Cosmological Lithium Problem

• Cosmological Lithium Problem is defined by a 3–4 times discrepancy between the high 7Li abundance predicted by Big Bang nucleosynthesis and the lower levels measured in Population II stars.
• It integrates chemical evolution models, detailed stellar evolution, and hierarchical structure formation to explain the persistent Spite plateau across different galactic environments.
• The resolution involves accounting for primordial inflow, early star formation, and astrophysical depletion processes that collectively shape the observed lithium abundance.

The cosmological lithium problem refers to the well-documented discrepancy between the mean primordial ^7Li abundance predicted by standard big bang nucleosynthesis (BBN)—anchored by precise measurements of the baryon-to-photon ratio from cosmic microwave background (CMB) data—and the lower value observed in the atmospheres of old metal-poor (Population II) “Spite plateau” stars. This discordance, approximately a factor of 3–4, remains unresolved after decades of scrutiny integrating stellar evolution, chemical enrichment models, nonstandard nuclear physics, and particle physics. Explanations have invoked both cosmological and astrophysical processes, ranging from new particle sectors to revised chemical evolution in the context of hierarchical structure formation.

1. Discrepancy Between Primordial Nucleosynthesis and Stellar Lithium Observations

BBN, as constrained by CMB-determined η, robustly predicts light element abundances. The predicted primordial ^7Li/H is

$$\mathrm{^7Li/H}_{\mathrm{BBN}} \approx (4.94 \pm 0.72) \times 10^{-10}$$

Empirical determinations from surface lithium abundances of Spite plateau stars yield values in the range

$$\mathrm{^7Li/H}_{\text{obs}} \sim (1.6 \pm 0.3) \times 10^{-10}$$

(Miranda, 13 Aug 2025)

This ≈3× discrepancy is confirmed across Galactic halo field stars, extragalactic dwarfs, and globular clusters (e.g., ω Centauri (Monaco et al., 2010), M54 in Sagittarius (Mucciarelli et al., 2014)), indicating the effect is independent of local galactic chemical evolution and must be universal. Various observational campaigns, employing high-resolution spectroscopy (e.g., FLAMES-GIRAFFE/VLT), consistently observe the Spite plateau—a near-constant lithium abundance in warm, metal-poor main sequence or early subgiant stars—despite differing metallicities, star formation histories, and host environments.

2. Chemical Evolution, Structure Formation, and the Spite Plateau

Resolution of the lithium problem requires integrating BBN predictions within an explicit chemical evolution model tied to the cosmic star formation history and hierarchical structure formation. In models coupling standard chemical enrichment with Press–Schechter–like halo assembly, baryonic inflow is partitioned into H, He, and lithium according to BBN yields. The primordial lithium supply is accreted into nascent halos according to

$$a_{b-\mathrm{Li}}(t) = 4.94 \times 10^{-10} \cdot a_b(t)$$

where $a_b(t)$ is the baryonic mass accretion rate (Miranda, 13 Aug 2025). Star formation acts upon this infall, and the subsequent capture and astration by Population III and II stars determines the time-dependent galactic lithium content.

Chemical enrichment tracks yields from both Pop III (massive, zero-metallicity stars) and Pop II (lower mass) stars. The model distinguishes among Pop III branches:

• HW10/CL08 (10–100 M☉): some lithium incorporation and delayed production.
• HW02 (140–260 M☉, pair-instability supernovae): prompt lithium removal along with rapid iron enrichment.

As metallicity in halo gas increases beyond transition thresholds (e.g., $Z = 10^{-6}, 10^{-4}$), Pop II star formation ensues, with stellar yields (including from novae and cosmic-ray spallation) restoring lithium at metallicities [Fe/H] ≳ –3.

Within this hierarchical paradigm, a substantial fraction of primordial lithium is locked up in (or processed by) early stars before the bulk of observed Pop II halo stars form. The subsequent tracking of lithium abundance as a function of [Fe/H] shows an extended plateau at

$$\mathrm{^7Li/H}_{\text{plateau}} \sim 1.81 \times 10^{-10}\,, \quad -8.0 \lesssim [\mathrm{Fe/H}] \lesssim -2.0$$

consistent with observations (Miranda, 13 Aug 2025).

3. Constraints from Extremely Metal-Poor Stars and Model Calibration

Empirical calibration is facilitated by a comparison with extremely metal-poor stars (EMPS), such as J0023+0307 and SMSS J0313–6708, which have [Fe/H] upper limits of approximately –6.1 and –7.1, respectively (Miranda, 13 Aug 2025). Stellar models fit these abundances by accounting for the time delay after the first Pop III deaths and associated infall dilution. The formation times relative to Pop III explosions are inferred to be

Star	Formation Time Post-Pop III	Observed A(Li)	Modeled Pop III Mass
J0023+0307	4.4×10⁵ – 1.3×10⁶ yr	2.02	∼60–100 M☉
SMSS J0313–6708	2.2×10⁵ – 4.4×10⁵ yr	0.7	∼60 M☉ (progenitor)

The lithium abundances in these EMPS stars are explained by the model as resulting from prompt astration and dilution events following the first massive star deaths in the associated minihalos.

4. Astrophysical and Stellar Depletion Processes

Any model of the lithium problem must also contend with depletion mechanisms intrinsic to stellar evolution. Proposed astrophysical processes—such as protostellar accretion-induced PMS burning (Cassisi et al., 2020, Tognelli et al., 2020), turbulent mixing, or diffusion—can alter lithium abundances post-formation. For instance, certain cold accretion scenarios for Pop II low-mass stars can lead to significant pre-main-sequence lithium depletion if initial seed masses and radii are sufficiently small. However, these mechanisms are effective only in a restricted parameter space and require fine tuning, and do not universally produce the observed plateau unless such conditions are ubiquitously met in star-forming regions.

Conversely, models depending on enhanced lithium destruction via massive Pop III stars or mixing processes must not overproduce heavy metals or otherwise disrupt the established Spite plateau in different galactic environments (Spite et al., 2012, Monaco et al., 2010, Mucciarelli et al., 2014).

5. Impact of Pop III and Pop II Star Yields, Nova Systems, and Cosmic Ray Spallation

The model captures detailed lithium production/destruction mechanisms using mass-dependent yields. Pop II yields are calculated using evolutionary codes (e.g., MONSTAR with OPAL opacities), while nova contributions (relevant at [Fe/H] > –1.0) are obtained via binary population synthesis and delayed by ∼1 Gyr. Lithium from Galactic cosmic-ray (GCR) spallation emerges at [Fe/H] > –3.0, determined by the integrated GCR flux and ambient ISM CNO content (Miranda, 13 Aug 2025). These mechanisms combine with the primordial lithium accretion term to ensure the plateau is preserved at low metallicity but the meteoritic ^7Li abundance is recovered at Solar metallicity due to later accumulation of nova and GCR contributions.

6. Universality and Hierarchical/Environmental Effects

Multiple lines of evidence confirm the universal nature of the lithium discrepancy:

• The Spite plateau is observed in disparate environments (ω Centauri, M54 in Sagittarius, EMPS of the Milky Way), excluding galaxy-specific or finely-tuned local astration as solutions (Monaco et al., 2010, Mucciarelli et al., 2014).
• The model demonstrates the necessity of including primordial lithium inflow in the baryon accretion term to reproduce observed plateaus.
• The effects of hierarchical structure formation imply that halo environments, subhalo formation (e.g., globular cluster progenitors), and the timing/location of Pop III star formation influence the detailed history of lithium depletion or retention.

When these hierarchical processes are included, even contributions from Pop III pair-instability SNe (140–260 M☉), which can rapidly astrate lithium and enrich the halo in metals, are compatible with a persistent plateau if primordial lithium is continually accreted into the star-forming regions.

7. Conclusion: Reconciling BBN and the Spite Plateau in a Hierarchical Cosmological Framework

The cosmological lithium problem, when evaluated in the context of modern hierarchical structure formation and detailed chemical evolution modeling, no longer appears as an irreconcilable discrepancy. The extended Spite plateau observed in low-metallicity field and cluster stars emerges naturally when global infall of primordial gas, the yields from Pop III and II stars, and later contributions from novae and GCR spallation are self-consistently included (Miranda, 13 Aug 2025). The plateau thus constitutes a signature of early star formation, linked both to the timing of the first stellar generations and to the assembly history of halos at high redshift. The apparent underabundance of lithium relative to BBN predictions is explained not by unaccounted-for destruction in stars or by new fundamental physics, but by the interplay of baryonic infall, star formation efficiency, and the selective removal or sequestration of lithium by high-mass Pop III stars and subsequent galactic chemical evolution.

In this scenario, the Spite plateau’s existence, and its extension to the most iron-poor stars, directly reflect the earliest epochs of cosmic star formation and the physics of baryon cycling in hierarchical galaxy assembly. Future refinement of this integrated chemical-hierarchical framework and targeted observations of primitive systems will further illuminate the links between BBN, the first stars, and observed lithium abundances.