mathrm{GK}$) inhomogeneity distance scale to $r_i\approx (1.3–2.6)\times {10}^5\mathrm{cm}$.

Figure 1

Contours consistent with the $\pm 2\sigma$ measured abundance ratio $\mathrm{D}/\mathrm{H}$ of deuterium [28] are shown in long dashed lines. The CMB constraints from the WMAP measurements [5] are also shown as solid lines. The WMAP constraint limits the allowed parameter space to three regions.

Figure 2

Constraints from deuterium and CMB observations are shown with the $+2\sigma$ maximum constraint of the ${}^4\mathrm{He}$ mass fraction $Y_p$ by Izotov and Thuan [29]. The contour for the $+2\sigma$ maximum constraint of $Y_p$ is shown by dashed line for the world average neutron lifetime [7] and solid line for the Serebrov et al. lifetime [8]. The region to the right of the maximum constraint is excluded. The $+2\sigma$ minimum constraint corresponds to values of $\eta$ so low it is not necessary to show in this figure. The lifetime effect is to shift the $Y_p$ contour line to a higher $\eta$ by $\approx 1\times {10}^{-10}$.

Figure 3

(Color Online) Contours for the $\pm 2\sigma$ abundance constraints on ${}^7\mathrm{L}\mathrm{i}/\mathrm{H}$ by Ryan et al. [31] are shown along with the constraints on deuterium [28], CMB constraint from WMAP [5], and $+2\sigma$ maximum constraint on ${}^4\mathrm{He}$ [29] for the case of ${\tau }_{\mathrm{n}}=878.5.\pm {0.7}_{\mathrm{stat}}\pm {0.3}_{\mathrm{sys}}$ [8]. The region of concordance between WMAP, ${}^4\mathrm{He}$ and deuterium is shown in yellow. The contour lines for ${}^7\mathrm{Li}$ allow for depletion factors from 2.5 to 9.3 to bring all three observational constraints and CMB constraints in concordance with each other.

Figure 4

(Color Online) Same as in Fig. 3 but with $\pm 2\sigma$ constraints on ${}^7\mathrm{L}\mathrm{i}/\mathrm{H}$ by Melendez and Ramirez [32]. A thin region of concordance between the $+2\sigma$ limit of the ${}^7\mathrm{Li}$ constraints and the other constraints exists for $r_i\le 1000\mathrm{cm}$. A depletion factor of 1.2 improves concordance. A depletion factor of 4.47 would bring these ${}^7\mathrm{Li}$ measurements in concordance with the other constraints for $r_i=(1.3–2.6)\times {10}^5\mathrm{cm}$.