Perturbation-level viability and empirical discrimination of evolving dark matter as the origin of the DESI expansion-history anomaly

DESI DR2 baryon-acoustic-oscillation data, combined with the CMB and supernovae, prefer a late-time expansion history that, under the assumption of purely cold dark matter, is usually interpreted as evolving (even phantom, $w<-1$) dark energy. Chen and Loeb showed that the same background data can instead be accounted for if roughly 10–20% of dark matter is an 'exotic dark matter' (EDM) component whose equation of state evolves or oscillates within $-1<w<1$, avoiding null-energy-condition violation. The background-level viability and template fits have since been established, but the scenario remains unverified at the perturbation and structure-formation level, and no observable has been worked out that empirically distinguishes evolving dark matter from genuinely evolving dark energy. The open problem is to establish or rule out EDM as the origin of the DESI-indicated deviation through perturbation-level analysis (including the model-dependent sound speed of concrete microphysical models), N-body/nonlinear structure verification against CMB anisotropies, lensing, growth, and halo profiles, fits of microphysical rather than purely phenomenological templates, and targeted probes such as cosmic voids and small-scale escape-speed thresholds.

Background

The equation of state (EOS) of a cosmic fluid is the ratio $w$ of its pressure to its energy density. In the standard $\Lambda$CDM model, cold dark matter (CDM) is pressureless ($w=0$) and dark energy is a cosmological constant ($w=-1$). In 2024–2025 the Dark Energy Spectroscopic Instrument (DESI) measured baryon acoustic oscillations (BAO, the standard-ruler imprint of primordial sound waves on the galaxy distribution) in its second data release (DR2); combined with cosmic microwave background (CMB) and Type Ia supernova (SNe) distances, the data mildly favor a time-dependent dark-energy EOS, conventionally parameterized as $w(a)=w_0+w_a(1-a)$ (the Chevallier–Polarski–Linder, or CPL, form). The best-fit behavior crosses below $w=-1$ (the 'phantom divide') at early times, which violates the null energy condition (NEC) — a property of ordinary local, causal theories that phantom behavior conflicts with and that makes UV-complete model building problematic. An alternative, proposed by Chen and Loeb (JCAP 07 (2025) 059), keeps dark energy a cosmological constant and instead lets a subcomponent of dark matter — 'exotic dark matter' (EDM) — carry an evolving, typically oscillating EOS with $-1<w<1$, sourced microscopically by a scalar field oscillating in a non-quadratic potential whose effective EOS depends on the local density. If the dark matter is assumed to be entirely cold when fitting, such a component is misread as evolving, possibly phantom, dark energy; the two scenarios are degenerate in background expansion data, i.e. they can produce nearly identical Hubble rates $H(a)$. The original paper analyzed only the background expansion, using piecewise-constant step templates for $w_{\rm EDM}(a)$, and identified what remains open: perturbation-level analysis and N-body simulations for the concrete microphysical potentials (including the role of the EDM sound speed $c_s$, with $c_s^2$ the derivative of pressure with respect to energy density in the fluid rest frame, which is model-dependent — in the source's canonical oscillating-scalar example it can be effectively zero over a vast range of sub-Hubble scales despite the evolving EOS, while a finite sound speed would prevent the component from falling into shallow gravitational potential wells), full parameter-estimation fits, other microphysical realizations, effects on the Hubble tension (the discrepancy between locally measured and CMB-inferred values of the present expansion rate $H_0$), and discriminating probes such as cosmic voids (large underdense regions whose density profiles are sensitive to the growth history) and small-scale escape-speed thresholds (a component with finite sound speed cannot be gravitationally bound in halos whose escape speed falls below that sound speed, so its presence on dwarf versus cluster halo scales is diagnostic). Perturbations of non-standard dark matter have a framework — generalized dark matter (Hu 1998), where the clustering of a fluid on cosmological scales is governed by its EOS and rest-frame sound speed — and the cosmic-history-averaged dark-matter EOS had earlier been bounded near zero (Kopp et al. 2018), but those treatments use constant or slowly varying ansätze, not the late-time oscillating reinterpretation at issue here. The degeneracy between evolving dark energy and evolving dark matter in $H(a)$ alone means the question can only be settled by the perturbation and nonlinear regime and by observables that separate the two scenarios.

Problem Statement

Can the late-time expansion-history deviation indicated by DESI DR2 BAO, CMB, and supernova data be attributed to a subcomponent (~10–20%) of dark matter with an evolving or oscillating equation of state within $-1<w<1$ rather than to genuinely evolving (phantom-crossing) dark energy — and, given that the two scenarios are degenerate in background expansion data, can this exotic-dark-matter (EDM) interpretation be established or ruled out at the perturbation and structure-formation level and empirically distinguished from evolving dark energy? Concretely, for concrete microphysical realizations (such as the oscillating-scalar potentials of Chen & Loeb, whose effective equation of state depends on local density and whose rest-frame sound speed is model-dependent — effectively zero over a vast range of sub-Hubble scales in their canonical example, but possibly finite in other realizations): (1) perform the perturbation-level analysis and nonlinear/N-body simulations verifying whether linear and nonlinear structure formation, CMB anisotropies, lensing, and halo density profiles remain consistent with observations for the parameter ranges that fit the background data, including the role of the finite sound speed; (2) fit microphysical EDM models (beyond smooth phenomenological templates) self-consistently to combined DESI, CMB, and supernova data and quantify whether they can also affect other tensions such as the Hubble tension; and (3) identify and quantify targeted astrophysical probes — cosmic-void measurements, small-scale escape-speed thresholds, growth-rate and lensing analyses — whose outcome would empirically distinguish evolving dark matter from evolving dark energy. These components jointly serve one objective: determining whether the EDM interpretation of the DESI-indicated deviation is viable and distinguishable, or must be discarded in favor of evolving dark energy. These sub-questions concern concrete microphysical realizations, with the canonical oscillating-scalar realization of Chen & Loeb as the representative case. The EDM interpretation is discarded if the consistency checks of (1) fail, or if the microphysical fits of (2) cannot reproduce the data; if (1) and (2) establish viability but (3) yields no observable that empirically distinguishes evolving dark matter from evolving dark energy, the verdict is that EDM remains viable but is not yet empirically distinguishable.

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