Modified big bang nucleosynthesis with nonstandard neutron sources

During big bang nucleosynthesis, any injection of extra neutrons around the time of the ${}^7\mathrm{Be}$ formation, i.e. at a temperature of order $T\simeq 50\mathrm{keV}$, can reduce the predicted freeze-out amount of ${}^7\mathrm{Be}+{}^7\mathrm{Li}$ that otherwise remains in sharp contradiction with the Spite plateau value inferred from the observations of Pop II stars. However, the growing confidence in the primordial $\mathrm{D}/\mathrm{H}$ determinations puts a strong constraint on any such scenario. We address this issue in detail, analyzing different temporal patterns of neutron injection, such as decay, annihilation, resonant annihilation, and oscillation between mirror and standard model world neutrons. For this latter case, we derive the realistic injection pattern taking into account thermal effects (damping and refraction) in the primordial plasma. If the extra-neutron supply is the sole nonstandard mechanism operating during the big bang nucleosynthesis, the suppression of lithium abundance below $\mathrm{Li}/\mathrm{H}\le 1.9\times 10^{-10}$ always leads to the overproduction of deuterium, $\mathrm{D}/\mathrm{H}\ge 3.6\times 10^{-5}$, well outside the error bars suggested by recent observations.

Figure 1

The neutron damping rate ${\mathrm{\Gamma }}_{\text{eff}}(T)$ is units of eV plotted as a function of temperature $T$, in units of keV. The change from the predominantly electromagnetic to the strong force scattering occurs at $T\simeq 40\mathrm{keV}$, right after ${}^7\mathrm{Be}$ formation.

Figure 2

The $n\leftrightarrow n^{\prime }$ oscillation rate normalized on the Hubble rate, ${\mathrm{\Gamma }}_{n\leftrightarrow n^{\prime }}/H$, as a function of temperature $T$, expressed in keV. The top curve is for the choice $\mathrm{\Delta }m=10^{-10}\mathrm{eV}$, and $m_{12}=10^{-13}\mathrm{eV}$, and the bottom curve is for $\mathrm{\Delta }m=10^{-11}\mathrm{eV}$, and $m_{12}=3\times 10^{-15}\mathrm{eV}$. The top curve becomes larger than one during ${}^4\mathrm{He}$ formation at $T\sim 80\mathrm{keV}$, while the bottom curve reaches one only for a brief period around $T\sim 40\mathrm{keV}$.

Figure 3

Time evolution of abundances in a model of $n-n^{\prime }$ oscillation, assuming $\eta ={\eta }_{\mathrm{CMB}}$, $x=0.2$ and ${\eta }^{\prime }=1$. The curves represent mass fractions of ordinary (solid) or mirror (dash) isotopes calculations, with only neutrons allowed to flow from one world to the other. Is shows, in our world, an increase of the neutron abundance resulting in a reduction of the Beryllium-7 one.

Figure 4

$n-n^{\prime }$ oscillation. Contour plots in the space of the two physical parameters $(\mathrm{\Delta }m,m_{12})$ assuming $\eta ={\eta }_{\mathrm{CMB}}$ and $x=0.2$ respectively with ${\eta }^{\prime }=10^{-10}$ (left) and ${\eta }^{\prime }=3\times 10^{-10}$ (middle) and $x=0.5$ and ${\eta }^{\prime }=10^{-10}$ (right). The blue strip corresponds to models for which the BBN predictions are compatible with the observational constraints for both helium-4 and lithium-7. The solid lines indicate the prediction of deuterium abundance $\mathrm{D}/\mathrm{H}=\{3.6,3.8,4.0,4.2,4.4,4.6\}\times 10^{-5}$ from top to bottom. The green area corresponds to the upper limit $\mathrm{D}/\mathrm{H}<3.25\times 10^{-5}$ from Ref. [26], while other limits [4, 26] fall out of the frame. The yellow background reflects the region allowed by ${}^4\mathrm{He}$ observations [11] (the whole frame in these cases).

Figure 5

Decay of massive particles. Contour plot assuming $\eta ={\eta }_{\mathrm{CMB}}$ for the two parameters of the model: the lifetime ${\tau }_x$ of the massive particle and the decay rate ${\lambda }_0\exp (-t/{\tau }_X)$. This can be compared to the case 4 of Ref. [15]. The solid dashed lines indicate the prediction of deuterium abundance $\mathrm{D}/\mathrm{H}=\{3.6,3.8,4.0,4.2,4.4,4.6\}\times 10^{-5}$ from top to bottom. The green area corresponds to the $\mathrm{D}/\mathrm{H}$ observational limits from Ref. [26], while those of Ref. [4] lie outside of the frame. The yellow background reflects the region allowed by ${}^4\mathrm{He}$ observations [11].

Figure 6

Decay of massive particles. The abundance of lithum-7 produced during BBN, as a function of the two parameters $({\tau }_X,{\lambda }_0)$ has a valley. See text for an explanation of the shape of this surface and compare with Fig. 5.

Figure 7

Particle annihilation. Abundance of helium-4, deuterium, tritium and helium-7 as a function of the annihilation rate ${\lambda }_0$. Standard BBN is recovered in the limit ${\lambda }_0\to 0$. It is easily concluded that solving the lithium-7 problem would be at the origin of deuterium problem.

Figure 8

Resonant annihilation. Contour plot, as in Fig. 5, but assuming $\eta ={\eta }_{\mathrm{CMB}}$ for the two parameters of the model: the resonance energy $E_R$ and the reaction rate ${\lambda }_0\exp (-E_R/\mathrm{k}T)$ (this corresponds to the case 5 of Ref. [15]).

Figure 9

Each dot is the prediction of a model in the space ($\mathrm{D}/\mathrm{H}$, ${}^7\mathrm{Li}/\mathrm{H}$). The left rectangle corresponds to the $\mathrm{D}/\mathrm{H}$ data of Ref. [4] ($2.49\times 10^{-5}-2.57\times 10^{-5}$) while the right rectangle corresponds to the data of Ref. [26] ($2.79\times 10^{-5}-3.25\times 10^{-5}$). The lithium abundance corresponds to the value of Ref. [10] ($1.27\times 10^{-10}–1.89\times 10^{-10}$). This demonstrates that no model can be in agreement with both lithium-7 and deuterium. The blue, red and green dots correspond to n-n’ oscillation models respectively with $(x,{\eta }^{\prime })=(0.2,3)$, $(x,{\eta }^{\prime })=(0.2,1)$, $(x,{\eta }^{\prime })=(0.5,1)$; the light blue dots correspond to resonant annihilation models and the pink dots to particle decay models.