Gravitational-Susceptibility Dip Behind DESI's results: Addressing the Phantom Crossing by Local limit of Nonlocal Gravity

Abstract: The second data release of the Dark Energy Spectroscopic Instrument (DESI), based on more than fourteen million galaxies and quasars, prefers a dark energy component whose equation of state is dynamical. In the simplest two-parameter description of this behavior, the Chevallier--Polarski--Linder (CPL) parametrization, the data favor the quadrant $w_0>-1$, $w_a<0$, which implies that the equation of state crosses the phantom divide $w=-1$ at a redshift $z\simeq0.4$. We show that the local limit of nonlocal gravity, a teleparallel extension of general relativity governed by a scalar function called gravitational susceptibility $S(x)$, offers a natural explanation. In this model a cosmological constant is not allowed; dark energy is necessarily dynamical. The phantom crossing seen by an observer is an effective phenomenon generated by the time evolution of $S(z)$. We establish a correspondence: to every general-relativistic dark energy model with equation of state $w(z)$, there corresponds a modified TEGR cosmology with $w=-1$ and a suitable susceptibility $S(z)$ that are indistinguishable at the level of the background expansion. We construct the susceptibility functions that reproduce the CPL behavior favored by DESI data, and we confront the model with the combined CMB,BAO, and SNe data using Boltzmann solver codes. The recovered susceptibility displays a characteristic low-redshift dip with depth $β= -0.025 \pm 0.007$ at $z\simeq 0.4$, and its derivative changes sign at a redshift equal to the phantom-crossing epoch.