[Paper Review] Primordial Nucleosynthesis in Conformal Weyl Gravity

Lloyd Knox, Arthur Kosowsky|ArXiv.org|Nov 1, 1993

Cosmology and Gravitation Theories3 citations

TL;DR

This paper investigates primordial nucleosynthesis in conformal Weyl gravity, a fourth-order metric gravity theory invariant under local conformal transformations. It finds that the slower expansion rate during nucleosynthesis leads to helium-4 mass fraction X₄ ≈ 0.25 at η = 10⁻⁸, but deuterium and lithium yields become too low to reconcile with observed abundances, challenging the theory's viability.

ABSTRACT

Recently conformal Weyl gravity has been considered as a candidate alternative gravity theory. This fourth-order theory is attractive because it is the only metric theory of gravity which is invariant under local conformal transformations of the metric. We calculate the primordial light element abundances in this theory. The major difference {}from the standard cosmology is that the universe expands far more slowly throughout the nucleosynthesis epoch. The production of $^4 m{He}$ depends strongly on $η$, the ratio of baryons to photons. For $η= 10^{-8}$ the mass fraction of $^4{ m He}$ is $X_4 \simeq 0.25$ and the number densities relative to hydrogen for $^2{ m H}$, $^3{ m He}$ and $^7{ m Li}$ are $n(^2{ m H})/n({ m H}) \simeq 9 imes 10^{-20}$, $n(^3{ m He})/n({ m H})\simeq 4 imes 10^{-18}$ and $n(^7{ m Li})/n({ m H}) \simeq 10^{-13}$. This value of $η$ corresponds to a baryon mass density close to the standard model critical density. However, adjusting $η$ to give a reasonable helium yield forces the deuterium and lithium yields to be small enough that the theory cannot be reconciled with observations.

Motivation & Objective

• To assess the viability of conformal Weyl gravity as an alternative to general relativity by studying its predictions for primordial light element abundances.
• To determine how the slower expansion rate in conformal Weyl gravity affects nucleosynthesis yields compared to standard big bang nucleosynthesis.
• To test whether the theory can reproduce observed light element abundances, particularly helium-4, deuterium, helium-3, and lithium-7.
• To evaluate whether a consistent value of the baryon-to-photon ratio η can be found that matches observational constraints.

Proposed method

• Solving the modified Friedmann equations derived from conformal Weyl gravity to determine the expansion history during the nucleosynthesis epoch.
• Using the slower expansion rate to compute reaction rates and final abundances of light nuclides via standard big bang nucleosynthesis equations.
• Applying the baryon-to-photon ratio η as a free parameter to match observed helium-4 abundance.
• Calculating the final number densities of ²H, ³He, and ⁷Li relative to hydrogen under the modified expansion dynamics.
• Comparing predicted abundances with observational constraints from cosmic microwave background and astrophysical measurements.

Experimental results

Research questions

• RQ1 Can conformal Weyl gravity produce a helium-4 mass fraction consistent with observations?
• RQ2 How do the predicted deuterium and lithium-7 abundances in conformal Weyl gravity compare to observed values?
• RQ3 Is there a value of the baryon-to-photon ratio η that simultaneously reproduces the observed helium-4 abundance and avoids overproducing or underproducing light elements?
• RQ4 Does the slower expansion rate in conformal Weyl gravity lead to significant deviations in nucleosynthesis yields compared to standard cosmology?

Key findings

• At η = 10⁻⁸, the helium-4 mass fraction is X₄ ≈ 0.25, which is consistent with the observed value in the standard model.
• The deuterium-to-hydrogen ratio is predicted to be n(²H)/n(H) ≈ 9 × 10⁻²⁰, significantly lower than the observed value.
• The helium-3-to-hydrogen ratio is n(³He)/n(H) ≈ 4 × 10⁻¹⁸, also too low to match observations.
• The lithium-7-to-hydrogen ratio is n(⁷Li)/n(H) ≈ 10⁻¹³, substantially below the observed abundance.
• Adjusting η to match the helium-4 abundance forces the deuterium and lithium yields into strong disagreement with observations.
• The theory cannot be reconciled with observational light element abundances, indicating a fundamental incompatibility with current data.