Alleviating Cosmological Tensions with a Coupled Scalar Fields Model

In this paper, we investigate the interaction between early dark energy (EDE) and scalar field dark matter, proposing a coupled scalar fields model to address the Hubble tension and $S_8$ tension. While the EDE model successfully alleviates the Hubble tension, it exacerbates the $S_8$ tension. To mitigate the negative impact of EDE, we introduce the interaction between EDE and dark matter. Specifically, we replace cold dark matter with scalar field dark matter, given its capability to suppress structure growth on small scales. We constrained the new model using cosmological observations including the temperature and polarization anisotropy power spectra data of cosmic microwave background radiation (CMB) from \textit{Planck} 2018 results, baryon acoustic oscillations (BAO) measurements extracted from 6dFGS, SDSS and BOSS, the Pantheon sample of type Ia supernovae (SNIa), the local distance-ladder data (SH0ES), and the Dark Energy Survey Year-3 data. Employing Markov Chain Monte Carlo method, we find that this novel model yields best-fit values of $H_0$ and $S_8$ equal to $71.13$ km/s/Mpc and $0.8256$, respectively. Compared to the $\Lambda$CDM model, the new model alleviates the Hubble tension but still fails to resolve the $S_8$ tension. However, we obtain a smaller value of $S_8$ compared to the result of $0.8316$ obtained for EDE model, which mitigates to some extent the shortcoming of the EDE model.