Interacting bosonic dark energy and fermionic dark matter in Einstein scalar Gauss-Bonnet gravity

Abstract

We explore a cosmological framework in which a Gauss-Bonnet (GB) coupled scalar field, acting as dark energy, interacts with a fermionic dark matter field through a coupling obtained from the point of view of particle physics. This setup is inspired by string/M-theory, and two representative scalar field potentials are investigated: exponential and power-law. A distinctive feature of the GB-coupled models is their potential to alter the propagation speed of gravitational waves (GWs), a property with significant implications in light of recent multi-messenger astrophysical observations. To account for this, we analyze models under two scenarios: one where the GW speed differs from that of light and the other where they are equal, but all consistent with current observational constraints. The dynamical evolution of the system is investigated by reformulating the field equations into an autonomous dynamical system, enabling a detailed analysis of the Universe's long-term behavior, including the radiation-, matter- and dark energy-dominated epochs. We constrain the model parameters using a broad set of recent observational data, including mock high-redshift measurements from the Roman Space Telescope. Our findings indicate that both potentials yield cosmologies that are in excellent agreement with current data, closely tracking the expansion history predicted by the standard \(Λ\)CDM model, while still allowing room for subtle deviations that could be tested by future observations.

Figures (7)

• Figure 1: The evolution of the cosmological parameters $\Omega_{\phi}$, $\Omega_{\psi}$, $\Omega_{r}$, $\Omega_b$ and $w_{\text{tot}}$ for Model I is shown as a function of $N$. The system is initialized with the parameter values: $\beta = 10^{-8}$, $W_0 = 1$, $x_0 = 10^{-13}$, $y_0 = 0.82$, $z_0 = 0.005$, $v_0 = 10^{-35}$, $B=0.1$, $\Omega_{r,0} = 0.0009$, $\Omega_{b,0}h^2=0.0223$. We also examine the evolution of the gravitational wave (GW) constraint for the same initial configuration, ensuring consistency with observational limits. The main panel shows the full cosmological evolution up to the present epoch, where $c_{T}^2 \rightarrow 1$ The inset displays the early-time behavior on a logarithmic scale, clearly demonstrating a smooth exponential decay. The slight irregularity near $10^{-16}$ arises from the machine-precision limit of the numerical solver and is not physical.
• Figure 2: Evolution of the Hubble parameter $H(z)$ as a function of redshift $z$ for distinct initial conditions $y_0$ for Model I. The curves correspond to theoretical predictions for $y_0 \in (0.81, 0.85)$, along with the standard $\Lambda$CDM model. The data points with error bars represent cosmic chronometer (CC) measurements of $H(z)$. The plot illustrates the impact of varying $y_0$ on the expansion history and its consistency with observational data. All model curves are generated for the fixed value of $H_0 = 70\, \text{km/s/Mpc}$.
• Figure 3: The evolution of the cosmological parameters $\Omega_{\phi}$, $\Omega_{\psi}$, $\Omega_{r}$, $\Omega_b$ and $w_{\text{tot}}$ for Model II is shown as a function of $N$ in which we set $c_T = 1$, so the gravitational wave constraint is identically satisfied. In order to explicitly realize a radiation-dominated epoch and verify consistency with the standard cosmological sequence, the density-parameter evolution is obtained by imposing initial conditions deep in the radiation era at $N=-20$ and evolving the system forward. For completeness, the dynamical phase-space variables are displayed and the system is initialized at the present epoch with parameter values: $\gamma=10^{-6}$, $\mu=- 10^{-4}$, $x_0=10^{-5}$, $y_0 = 0.8$, $z_0 = 0.5$, $\Theta_0 = 10^{-23}$, $\Omega_{r0} = 0.00009$, $\Omega_{b0}=0.223$.
• Figure 4: Evolution of the Hubble parameter $H(z)$ as a function of redshift $z$ for different values of the model parameter $y_0$ for Model II. The curves correspond to theoretical predictions for $y_0 \in (0.81,0.85 )$, along with the standard $\Lambda$CDM model. The data points with error bars represent cosmic chronometer (CC) measurements of $H(z)$. The plot illustrates the impact of varying $y_0$ on the expansion history and its consistency with observational data. All model curves are generated using the same set of initial conditions and a fixed value of $H_0 = 70\, \text{km/s/Mpc}$.
• Figure 5: Marginalized one- and two-dimensional posterior distributions (68% and 95% CL) for $H_0$, $\Omega_{\phi} = x_0^2 + y_0^2$, $z_0$, and $\Omega_{b0}h^2$ in interacting Models I and II, derived from the combined CMB+CC+DESI datasets with PP, DESY5 and Roman supernova samples, as shown in the legend.