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 $\Lambda$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 \texttt{DESI 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 \texttt{DESI DR2}, we obtain the Hubble constant $H_ 0 = 65.2^{ + 1.8}_{ - 2.2} \ \mathrm{km} \cdot \mathrm{s}^{ -1 } \cdot \mathrm{Mpc}^{ -1 }$, which is larger than $H_ 0 = 64.0 \pm 2.1 \ \mathrm{km} \cdot \mathrm{s}^{ -1 } \cdot \mathrm{Mpc}^{ -1 }$ for the PL case. After considering nontrivial weak lensing effect and spatial curvature as well as adding \texttt{Pantheon+}, BI fits 3.1$\sigma$ confidence of $\Lambda$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 $w_{ \mathrm{a}} = -0.15^{ +0.28}_{ -0.25}$.