Testing $\mathrm{\Lambda }$LTB as an alternative to dynamical dark energy

A cosmological constant $\mathrm{\Lambda }$ in a universe weakly violating the cosmological principle (CP) can mimic a dynamical dark energy (DDE) in a FRW universe, and therefore challenging the recently reported DDE evidences. We test this scenario in the form of $\mathrm{\Lambda }$LTB cosmology, against two data combinations. (1) DESI DR2 BAO, Planck CMB, together with any of the four SNe Ia compilations (UNION3, Pantheon+, DES SN5YR, and DES Dovekie) show no preference over DDE or $\mathrm{\Lambda }$LTB. (2) The inclusion of the kinematic Sunyaev Zel’dovich (kSZ) effect rules out a large portion of the CP violation parameter space allowed by (1). However, the existence of a $\sim 300$ Mpc$\mathrm{/}h$ region with $\sim 10\mathrm{\%}$ matter density excess is still allowed by the current data, and therefore remains a viable alternative to DDE. To facilitate further tests, we present analytical expressions of the distance-redshift relation and the kSZ effect in a universe with weak CP violation.