The Big Bang Nucleosynthesis (BBN) is the phase of cosmic evolution during which it is thought that the primordial nuclei of light elements, in particular, D, 3He, 4He and 7Li, were formed. In 1957 Burbidge et al [7] hypothesized reactions that could have arisen within the stars in order to achieve results that well agree with the observations. Actually, the abundances calculated from the four scientists were close enough to those observed. In addition, the observation of the Cosmic Microwave Background (CMB) radiation [8], corresponding to a blackbody spectrum with a temperature of 2.73 K, was of paramount importance in this regard. Today we know that the lighter elements (H, D and He) were formed mainly in the moments immediately after the Big Bang, while the elements heavier than He, would actually synthesize in the center of stars. The first question that metals could form in the core of the stars was in the early 50s of the last century when in some stars was observed the spectrum of Tc, a radioactive element produced artificially in 1937. This nucleus shows a rather quickly decay (its mean-life is 3 million years) ruling out the possibility to be produced at the dawn of the universe. After the first initial flare the universe continued to expand and cool down to the point that when it reached the age of 10−6 seconds, the temperature had dropped to 1012 K. It was then that the primordial nucleons were formed from the quark-gluon plasma. At this time quarks combined together in threes to form protons and neutrons.
Subsequently, in an age of between three and five minutes from the start, the temperature dropped further to reach one billion degrees, and the density was reduced drastically. Therefore, were soon created ideal conditions because the collisions between protons and neutrons would become very effective and frequent enough to form the first nuclei. At this time nuclei of D, T, 3He, and 4He were formed. From the fusion of one T and two D was formed also a few of nuclei of 7Li and 7Be. From this moment, and for a few hundreds of thousands of years, the universe continued to expand and cool. However, when the temperature reached a few thousand degrees, the electrons, which until then had been in constant movement, slowed down allowing the charged nuclei to capture them and forming the first neutral atoms (Recombination). The formation of neutral atoms (mostly H and He) was a moment of crucial importance because since then the universe became transparent to electromagnetic radiation, which started to travel freely through space (Decoupling). Before electrons were captured by the atomic nuclei, the universe was indeed a very hot and dense plasma of charged particles, which prevented the photons from travelling freely. At that time the universe was completely opaque. During the electrons-positrons annihilation (4-200 s after expansion began) the number density of photons increased. As the universe expands, the number of photons is roughly constant, however, the energy of each photon decreases. During the further expansion, photons from the decoupling will continue to exist without any further interaction. The present-day temperature of the CMB radiation, T = 2.725 ± 0.001 K provides the photon number density after that epoch, which is given by nγ = 410.5 cm−3 [9].
Within the framework of the standard BBN theory, precise predictions of primordial abundances are feasible since they rely on well-measured cross-sections and a well-measured neutron lifetime [10]. Indeed, even prior to the WMAP era, theoretical predictions for D, 3He, and 4He were reasonably accurate [11], however, uncertainties in nuclear cross-sections leading to 7Be and 7Li were relatively large. This led to the problem of the primordial 7Li abundance, which still represents a challenging issue nowadays [12]. The amount of Li created through the BBN depends primarily on the relative amounts of light and matter. This is obtained by the photon-to-baryon ratio, which we can measure from the CMB radiation. The Li abundance measured in the Galaxy and that predicted by the BBN theory are not consistent. Indeed, the predicted primordial Li abundance is about a factor of three higher than the abundance determined from absorption lines seen in a population of metal-poor galactic halo stars [13]. These stars, some of which are old as the own Galaxy, act as an archive of the production of the primordial Li. This conclusion is supported by numerous data on the presence of light elements in the atmospheres of metal-poor stars [14], where the interstellar matter is incorporated early in their condensation. Due to convective motions, the surface material of such stars can be dragged into the inner regions, where the temperature is higher and Li is depleted. This effect is evidenced by the low Li abundance in the cold stars of the halo, which are fully convective stars. However, the hottest and most massive stars have only a thin convective layer on the surface, showing no correlation between Li abundance and the temperature [15]. Figure 1 shows the abundance of Li and Fe in a sample of halo stars. The [Li/H] ratio is practically independent of [Fe/H]. Heavy elements are produced by stellar nucleosynthesis and thus their abundance increases over time as the matter circulates in and out of the stars. The independence of Li abundance from that of Fe indicates that 7Li is not related to galactic nucleosynthesis and therefore is of primordial origin. This flat trend is known as Spite Plateau [16], and its value represents the primordial abundance of Li. Li abundance has been measured in several galactic halo poor-metal stars [12, 13]. According to the observations the currently accepted value is [Li/H] = (1.23 − 0.32 + 0.68) × 10−10, where 95% of the error is systematic [17]. In addition, Li was observed in stars of a metal-poor dwarf Galaxy and [Li/H] abundances were consistent with the Spite plateau, indicating its universality [18]. Furthermore, a recent study [19] has shown an agreement between the Li abundances of low-metallicity gas in the ISM of the Small Magellanic Cloud and the value of BBN + WMAP predictions. The measured 7Li abundances, which is independent of stars, provides an alternative constraint on the primordial abundance and cosmic evolution of Li that is not susceptible to the in situ modifications that may affect stellar atmospheres. However, the results show a disagreement between predictions and measurements if there is any post-BBN Li production, as it is expected.
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Figure 1. Lithium abundances in selected metal-poor galactic halo stars. The values obtained for both Li isotopes are shown as a function of metallicity. The metallicity-independence of 7Li is known as Spite plateau. It indicates that the abundance of Li is unrelated to galactic nucleosynthesis and therefore represents primordial abundance. The horizontal line is the predicted 7Li abundance from BBN and the baryon density as determined by WMAP. Data collected from [12]. |
6Li production in primordial nucleosynthesis is much lower than that of its mass isotope 7Li. The 6Li and 7Li are spectroscopically distinguishable by the shift in their atomic lines. This isotopic split is much smaller than the thermal doppler broadening of the Li lines occurring in the stars, nevertheless, the high spectral resolution measures reach the precision needed to determine the presence of 6Li. The isotope was observed in several poor-metal halo stars and an isotopic ratio of [6Li/7Li] ≃ 0.05 was obtained [13]. Figure 1 shows a metallicity-independence pattern also for the [6Li/H] abundance, suggesting a primordial origin. 6Li observations remain controversial: some studies argue that stellar convective motions may have altered the delicate shape of spectral lines thus mimicking the presence of 6Li [20]. A prudent approach is to consider the observations of the abundance 6Li as an upper limit. In any case, the analysis of this isotope also confirms that most of the primordial lithium is in the form of 7Li.
The precise mapping of the primordial anisotropies obtained by WMAP has been used to test the main cosmological models such as the BBN. The CMB radiation carries a record of the conditions in the early universe at a time of the last scattering when H and He nuclei recombined with electrons to form neutral atoms. As a result, photons decoupled from baryons and the universe became transparent to radiation. It is expected that there would be temperature anisotropies in different parts of the present microwave sky, reflecting the oscillations in the photon-baryon fluid around the time of the decoupling (the so-called baryonic acoustic oscillations). The measurement of the cosmic baryon-to-photon ratio, ηWMAP = (6.19 ± 0.15) × 10−10 is one of the most accurate results obtained by WMAP [21]. Before the WMAP measurements, η was the only free parameter in the BBN model, and the only way to obtain its value was from the observed abundance of D, 4He, and 7Li. The new WMAP baryon density is much more accurate and allows us to eliminate the last free parameter in the BBN theory, providing a new way for verifying the validity of this model. Using ηWMAP as input in the BBN model and propagating errors, it is possible to compare the expected and observed abundances for all light elements. The observations of D and 4He are in agreement with the theory (the abundance measured at z ∼ 3, the theory predictions at z ∼ 1010 and the WMAP data at z ∼ 1 are all consistent). [3He/H] measurements have not been reported since are still unreliable. As for Li, the BBN + WMAP expectation and the measurements are in complete disagreement: using η = ηWMAP the expected abundance of Li becomes [Li/H]BBN+WMAP ≃ (5.1 ± 0.6) × 10−10, quite different from that given by the Spite plateau. In conclusion, the value of the theoretical model is above the observations of a factor ≃ 2.4-4.3, which represents a discrepancy of 4.2-5.3 σ.
A number of explanations were put forward to solve the cosmological problem of Li. The issues to consider for a possible solution are numerous and belong to different fields of physics. They included (i) astrophysical solutions: the problem may lie in the observations, leading to an incorrect estimation of the primordial Li abundance, (ii) nuclear solutions: reevaluate rate and cross-sections reactions that lead to the creation or depletion of A = 7 nuclei, (iii) solutions beyond standard physics: by building new models that go beyond the standard models of cosmology and particle physics. Regarding the astrophysical field, the Li problem might be hidden behind an underestimation of the Spite plateau, caused by systematic errors or improper determination of the stellar temperatures. In fact, in the concerned stars, Li is mostly ionized, therefore the measured abundance (obtained from the neutral Li line at 670.8 nm) needs a correction based on the [Li+/Li0] ratio, which varies exponentially with temperature. Another point to consider is to see whether the current Li content in the stars is actually primordial or whether factors that caused its depletion have occurred over time such as convective motions, turbulence or gravitational effects. More radical solutions involve elements that go beyond the standard models of cosmology and/or particles and could point to new physics. Some observations might bring into question the cosmological principle, highlighting large-scale inhomogeneities. If the baryon-to-photon ratio varied depending on the inhomogeneity, the BBN could have been different [12].
According to the BBN nuclear network, about 90% of Li is produced by Be decay, while only 10% is produced directly in primordial nucleosynthesis. 7Be is radioactive and decays, with a half-life of about 53 days, into stable atoms of 7Li through the only energy-efficient decay channel: electronic capture. This process takes place at later stages in BBN, since the 7Be electronic capture probability is virtually zero in the primordial universe due to the low electronic density [22]. Actual abundance of 7Li is directly related to the quantity of 7Be produced in the BBN, even though it is not possible to observe 7Be in the stars at present, as it is now completely decayed. An investigation of the processes that created and destroyed 7Be through the history of the universe could resolve the disagreement between predictions and observations of Li. The problem could, in fact, be caused by a poor estimate of the production and destruction rates of the Be, probably due to an incorrect calculation of cross-sections. The main Be production reaction, 3He(α,γ)7Be, has been well studied and the cross-section is known with a precision of approximately 3% [23, 24]. Destruction of Be occurs mainly through the reactions 7Be(n,p)7Li and 7Be(n,α)4He. Data on these reactions are scarce or completely missing, thus affecting the abundance of 7Li predicted by the BBN. Regarding the 7Be(n,p)7Li reaction no cross-section measurements have yet been made in the MeV region, i.e., in the energies of interest for the BBN. A measure of (n,p) at higher energies is scheduled at the Time-of-Flight facility (n_TOF) at CERN [25]. A secondary contribution is given by the 7Be(n,α)4He process which accounts only for 2.5% of the total Be destruction, with an associated uncertainty of 10%. It has never been tested in the range of BBN temperatures and only one measurement, at thermal neutron energy, has been performed so far by Bassi et al [26] at the ISPRA reactor. Several theoretical extrapolations have been carried out, yielding various estimated cross-section trends with discrepancies of up to two orders of magnitude [27]. A new measured S-factor for the T(3He,γ)6Li reaction rules out an anomalously-high 6Li production during the Big Bang as an explanation to the high observed values in metal-poor first generation stars. The value is also inconsistent with values used in previous BBN calculations [28]. Nevertheless, energy-dependent cross-section of the (n,α) reaction, has been recently measured for the first time from 10 meV to 10 keV neutron energy [29]. Results are consistent, at thermal neutron energy, with the only previous measurement performed in the 60s at a nuclear reactor, but regarding the trend of the cross-section as a function of neutron energy, the experimental data are clearly incompatible with the theoretical estimate used in BBN calculations.
Furthermore, in a recent publication by Hou et al [30] a team of scientists has proposed an elegant solution to the problem. One assumption in BBN is that all the nuclei involved in the process are in thermodynamic equilibrium and their velocities follow the classical Maxwell-Boltzmann distribution. The authors claim that Li nuclei do not obey this classical distribution in the extremely complex, fast-expanding Big Bang hot plasma. By applying the what is known as non-extensive statistics [31] the problem can be solved instead. The modified velocity distributions described by these statistics violate the classical distribution in a very small deviation of about 6.3-8.2%, and can successfully and simultaneously predict the observed primordial abundances of D, He, and Li (Fig. 2).
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Figure 2. Distribution of early primordial light elements in the universe by time and temperature. The model (dotted lines) successfully predicts a lower abundance of the Be isotope - which eventually decays into Li - relative to the classical Maxwell-Boltzmann distribution (solid lines), without changing the predicted abundances of D or He [30]. |
Alternative proposed solutions to the problem are the modification of the expansion rate during BBN [32] or depletion of 7Li in stellar interiors [33]. Clearly, the problem of 7Li is still an open issue in astrophysics and it represents an exciting challenge for the future.