Observational implications of Wald-Gauss-Bonnet topological dark energy

TL;DR

This paper develops Wald–Gauss–Bonnet (WGB) topological dark energy by applying the gravity–thermodynamics conjecture to the Universe’s apparent horizon with Wald–Gauss–Bonnet entropy. The resulting modified Friedmann equations tie the dark-energy sector to black-hole formation and merger activity, modeled via the star-formation rate, and introduce an astrophysical contribution to the effective cosmological constant. The authors analyze two models—Model I with Λ = 0 and Model II with Λ ≠ 0—against late-Universe data (SNIa, BAO, CC) and find ΛCDM remains preferred, while Model I is statistically compatible with it and Model II is in moderate tension; perturbation analysis shows negligible DE clustering and an effective Newton constant very close to G_N, with fσ8 closely following ΛCDM. The framework thus provides a physically motivated link between BH astrophysics and dark energy, yielding a consistent, observationally viable alternative that preserves the standard thermal history and offers potential avenues to address H0 tensions via phantom-DE behavior.

Abstract

We investigate the observational implications of Wald--Gauss--Bonnet (WGB) topological dark energy, a modified cosmological framework derived from the gravity-thermodynamics conjecture applied to the Universe's apparent horizon, with the Wald--Gauss--Bonnet entropy replacing the standard Bekenstein--Hawking one. Assuming a topological connection between the apparent horizon and interior black hole (BH) horizons, we derive modified Friedmann equations where the evolution of dark energy depends on BH formation and merger rates, which are approximated by the cosmic star formation rate. These equations introduce an additional, astrophysics--dependent contribution to the cosmological constant. We test two scenarios, one with a vanishing cosmological constant ($Λ= 0$) and another with a modified $Λ$ against late--Universe data (SNIa, BAO, Cosmic Chronometers) via a Bayesian analysis. Although the WGB framework is consistent with observations, information criteria statistically favor the standard $Λ$CDM model. An analysis of linear perturbations shows that the growth of cosmic structures is nearly indistinguishable from that of $Λ$CDM, with negligible dark energy clustering and minimal deviation in the effective Newton's constant. The standard thermal history is also preserved. In conclusion, WGB cosmology presents a phenomenologically rich alternative that connects dark energy to black hole astrophysics while remaining compatible with current cosmological data.

Figures (6)

• Figure 1: Two-dimensional posterior distributions for the free parameters of both WGB models, for all dataset combinations. The contours correspond to the $68\%$ and $95\%$ confidence levels, defined in a mode-independent way via quantiles.
• Figure 2: Reconstruction of the Hubble parameter for WGB cosmology, using the best fit values from CC/Pantheon+/SH0ES/BAOs dataset. The grey shaded areas, correspond to $1\sigma$ (deep grey) and $2\sigma$ (light grey) regions. The red line corresponds to the best fit parameter values for the WGB scenario and the black dashed line to the Hubble rate for the $\Lambda$CDM scenario. Upper panel: Model I Lower panel: Model II.
• Figure 3: Evolution of $f\sigma_8$ in Model I is represented (red dashed line) and Model II (green dash-dot-line) using the best fit parameters from the complete dataset CC/Pantheon+/SH0ES/BAOs, considering for various values of the effective speed sound of DE $c_e$ with each value noted with a distinct color. The $f\sigma_8$ for $\Lambda$CDM appears with blue line. In the above calculations we have used $\sigma_8=0.81$Stolzner:2025htz. The data points with their error-bars have been obtained from Avila:2022xad.
• Figure 4: The evolution of the DE equation of state parameter in Model I is represented (red line) and Model II (blue line), using the best fit parameters from the datasets CC/Pantheon+/SH0ES/BAOs (dashed), Pantheon+/SH0ES/BAOs (dashed - dotted) and CC/BAOs (dotted).
• Figure 5: The difference $\Delta f\sigma_{8} = f\sigma_{8}(c_e=1) - f\sigma_{8}(c_e=0)$, with respect to the acoustic speed of DE $c_e$, in Wald-Gauss-Bonnet cosmology, Model I (red) and Model II (blue), for the best fit parameters in the following datasets: CC/Pantheon+/SH0ES/BAOs (dashed), Pantheon+/SH0ES/BAOs (dashed - dotted), CC/BAOs (dotted). In the above calculations we have used $\sigma_8=0.81$Stolzner:2025htz.