Does DESI Provide Evidence for Dynamical Dark Energy?

arXiv:2608.21405v1 Announce Type: new Abstract: Recent results from the Dark Energy Spectroscopic Instrument (DESI) have been announced as evidence that dark energy is dynamical. We distinguish three claims the headline announcement conflates: (D1) the data disfavour the $Lambda$CDM expansion history; (D2) within GR plus a smooth fluid with Chevallier--Polarski--Linder (CPL) equation of state, the data prefer $(w_0,w_a)\neq(-1,0)$; and (D3) there exists a dynamical dark-energy component---a physical degree of freedom in the matter sector, coupled to gravity and to the standard sectors only gravitationally, with an evolving equation of state. We show that DESI establishes D2 and thereby supports D1 but not D3. Two results carry the negative claim: the \lq{}designer\rq{} construction in $f(R)$ gravity shows that observables fixed by the background expansion history cannot discriminate, even in principle, between 'fluid' and 'gravitational' readings of that history, and non-minimally coupled theories free of internal pathology fit the DESI-preferred phenomenology as well as the fluid template does, so no one has shown the gravitational reading to fail. A further argument bites: the phantom crossing the fits select demands exotic matter under the fluid reading and arises without pathology under the gravitational one. We characterise the resulting underdetermination between matter-sector and gravitational-sector and draw a moral for survey reporting.