Barrow Cosmology and Big-Bang Nucleosynthesis

TL;DR

Barrow cosmology modifies the horizon entropy with a fractal exponent $\delta$, and through the thermodynamics–gravity correspondence derives a $\delta$-dependent Friedmann equation featuring an effective gravitational constant $G_{eff}$. The authors constrain $\delta$ using Big-Bang Nucleosynthesis, finding a bound around $\delta \sim 0.01$ from the freeze-out temperature shift $|\delta T_f/T_f|$, while an abundance-based analysis of $^4$He, D, and Li yields largely compatibility only for very small deformation and shows tension with Li data. They also derive a modified time–temperature relation, showing that the early-universe temperature rises with larger $\delta$, highlighting how the fractal horizon structure can affect the thermal history. Overall, the deformation must be small to preserve BBN predictions, and the work points to extending the framework to other entropy-corrected cosmologies and to a more detailed treatment of the $t$–$T$ relation in the early universe.

Abstract

Using thermodynamics-gravity conjecture, we present the formal derivation of the modified Friedmann equations inspired by the Barrow entropy, $S\sim A ^{1+δ/2}$, where $0\leqδ\leq 1$ is the Barrow exponent and $A$ is the horizon area. We then constrain the exponent $δ$ by using Big-Bang Nucleosynthesis (BBN) observational data. In order to impose the upper bound on the Barrow exponent $δ$, we set the observational bound on $\left| \frac{δT_f} {T_f }\right|$. We find out that the Barrow parameter $δ$ should be around $ δ\simeq 0.01$ in order not to spoil the BBN era. Next we derive the bound on the Barrow exponent $δ$ in a different approach in which we analyze the effects of Barrow cosmology on the primordial abundances of light elements i.e. Helium $_{}^{4}\textit{He}$, Deuterium $D$ and Lithium $_{}^{7}\textit{Li}$. We observe that the deviation from standard Bekenstein-Hawking expression is small as expected. Additionally we present the relation between cosmic time $t$ and temperature $T$ in the context of modified Barrow cosmology. We confirm that the temperature of the early universe increases as the Barrow exponent $δ$ (fractal structure of the horizon) increases, too.

Figures (5)

• Figure 1: The behavior of $\delta T_f/T_f$ vs $\delta$ in the modified Barrow cosmology for early universe. Here $\delta T_f/T_f$ is defined in (\ref{['theo']}), while the observational upper bound of $\delta T_f/T_f$ is given by Eq. (\ref{['dtftf']}). Constraints from BBN requires $\delta \simeq 0.01$.
• Figure 2: $Z_{_{}^{4}\textrm{He}}$ vs $\delta$. The experimental range is reported in (\ref{['zhe']}). We have fixed $\eta_{10}=6$ and varied the temperature of freeze-out in the range $T_f=[0.01,10] MeV$.
• Figure 3: $Z_{_{}^{2}\textrm{H}}$ vs $\delta$. The experimental range is reported in (\ref{['zobs']}). We have fixed $\eta_{10}=6$ and varied the temperature of freeze-out in the range $T_f=[0.01,10] MeV$.
• Figure 4: $Z_{Li}$ vs $\delta$. The experimental range is reported in (\ref{['lit']}). We have fixed $\eta_{10}=6$ and varied the temperature of freeze-out in the range $T_f=[0.01,10] MeV$.
• Figure 5: The behavior of $T$ vs $t$ in modified Barrow cosmology for early universe.