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The response of primordial abundances to a general modification of $G_{\rm N}$ and/or of the early universe expansion rate

C. Bambi, M. Giannotti, F. L. Villante

TL;DR

This work analyzes how a time variation of the Newton constant $G_{\rm N}$ would alter Big Bang Nucleosynthesis (BBN) predictions for light-element abundances. It derives analytic relations linking $G_{\rm N,f}$ and $G_{\rm N,d}$ to primordial yields and introduces response functions $\varrho_i(\eta,T)$ to map arbitrary $H(T)$ histories to abundance changes, complemented by numerical results that reveal two key epochs: the weak freeze-out and the deuterium bottleneck. The findings show that $^4$He is most sensitive to the freeze-out epoch, while deuterium, $^3$He, and $^7$Li respond mainly to the deuterium bottleneck, with quantified coefficients that capture their epochal dependencies. Using observational data for $D/H$ and $^4{\rm He}$, and priors from CMB/LSS on the baryon-to-photon ratio, the study places robust bounds on $\delta G_{\rm N}$ during BBN, finding results compatible with no variation and outlining a framework applicable to broader non-standard cosmologies and varying constants.

Abstract

We discuss the effects of a possible time variation of the Newton constant $G_{\rm N}$ on light elements production in Big Bang Nucleosyntesis (BBN). We provide analytical estimates for the dependence of primordial abundances on the value of the Newton constant during BBN. The accuracy of these estimates is then tested by numerical methods. % Moreover, we determine numerically the response of each element to an arbitrary time-dependent modification of the early universe expansion rate. Finally, we determine the bounds on possible variations of $G_{\rm N}$ which can be obtained from the comparison of theoretical predictions and observational data.

The response of primordial abundances to a general modification of $G_{\rm N}$ and/or of the early universe expansion rate

TL;DR

This work analyzes how a time variation of the Newton constant would alter Big Bang Nucleosynthesis (BBN) predictions for light-element abundances. It derives analytic relations linking and to primordial yields and introduces response functions to map arbitrary histories to abundance changes, complemented by numerical results that reveal two key epochs: the weak freeze-out and the deuterium bottleneck. The findings show that He is most sensitive to the freeze-out epoch, while deuterium, He, and Li respond mainly to the deuterium bottleneck, with quantified coefficients that capture their epochal dependencies. Using observational data for and , and priors from CMB/LSS on the baryon-to-photon ratio, the study places robust bounds on during BBN, finding results compatible with no variation and outlining a framework applicable to broader non-standard cosmologies and varying constants.

Abstract

We discuss the effects of a possible time variation of the Newton constant on light elements production in Big Bang Nucleosyntesis (BBN). We provide analytical estimates for the dependence of primordial abundances on the value of the Newton constant during BBN. The accuracy of these estimates is then tested by numerical methods. % Moreover, we determine numerically the response of each element to an arbitrary time-dependent modification of the early universe expansion rate. Finally, we determine the bounds on possible variations of which can be obtained from the comparison of theoretical predictions and observational data.

Paper Structure

This paper contains 5 sections, 17 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The role of $G_{\rm N}$ in BBN
  3. Response functions
  4. The BBN bound on $\delta G_{\rm N}$
  5. Summary and conclusions

Figures (2)

  • Figure 1: The response functions $\varrho_{i}(\eta,T)$ as a function of the temperature $T$, for $\eta=\eta_{\rm CMB}$. The functions $\varrho_{i}(\eta,T)$ describe the effect of an arbitrary time-dependent modification of the early universe expansion rate on the various elemental abundances (see text for details).
  • Figure 2: The bounds on $\delta G_{\rm N}$ which can be obtained from $^2{\rm H}$ and $^4{\rm He}$ observational data. The upper panels are obtained considering BBN alone. The lower panels are obtained by combining BBN data with the measurement of the baryon to photon ratio from CMB and LSS (see text for details).