Effective CPL reconstruction of tachyon dark energy: Background dynamics and observational constraints

We investigate a tachyon dark-energy model with an exponential potential and ask how accurately its late-time background evolution can be represented by an effective Chevallier–Polarski–Linder (CPL) equation of state. The CPL form is not assumed as the fundamental model. Instead, it is reconstructed from the numerical tachyon solution and used as a phenomenological proxy for the underlying non-canonical dynamics. The model is constrained with a joint background likelihood built from DESI DR1 baryon acoustic oscillation measurements, cosmic-chronometer determinations of H ( z ), and the Pantheon+ Type Ia supernova compilation. We perform a refined scan over the exponential slope and the initial conditions of the tachyon field. The preferred solutions lie close to a quasi-frozen regime, with a representative configuration near λ ≃ 0.28, ϕ i n i = 0.10 , and ( d ϕ / d N ) i n i = 0.005 . In this region the reconstructed CPL parameters remain very close to the cosmological-constant limit, and the exact tachyon background is reproduced with fractional differences in H ( z ) of order 10 − 6 . The tachyon solution is therefore competitive with ΛCDM at the level of raw χ 2 , but the improvement is too small to overcome the penalty associated with the additional model freedom. Current late-time background data do not require tachyon dark energy; rather, they allow it mainly in a regime already nearly indistinguishable from ΛCDM and from its own effective CPL reconstruction. This provides a concrete example of how a physically motivated non-canonical scalar-field model can collapse, at the homogeneous level, into a low-dimensional phenomenological description.