Bounce Inflation with Dynamical Dark Energy in Light of DESI DR2

Recently, the Dark Energy Spectroscopic Instrument Data Release 2 (DESI DR2) suggests that the dark energy in our universe might be evolving, favoring the Chevallier-Polarski-Linder (CPL) parameterization and a lower Hubble constant. In our previous work, it has been reported that cosmological model with the non-singular bounce inflation (BI) scenario and $\mathrm{\Lambda }$CDM might alleviate the Hubble tension into 3$\sigma$ confidence. In this paper, we study the cosmological model of BI with a dynamical dark energy. We find that individual consideration of the CPL parameterization and the data $\mathtt{\text{DESI}}\mathtt{\text{DR2}}$ tend to larger Hubble constants for both BI and power law (PL) case with cosmic microwave background (CMB) data. Employing BI with combined CPL parameterization and $\mathtt{\text{DESI}}\mathtt{\text{DR2}}$, we obtain the Hubble constant $H_0=65.2_{-2.2}^{+1.8}\mathrm{k}\mathrm{m}\cdot {\mathrm{s}}^{-1}\cdot {\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$, which is larger than $H_0=64.0\pm 2.1\mathrm{k}\mathrm{m}\cdot {\mathrm{s}}^{-1}\cdot {\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$ for the PL case. After considering nontrivial weak lensing effect and spatial curvature as well as adding $\mathtt{\text{Pantheon+}}$, BI fits 3.1$\sigma$ confidence of $\mathrm{\Lambda }$CDM with $w_0=-0.919\pm 0.038$ and $w_{\mathrm{a}}=-0.37\pm 0.12$, and it prefers evolving dark energy than the PL case with $w_0=-0.960\pm 0.074$ and $w_{\mathrm{a}}=-0.15_{-0.25}^{+0.28}$.