Big bang nucleosynthesis constraints on scalar-tensor theories of gravity

TL;DR

This work introduces a comprehensive numerical framework to test scalar-tensor theories of gravity against Big Bang Nucleosynthesis by embedding arbitrary self-interaction potentials and matter couplings into a BBN code. It validates the approach with a massless dilaton and quadratic coupling, analyzes the impact of mass thresholds on field dynamics, and quantifies the resulting changes in light-element abundances, especially ^4He, under WMAP-determined baryon density. The study further extends the model to include a cosmological constant, examining Einstein-frame and Jordan-frame realizations and showing late-time impacts without altering BBN-era attraction toward GR. By pairing BBN with CMB constraints and solar-system tests, the paper emphasizes the complementarity of probes for gravity beyond GR and provides a flexible tool for exploring extended quintessence and other scalar-tensor scenarios. The results indicate that, for sufficiently large β, deformations from GR during BBN are tightly constrained mainly by ^4He, while D/H remains largely insensitive, and Li-7 persists as a challenge, guiding future explorations of gravity theories with cosmological implications.

Abstract

We investigate BBN in scalar-tensor theories of gravity with arbitrary matter couplings and self-interaction potentials. We first consider the case of a massless dilaton with a quadratic coupling to matter. We perform a full numerical integration of the evolution of the scalar field and compute the resulting light element abundances. We demonstrate in detail the importance of particle mass thresholds on the evolution of the scalar field in a radiation dominated universe. We also consider the simplest extension of this model including a cosmological constant in either the Jordan or Einstein frame.

Figures (22)

• Figure 1: $a_{\rm out}$ as a function of $a_{\rm in}$ for different values of $\beta$ between 1 and 100. We see that $a_{\rm out}<a_{\rm in}$ which reflects the attraction towards general relativity during electron-positron annihilation.
• Figure 2: The general structure of $a_{\rm out}$ as a function of $a_{\rm in}$ and $\beta$. This illustrates the complexity of the solutions of Eq. (\ref{['kgqq']})
• Figure 3: Evolution of the scalar field in phase space during a transition for $\beta=1,5,50$ from top to bottom when we assume $\varphi_{*{\rm in}}=1$. The solid line corresponds to the exact solution of Eq. (\ref{['kgqq1']}) while the dashed line corresponds to the solution of the approximate equation (\ref{['kgqapprox']}).
• Figure 4: Evolution of $a_{\rm out}/a_{\rm in}$ as a function of $\beta$. (Top): when we used the approximate equation (\ref{['kgqapprox']}), it does not depend on the initial value of the scalar field, $\varphi_{*{\rm in}}$. (middle and bottom): we use the exact equation (\ref{['kgqq1']}). This equation being non-linear the ratio depends on the initial value of $\varphi_{*{\rm in}}$.
• Figure 5: The source function, $\Sigma(T)$, entering the Klein-Gordon equation when the mass thresholds corresponding to the particles listed in the text. The dashed curves show the individual particle contributions, $\Sigma_i(T)$, and the solid curve shows the sum, $\Sigma(T)$.