Quintom-B: Dark Energy Crossing Dynamics

• Quintom-B is a class of dark-energy models where the equation of state crosses from w < -1 at high redshift to w > -1 at low redshift.
• Observational reconstructions using DESI BAO, supernovae, and CMB data reveal varying crossing redshifts, highlighting a data-favored trend rather than a fixed value.
• Theoretical frameworks—including modified gravity, EFT approaches, and field-theoretic models—demonstrate viable mechanisms for this transition while addressing stability and UV completion issues.

Quintom-B denotes the subclass of quintom cosmologies in which the dark-energy equation-of-state parameter crosses the cosmological-constant boundary $w=-1$ from the phantom regime to the quintessence regime as the universe expands. In the recent dark-energy literature, it is defined by $w(z\gg 1)<-1$, $w(z\approx 0)>-1$, and at least one crossing redshift $z_c$ with $w(z_c)=-1$ and $dw/dz|_{z_c}>0$. DESI-motivated reconstructions have made this pattern a concrete observational target, while model-building studies have explored its realization in modified gravity, two-field systems, teleparallel frameworks, spinor cosmology, quantum cosmology, bounce scenarios, and UV-complete constructions (Yang et al., 2024, Yang et al., 9 Apr 2025, Qiu et al., 25 Nov 2025, Koutroulis, 25 Mar 2026).

1. Definition and terminological scope

The term “quintom” was coined in April 2004 to describe dark-energy models whose equation-of-state parameter $w\equiv p/\rho$ can evolve smoothly across the cosmological-constant boundary $w=-1$. Within this classification, Quintom-A refers to trajectories with $w>-1$ at high redshift and $w<-1$ at low redshift, whereas Quintom-B refers to the reverse trajectory, with $w(z\gg 1)<-1$0 at early times and $w(z\gg 1)<-1$1 at late times (Qiu et al., 25 Nov 2025).

In the background formulation used in recent DESI analyses, the effective dark-energy equation of state is defined through

$w(z\gg 1)<-1$2

with $w(z\gg 1)<-1$3 and $w(z\gg 1)<-1$4, leading to

$w(z\gg 1)<-1$5

Quintom-B is then the case in which $w(z\gg 1)<-1$6 crosses $w(z\gg 1)<-1$7 from below to above as $w(z\gg 1)<-1$8 decreases, with $w(z\gg 1)<-1$9 and $w(z\approx 0)>-1$0 (Yang et al., 2024).

The nomenclature is not completely uniform across subliteratures. In one teleparallel study, the label “Quintom-B” is used for the sector retaining both non-minimal couplings to the torsion scalar $w(z\approx 0)>-1$1 and the boundary term $w(z\approx 0)>-1$2 (Bahamonde et al., 2018). In a quantum-cosmology construction, the “Quintom-B” case refers to a specific hyperbolic or sinh–cosh potential (Socorro et al., 2013). This suggests that, outside the standard dynamical-EoS classification, the label can also function as a model-specific designation.

2. Observational reconstruction after DESI

A central development has been the non-parametric reconstruction of $w(z\approx 0)>-1$3 and $w(z\approx 0)>-1$4 from baryon acoustic oscillation data. One analysis reconstructs the Hubble rate and its derivative from DESI 2024 BAO together with previous BAO data using Gaussian processes as implemented in GAPP, adopting the kernel

$w(z\approx 0)>-1$5

with hyperparameters $w(z\approx 0)>-1$6 determined by maximizing the GP likelihood. The datasets are DESI 2024 BAO points in five redshift bins $w(z\approx 0)>-1$7, previous BAO from SDSS, BOSS, WiggleZ, and eBOSS, and a fixed sound horizon $w(z\approx 0)>-1$8 from Planck 2018 for calibration (Yang et al., 2024).

A later analysis reconstructs $w(z\approx 0)>-1$9 from DESI DR2 BAO, Pantheon+ supernovae, and a compressed CMB acoustic-scale data point, again with Gaussian processes but now described as using a squared-exponential kernel. That reconstruction shows $z_c$0 below $z_c$1 for $z_c$2, a crossing around $z_c$3 at $z_c$4 CL, and a quintessence regime for $z_c$5 (Yang et al., 9 Apr 2025).

Reconstruction	Crossing result	Additional quantitative statement
P–BAO only	$z_c$6	Cubic fit $z_c$7; $z_c$8 at about $z_c$9
DESI+P–BAO	$w(z_c)=-1$0	Cubic fit $w(z_c)=-1$1; $w(z_c)=-1$2 at about $w(z_c)=-1$3
DESI DR2+Pantheon++CMB	$w(z_c)=-1$4	Mean values include $w(z_c)=-1$5, $w(z_c)=-1$6, $w(z_c)=-1$7

The difference between the $w(z_c)=-1$8 reconstruction from DESI 2024 plus previous BAO and the $w(z_c)=-1$9 reconstruction from DESI DR2 combined with SNe and CMB indicates that the inferred crossing location is sensitive to the dataset combination and redshift leverage. A plausible implication is that Quintom-B is currently better regarded as a data-favored trend than as a sharply fixed crossing redshift.

The review literature places these reconstructions in a broader observational context. One review states that DESI DR2 with CMB and DESY5 favors a dynamical dark-energy theory with the CPL parameters in the region

$dw/dz|_{z_c}>0$0

which it labels “Quintom-B,” and describes this region as excluded from pure $dw/dz|_{z_c}>0$1CDM at more than $dw/dz|_{z_c}>0$2 (Qiu et al., 25 Nov 2025).

3. Geometric realizations in modified gravity and metric-affine EFT

One response to the reconstructed crossing is to realize it geometrically rather than through explicit phantom matter. In $dw/dz|_{z_c}>0$3, $dw/dz|_{z_c}>0$4, and $dw/dz|_{z_c}>0$5 gravity, the action is written as

$dw/dz|_{z_c}>0$6

and the reconstructed deviation is fit by

$dw/dz|_{z_c}>0$7

with $dw/dz|_{z_c}>0$8 and $dw/dz|_{z_c}>0$9 today. In all cases, the quadratic coefficient satisfies $w\equiv p/\rho$0, which is interpreted as a mild preference for a positive quadratic deviation from $w\equiv p/\rho$1CDM (Yang et al., 2024).

Model	P–BAO coefficients $w\equiv p/\rho$2	DESI+P–BAO coefficients $w\equiv p/\rho$3
$w\equiv p/\rho$4	$w\equiv p/\rho$5	$w\equiv p/\rho$6
$w\equiv p/\rho$7 or $w\equiv p/\rho$8	$w\equiv p/\rho$9	$w=-1$0

For $w=-1$1 gravity, the Jordan-frame effective density and pressure are

$w=-1$2

$w=-1$3

with $w=-1$4 reconstructed from the GP $w=-1$5. The effective equation of state

$w=-1$6

crosses $w=-1$7 in the same way as the GP reconstruction. In teleparallel and symmetric teleparallel formulations, $w=-1$8 on the background, and the corresponding effective quantities in $w=-1$9 and $w>-1$0 reproduce the same phantom-to-quintessence transition (Yang et al., 2024).

A more general formulation is given by the metric-affine EFT of dark energy in unitary gauge, whose background action is

$w>-1$1

Mapping to $w>-1$2 and $w>-1$3 gives explicit EFT functions in terms of $w>-1$4 or $w>-1$5, and motivates the ansatz

$w>-1$6

with the same background history for $w>-1$7 after the replacement $w>-1$8 (Yang et al., 9 Apr 2025).

For this ansatz, the analytic Quintom-B condition is that $w>-1$9 and $w<-1$0 have the same sign, and for $w<-1$1 one gets $w<-1$2 at high redshift with a crossing to $w<-1$3 at low redshift provided additionally that $w<-1$4 and $w<-1$5. The MCMC constraints from DESI DR2+CMB+Pantheon+ are

$w<-1$6

When compared with a quadratic $w<-1$7 model, the information criteria give AIC/BIC values $w<-1$8 for the Quintom $w<-1$9 model and $w(z\gg 1)<-1$00 for the quadratic model, implying $w(z\gg 1)<-1$01 and $w(z\gg 1)<-1$02, while both models fit the data at the same quality. The paper emphasizes that only the Quintom-B model reproduces the crossing directly indicated by the reconstruction (Yang et al., 9 Apr 2025).

Viability conditions are also explicit. In the reconstructed $w(z\gg 1)<-1$03 case one requires $w(z\gg 1)<-1$04 and $w(z\gg 1)<-1$05, while in $w(z\gg 1)<-1$06 or $w(z\gg 1)<-1$07 one requires $w(z\gg 1)<-1$08 and $w(z\gg 1)<-1$09; these are stated to hold at the reconstructed best-fit level within $w(z\gg 1)<-1$10 (Yang et al., 2024).

4. Field-theoretic and teleparallel realizations

The canonical field-theory construction of quintom dark energy uses two minimally coupled scalars, one canonical and one phantom, with action

$w(z\gg 1)<-1$11

The total density and pressure are

$w(z\gg 1)<-1$12

so crossing $w(z\gg 1)<-1$13 requires both fields to be active. Frequently studied potentials include $w(z\gg 1)<-1$14 with either $w(z\gg 1)<-1$15 or $w(z\gg 1)<-1$16, as well as Coleman–Weinberg–type small-field potentials (Qiu et al., 25 Nov 2025).

A teleparallel generalization couples two scalar fields non-minimally to the torsion scalar $w(z\gg 1)<-1$17 and the boundary term $w(z\gg 1)<-1$18, with action

$w(z\gg 1)<-1$19

The power-law couplings are typically

$w(z\gg 1)<-1$20

and the potentials are separable exponentials,

$w(z\gg 1)<-1$21

On a spatially flat FLRW background, $w(z\gg 1)<-1$22 and $w(z\gg 1)<-1$23, and the phase-space analysis yields a matter saddle point $w(z\gg 1)<-1$24 with $w(z\gg 1)<-1$25 together with several de Sitter points or lines with $w(z\gg 1)<-1$26. Numerical evolution shows that the orbit can cross $w(z\gg 1)<-1$27 one or more times before settling into a final de Sitter attractor (Bahamonde et al., 2018).

A different one-field route is provided by spinor quintom cosmology in Einstein–Cartan–Sciama–Kibble theory. There the spinor potential can be chosen so that the equation of state crosses through

$w(z\gg 1)<-1$28

where $w(z\gg 1)<-1$29 and $w(z\gg 1)<-1$30. The explicit potential

$w(z\gg 1)<-1$31

leads to

$w(z\gg 1)<-1$32

and the model is presented as a “Quintom-B” trajectory of phantom $w(z\gg 1)<-1$33 quintessence type. The intrinsic-spin contribution stabilizes the pressure, avoids Big Rip singularities, and can produce an effective matter-dominated epoch (Dil, 2016).

These constructions illustrate the main model-building divide in the Quintom-B literature: some realizations use explicit phantom degrees of freedom, while others seek a purely geometric origin of the crossing. The modified-gravity reconstructions are explicit in presenting the latter as a way to bypass the “no-go” theorem for single scalar fields (Yang et al., 2024).

5. Quantum cosmology, bounce cosmology, and cyclic extensions

In quantum cosmology, the quintom system has been studied in a flat FRW minisuperspace with a phantom field $w(z\gg 1)<-1$34 and a canonical field $w(z\gg 1)<-1$35. The Wheeler–DeWitt equation is

$w(z\gg 1)<-1$36

with $w(z\gg 1)<-1$37. Using the Bohm-like amplitude-real-phase ansatz

$w(z\gg 1)<-1$38

and the separable superpotential

$w(z\gg 1)<-1$39

one obtains a family of potentials. The “Quintom-B” case is the hyperbolic form

$w(z\gg 1)<-1$40

equivalently

$w(z\gg 1)<-1$41

The first integral for the classical trajectories is

$w(z\gg 1)<-1$42

and inflationary behavior is obtained when $w(z\gg 1)<-1$43 (Socorro et al., 2013).

In early-universe quintom cosmology, the crossing of $w(z\gg 1)<-1$44 is also tied to non-singular bounce dynamics. In four-dimensional Einstein gravity,

$w(z\gg 1)<-1$45

A bounce requires $w(z\gg 1)<-1$46 and $w(z\gg 1)<-1$47 at the bounce point, which implies $w(z\gg 1)<-1$48, violation of the null-energy condition, and therefore $w(z\gg 1)<-1$49. After the bounce, $w(z\gg 1)<-1$50 must climb back above $w(z\gg 1)<-1$51 to allow a standard radiation- or matter-dominated phase; this double crossing is described as the hallmark of quintom bounce cosmology (Qiu et al., 25 Nov 2025).

Three explicit bounce realizations are highlighted in the review literature. The first is the two-scalar quintom bounce, with either a large-field potential $w(z\gg 1)<-1$52, $w(z\gg 1)<-1$53, or a small-field Coleman–Weinberg potential for $w(z\gg 1)<-1$54. The second is a single higher-derivative Lee–Wick bounce, in which the Lagrangian

$w(z\gg 1)<-1$55

can be rewritten as a two-field system with one wrong-sign mode. The third is a modified-gravity bounce in $w(z\gg 1)<-1$56 or $w(z\gg 1)<-1$57 cosmology, where one may posit

$w(z\gg 1)<-1$58

and reconstruct the gravitational action accordingly (Qiu et al., 25 Nov 2025).

The same review also describes a cyclic universe with quintom matter, based on the action

$w(z\gg 1)<-1$59

with potential

$w(z\gg 1)<-1$60

An exact solution is

$w(z\gg 1)<-1$61

which yields

$w(z\gg 1)<-1$62

Depending on $w(z\gg 1)<-1$63, the resulting cosmology can be purely oscillatory, growing-amplitude cyclic, perpetually expanding but pulsating, or shrinking quasi-cyclic (Qiu et al., 25 Nov 2025).

6. UV completion, stability criteria, and broader implications

One of the strongest theoretical objections to quintom models is the presence of phantom degrees of freedom. A recent proposal addresses this by embedding Quintom-B dark energy in a 5D anisotropic orbifold lattice, the Non-Perturbative Gauge-Higgs Unification model. The geometry is $w(z\gg 1)<-1$64, with a bulk SU(2) gauge field and two fixed 4D branes. The orbifold projection leaves on the 4D boundary a U(1) gauge field $w(z\gg 1)<-1$65 and a complex scalar $w(z\gg 1)<-1$66, identified with the dark-energy sector (Koutroulis, 25 Mar 2026).

Below the localization scale $w(z\gg 1)<-1$67, the 4D effective action contains dimension-6 higher-derivative operators and takes a Lee–Wick-type form with physical and phantom scalar and gauge fields:

$w(z\gg 1)<-1$68

The negative-sign kinetic terms of $w(z\gg 1)<-1$69 and $w(z\gg 1)<-1$70 make them phantom fields, while auxiliary $w(z\gg 1)<-1$71-ghosts are introduced to cancel extra Lee–Wick poles and render the theory perturbatively consistent (Koutroulis, 25 Mar 2026).

On an FRW background, the dark-energy equation of state is written as

$w(z\gg 1)<-1$72

The paper states that at early times one can choose the kinetic sector so that $w(z\gg 1)<-1$73, while at late times mass terms drive $w(z\gg 1)<-1$74. The crossing from below to above then occurs provided the gauge-ghost mass $w(z\gg 1)<-1$75 and field amplitude $w(z\gg 1)<-1$76 are sufficiently large relative to the scalars (Koutroulis, 25 Mar 2026).

The same work gives explicit stability criteria. For linear perturbations, absence of exponential growth requires $w(z\gg 1)<-1$77 for all $w(z\gg 1)<-1$78, which with $w(z\gg 1)<-1$79 yields the quartic $w(z\gg 1)<-1$80-ghost coupling range

$w(z\gg 1)<-1$81

for $w(z\gg 1)<-1$82 and $w(z\gg 1)<-1$83. Vacuum decay through graviton exchange is controlled by the finite lattice cutoff,

$w(z\gg 1)<-1$84

and the estimate

$w(z\gg 1)<-1$85

The choice $w(z\gg 1)<-1$86 is stated to both fit DESI and suppress catastrophic vacuum decay, while both physical and ghost scalars have $w(z\gg 1)<-1$87 and gauge modes have $w(z\gg 1)<-1$88 (Koutroulis, 25 Mar 2026).

Across the broader literature, stability conditions take different but structurally comparable forms. In reconstructed $w(z\gg 1)<-1$89 gravity they are $w(z\gg 1)<-1$90 and $w(z\gg 1)<-1$91; in reconstructed $w(z\gg 1)<-1$92 and $w(z\gg 1)<-1$93 gravity they are $w(z\gg 1)<-1$94 and $w(z\gg 1)<-1$95; in the UV-complete Lee–Wick-inspired construction they appear as positivity of perturbative frequencies together with a finite cutoff (Yang et al., 2024, Koutroulis, 25 Mar 2026). Taken together, these results indicate that Quintom-B has evolved from a purely phenomenological crossing pattern into a testing ground for the compatibility of dynamical dark energy with geometric reconstruction, EFT control, and UV-sensitive stability requirements.