Non-Phantom Dynamical Dark Energy (NPDDE)

• Non-Phantom Dynamical Dark Energy is defined by enforcing w(z) ≥ -1 across all redshifts, thereby excluding phantom behavior and aligning with quintessence-like models.
• Various parameterizations (e.g., CPL, XCDM, φCDM) are used to implement NPDDE, with each model balancing simplicity and physical viability against observational data.
• Recent analyses using DESI BAO, CMB, and supernovae data probe subtle deviations from ΛCDM, distinguishing intrinsic non-phantom physics from effective phantom behavior in interacting and modified models.

Non-Phantom Dynamical Dark Energy (NPDDE) denotes a class of dark-energy models in which the equation of state remains on the non-phantom side of the phantom divide, conventionally written as $w(z)\geq -1$, while still allowing temporal evolution distinct from a strict cosmological constant. In current usage, the term has both a strict and a looser phenomenological meaning. In the strict sense, NPDDE requires $w(z)\geq -1$ for all redshifts and therefore covers the parameter space of quintessence-like single-scalar-field models (Choudhury et al., 2018). In parts of the recent DESI-era literature, by contrast, “non-phantom” is sometimes used to describe only the present-day condition $w_0>-1$, even when the reconstructed history crosses into $w<-1$ at intermediate redshift; this distinction is central to the modern debate on whether current data favor genuine NPDDE or a crossing, “Quintom-B” evolution (Giarè et al., 2024).

1. Definition and conceptual scope

In the strict formulation, NPDDE is defined by the inequality

$w(z)\geq -1 \qquad \forall z,$

which excludes phantom dark energy and retains only quintessence-like behavior. Within the commonly used Chevallier–Polarski–Linder (CPL) parameterization,

$w(z)=w_0+w_a\frac{z}{1+z},$

this condition is implemented through the hard priors

$w_0\geq -1,\qquad w_0+w_a\geq -1,$

which ensure non-phantom behavior both today and in the asymptotic past (Choudhury et al., 2018).

This strict definition matters because several observational analyses now separate two questions that were often conflated in earlier work: whether the present-day equation of state is larger than $-1$, and whether the full redshift evolution remains above $-1$. Recent DESI-based reconstructions frequently find $w_0>-1$ together with $w(z)\geq -1$0, implying a present-day quintessence-like state but a past excursion into the phantom regime; such solutions are not NPDDE in the strict sense even though they are non-phantom today (Li et al., 27 Nov 2025).

NPDDE is therefore best understood as both a phenomenological prior and a theory space. As a prior, it restricts equation-of-state reconstructions to the non-phantom sector. As a theory space, it corresponds most directly to canonical minimally coupled scalar-field quintessence, thawing models, scaling-plus-thawing models, and related constructions in which the kinetic sector remains conventional and $w(z)\geq -1$1 does not cross $w(z)\geq -1$2 (Sohail et al., 22 Dec 2025).

2. Parametrizations and theoretical realizations

A wide range of parameterizations and explicit models have been used to represent NPDDE and to test it against data. The most widely used frameworks are summarized below.

Framework	Defining expression	NPDDE condition
XCDM	$w(z)\geq -1$3	$w(z)\geq -1$4
CPL	$w(z)\geq -1$5	$w(z)\geq -1$6
$w(z)\geq -1$7CDM	$w(z)\geq -1$8	$w(z)\geq -1$9 gives quintessence-like dynamics
PADE	$w_0>-1$0	coefficient-dependent
Divergence-free EoS	bounded $w_0>-1$1 with finite past/future limits	parameter-dependent

The XCDM and CPL forms are the standard phenomenological baselines. XCDM assumes a constant equation of state,

$w_0>-1$2

while CPL promotes it to

$w_0>-1$3

The $w_0>-1$4CDM model replaces the fluid description with a canonical scalar field on an inverse power-law potential,

$w_0>-1$5

with

$w_0>-1$6

The $w_0>-1$7CDM limit is recovered at $w_0>-1$8 (Peracaula et al., 2018).

The PADE approach instead parameterizes the normalized dark-energy density $w_0>-1$9 as a ratio of polynomials in $w<-1$0, and links it to the equation of state through

$w<-1$1

For the simplest case $w<-1$2,

$w<-1$3

This framework was introduced partly to avoid the divergence problems of linear expansions and to provide a well-behaved extension around $w<-1$4CDM (Mehrabi et al., 2018).

A different route to bounded behavior was proposed through a divergence-free parameterization with finite limits both at early and late times: $w<-1$5 This construction preserves two degrees of freedom like CPL but avoids past- and future-time divergences in the equation of state (Akarsu et al., 2015).

Beyond parameterizations, explicit NPDDE realizations have also been built in modified-gravity or high-energy frameworks. In no-scale Brans–Dicke gravity with an added scalar and a global $w<-1$6 symmetry broken to $w<-1$7, the resulting pseudo-Goldstone mode acquires a periodic quintessence potential,

$w<-1$8

and the canonical form of the kinetic term guarantees

$w<-1$9

so the model remains non-phantom by construction (Hong et al., 2 Jun 2025).

3. Observational development from pre-DESI analyses to the DESI era

Before DESI, one of the strongest observational suggestions of NPDDE came from a combined analysis of $w(z)\geq -1 \qquad \forall z,$0 using the full Planck 2015 likelihood. When the large-scale-structure bispectrum was included, XCDM and $w(z)\geq -1 \qquad \forall z,$1CDM departed from $w(z)\geq -1 \qquad \forall z,$2 at roughly $w(z)\geq -1 \qquad \forall z,$3 and $w(z)\geq -1 \qquad \forall z,$4, respectively. For the bispectrum-enhanced $w(z)\geq -1 \qquad \forall z,$5 combinations, the best-fit XCDM value was $w(z)\geq -1 \qquad \forall z,$6, while $w(z)\geq -1 \qquad \forall z,$7CDM yielded $w(z)\geq -1 \qquad \forall z,$8 and a present-day $w(z)\geq -1 \qquad \forall z,$9; the same analysis also reported a reduction of the $w(z)=w_0+w_a\frac{z}{1+z},$0 tension relative to $w(z)=w_0+w_a\frac{z}{1+z},$1CDM (Peracaula et al., 2018).

Other pre-DESI parameterizations gave a more ambiguous picture. In the PADE framework, the best-fit present-day equation of state was on the phantom side, but the data still allowed $w(z)=w_0+w_a\frac{z}{1+z},$2 at $w(z)=w_0+w_a\frac{z}{1+z},$3, and the simplest two-parameter PADE model remained statistically comparable to $w(z)=w_0+w_a\frac{z}{1+z},$4CDM under AIC and weakly favored under Jeffreys’ scale (Mehrabi et al., 2018).

The observational landscape changed substantially with DESI BAO. A 2024 analysis combining DESI BAO with Planck and either PantheonPlus or DESY5 supernovae found that the preference for dynamical dark energy is robust across several two-parameter equation-of-state forms. In all tested parameterizations, the present-day value remained in the quintessence regime, while the evolution parameter was negative, indicating a drift toward phantom values in the past. The significance reached roughly $w(z)=w_0+w_a\frac{z}{1+z},$5 with PantheonPlus and $w(z)=w_0+w_a\frac{z}{1+z},$6 with DESY5, and the analysis explicitly stated that restricting the model space to strict NPDDE, $w(z)=w_0+w_a\frac{z}{1+z},$7 for all $w(z)=w_0+w_a\frac{z}{1+z},$8, weakens the signal and pushes the fit to the boundary of the allowed region (Giarè et al., 2024).

This trend strengthened in later DESI DR2 analyses. Using joint ACT, SPT, and Planck CMB data together with DESI DR2 BAO and DESY5 supernovae, one study reported for the Barboza–Alcaniz parameterization

$w(z)=w_0+w_a\frac{z}{1+z},$9

corresponding to a $w_0\geq -1,\qquad w_0+w_a\geq -1,$0 deviation from the $w_0\geq -1,\qquad w_0+w_a\geq -1,$1CDM values and a reconstructed history in which dark energy was phantom-like in the past but quintessence-like today; the paper described this as a robust preference for the Quintom-B regime across six parameterizations (Li et al., 27 Nov 2025).

Not all post-DESI analyses draw the same inference from current data. A model-independent Gaussian-process reconstruction of the late-time dark-energy density using DESI DR2 BAO together with Pantheon+, Union3, and DESY5 supernovae found that $w_0\geq -1,\qquad w_0+w_a\geq -1,$2, a non-phantom thawing quintessence-type model, and CPL all agree with the reconstructed density at $w_0\geq -1,\qquad w_0+w_a\geq -1,$3 confidence, with the largest discrepancy arising for $w_0\geq -1,\qquad w_0+w_a\geq -1,$4CDM plus DESY5 at low redshift. On that basis, the authors concluded that claims of statistically significant evidence for evolving or phantom dark energy may still be premature (Souza et al., 17 Nov 2025).

A complementary DESI-2025 analysis similarly found that dark energy decay is strongly indicated but that the evidence for phantom behavior is less significant, with explicitly non-phantom models still compatible with current data at the $w_0\geq -1,\qquad w_0+w_a\geq -1,$5 level (Gialamas et al., 26 Jun 2025).

4. Intrinsic NPDDE versus effective phantom behavior

A central theme of the recent literature is that an observationally inferred phantom phase need not correspond to an intrinsically phantom dark-energy sector. This point has been developed in several distinct ways.

In interacting dark-energy models, the effective equation of state measured under the assumption of a non-interacting dark sector differs from the intrinsic one. For a dark-matter–dark-energy interaction $w_0\geq -1,\qquad w_0+w_a\geq -1,$6,

$w_0\geq -1,\qquad w_0+w_a\geq -1,$7

the effective equation of state is

$w_0\geq -1,\qquad w_0+w_a\geq -1,$8

Using a thawing quintessence-like intrinsic $w_0\geq -1,\qquad w_0+w_a\geq -1,$9, one DESI-motivated study found that the intrinsic equation of state remains non-phantom without imposing a non-phantom prior, while the effective equation of state can show a low-significance phantom crossing; the same analysis reported that a nonzero interaction is favored at more than $-1$0 around $-1$1 (Guedezounme et al., 24 Jul 2025).

A related mechanism appears in dissipative dark energy, where a quintessence field loses energy to dark matter through a friction term $-1$2,

$-1$3

In this setting the inferred effective equation of state becomes

$-1$4

so that $-1$5 can arise even though the underlying scalar field always satisfies $-1$6. The explicit claim of that analysis is that even weak late-time dissipation is sufficient to explain the apparent DESI phantom crossing without invoking pathological phantom dynamics (Chanda et al., 3 Jun 2026).

An even more radical reformulation replaces the dark-matter-plus-dark-energy split by a unified dark fluid with vanishing rest-frame sound speed and no anisotropic stress. The unified equation of state is defined as

$-1$7

and the model is constructed to reproduce the same background expansion history as the CPL best fit while remaining non-phantom by construction. Its linear observables differ from CPL only at the few-percent level, and current Planck, DESI DR2, and DESY5 data were found to fit this UDF nearly as well as CPL (Kou et al., 19 Sep 2025).

These analyses collectively challenge the common assumption that a background-level preference for $-1$8 automatically excludes NPDDE-like microphysics. A plausible implication is that background expansion data alone are insufficient to determine whether the underlying dark energy is intrinsically non-phantom, effectively phantom, or part of a more general dark-sector reparameterization.

5. Perturbative consistency, early-time behavior, and extended parameter spaces

The viability of NPDDE cannot be assessed from the background expansion alone. A stringent perturbative critique was presented in a full linear scalar-perturbation analysis of a non-interacting baryon–cold-dark-matter–scalar-field cosmology with relative entropic perturbations and effective scalar-field sound speed $-1$9. In that framework, the inclusion of non-adiabatic pressure perturbations makes structure growth extremely sensitive to departures from $-1$0, and an acceptable matter growth rate is achieved only for

$-1$1

Under those assumptions, the analysis concluded that a large class of canonical scalar-field dynamical dark-energy models, including quintessence-like NPDDE, is effectively ruled out (Zimdahl et al., 2019).

Other studies point to more model-dependent conclusions. Early-time non-phantom behavior in thawing, scaling-plus-thawing, and related scalar-field models has been constrained with current CMB, DESI DR2 BAO, Pantheon+, chronometer, and RSD data. The steepness of the scaling exponential potential was found to satisfy $-1$2–$-1$3, implying

$-1$4

and therefore $-1$5 around matter–radiation equality. The stated consequence is that scaling or tracker-type NPDDE cannot provide a substantial early-dark-energy component and cannot alleviate the Hubble tension (Sohail et al., 22 Dec 2025).

Interacting NPDDE has also been tested in a CPL-based framework with

$-1$6

For perturbative stability in the quintessence regime, the interaction must satisfy $-1$7, corresponding to energy transfer from CDM to dark energy. CMB-only data allow substantial degeneracy, but the most constraining combination $-1$8 tightens the bounds to $-1$9, $w_0>-1$0, $w_0>-1$1, with $w_0>-1$2; the study concludes that this class of models cannot fully resolve the Hubble tension (Giarè et al., 2024).

NPDDE priors also affect constraints on non-dark-energy parameters. In a 12-parameter extension including $w_0>-1$3, $w_0>-1$4, $w_0>-1$5, and $w_0>-1$6, imposing the non-phantom CPL bounds produced

$w_0>-1$7

from Planck+BK14+BAO, tighter than the quoted $w_0>-1$8 bound of $w_0>-1$9 eV from Planck+BAO. The interpretation given is that removing the phantom sector also removes part of the degeneracy between dark-energy evolution and neutrino mass (Choudhury et al., 2018).

A further extended NPDDE analysis using DESI DR2 BAO, Planck PR4, Planck and ACT lensing, Pantheon+ or DESY5 supernovae, and DES Y1 weak lensing reported a different phenomenological issue: once the equation of state is constrained to remain non-phantom, the fit prefers $w(z)\geq -1$00 at more than $w(z)\geq -1$01 for $w(z)\geq -1$02 and $w(z)\geq -1$03. In that setting, realistic quintessence-like NPDDE comes together with a significant lensing-amplitude anomaly rather than with a clean improvement over $w(z)\geq -1$04CDM (Choudhury et al., 30 Sep 2025).

6. Status, controversies, and outlook

The status of NPDDE in contemporary cosmology is unsettled because different analyses emphasize different observables, priors, and levels of modeling. One line of evidence, initiated before DESI by bispectrum-enhanced large-scale-structure analyses and extended by DESI BAO plus supernovae, points toward late-time dark-energy dynamics with a present-day quintessence-like equation of state, often at the $w(z)\geq -1$05–$w(z)\geq -1$06 level depending on the data combination and parameterization (Peracaula et al., 2018). Another line of evidence argues that the data specifically prefer histories that cross the phantom divide in the recent past, so that strict all-redshift NPDDE is not the statistically preferred realization even when $w(z)\geq -1$07 today (Li et al., 27 Nov 2025).

At the same time, model-independent reconstructions and non-crossing analyses show that current data do not yet decisively eliminate $w(z)\geq -1$08CDM or thawing quintessence-like NPDDE. This suggests that some of the apparent evidence for phantom behavior may be parameterization-dependent, particularly when inferred from background observables alone (Souza et al., 17 Nov 2025).

A recurring misconception is that NPDDE is automatically the theoretically safer option. Canonical scalar-field models do naturally obey $w(z)\geq -1$09, but once perturbations, entropy modes, or dark-sector couplings are treated more fully, the relation between “non-phantom” and “consistent” becomes model-dependent. Conversely, it is equally misleading to read every observational preference for $w(z)\geq -1$10 as evidence for intrinsic phantom dark energy, because interacting, dissipative, unified-fluid, and other frameworks can reproduce an effective phantom crossing while preserving an underlying non-phantom sector (Yao et al., 2 Aug 2025).

The likely direction of progress is therefore not simply tighter background constraints on $w(z)\geq -1$11, but a more integrated use of perturbation-level observables, higher-order large-scale-structure statistics, lensing, redshift-space distortions, and consistency tests across alternative dark-sector decompositions. Within that broader program, NPDDE remains an important benchmark class: it is the natural phenomenological envelope for quintessence-like theories, a useful prior for extended cosmological parameter estimation, and a central reference point in the ongoing effort to determine whether current hints of dynamical dark energy reflect genuine new physics or the current limits of cosmological inference.