Phantom: Cosmology, Instrumentation & Beyond

• Phantom is defined in cosmology as dark energy with an equation-of-state parameter w<-1, signifying super-accelerated cosmic expansion and potential instabilities.
• It also encompasses diverse phenomena in instrumentation and robotics, such as AFM phantom forces and stealth UAV designs, which alter conventional behavior.
• Phantom resources include datasets and software tools in machine learning and computational cosmology, enhancing research in adversarial defense and dark matter analysis.

Searching arXiv for recent and relevant papers on “phantom” across the main research senses represented here. arXiv search query: phantom cosmology equation of state crossing w=-1 modified gravity quintom Across the literature represented here, “phantom” denotes several technically distinct notions. In cosmology and gravitation it most often refers either to an effective dark-energy regime with equation-of-state parameter $w< -1$, or to scalar or electromagnetic sectors with a wrong-sign kinetic term; in that setting the term is tied to phantom crossing at $w=-1$, late-time acceleration, singularities, compact objects, and modified gravity (Hirano et al., 2010). In other areas, the same word names a current-induced force artifact in atomic force microscopy, a low-visibility spinning UAV, adversarial-safety datasets, halo-model software, and a face-swap protection framework (Wutscher et al., 2012). The shared label therefore does not identify a single theory or method; it marks a family of concepts whose common feature is typically an effective departure from ordinary behavior, whether in cosmological dynamics, force microscopy, robotics, or computational infrastructure.

1. Cosmological meaning of “phantom”

In cosmology, phantom behavior is defined by an equation-of-state parameter

$w \equiv \frac{p}{\rho}$

with $w<-1$. The line $w=-1$ is the “phantom divide,” separating cosmological-constant behavior from more negative effective pressure. In the standard classification summarized in the literature here, a cosmological constant has $w=-1$, quintessence-like dark energy has $-1<w<-\tfrac13$, and phantom dark energy has $w<-1$, implying super-accelerated expansion and, in standard field theory, frequent association with negative kinetic terms and ghost instabilities (Hirano et al., 2010).

A central distinction is between a fundamental phantom component and an effective phantom regime. Canonical single-field quintessence satisfies $w_\phi\ge -1$, whereas several papers here study mechanisms by which the effective dark-energy sector can exhibit $w_{\rm DE}<-1$ without introducing a fundamental wrong-sign scalar. The stability literature goes further: for a broad class of single-field effective scalar cosmologies with ghost freedom enforced through $w=-1$0 and $w=-1$1, the phantom divide acts as a “stability-protected boundary,” so continuous ghost-free evolution into $w=-1$2 is forbidden and $w=-1$3 emerges as a late-time attractor (Sahoo, 25 Jan 2026).

A common misconception is that “phantom” always denotes a fundamental ghost field. The corpus here shows a broader usage. “Phantom” can refer to an effective equation of state generated by modified gravity, to coupled quintessence reinterpreted through an observational dark-energy sector, or to composite mechanisms in which the observable $w=-1$4 becomes smaller than $w=-1$5 even though the underlying ingredients remain canonical (Andriot, 15 May 2025).

2. Phantom crossing and late-time dark-energy constructions

One line of work realizes phantom crossing through modified gravity rather than exotic matter. In the Dvali–Gabadadze–Porrati framework, the original self-accelerating DGP branch does not cross $w=-1$6, and the Dvali–Turner extension with constant $w=-1$7 also fails: $w=-1$8 for $w=-1$9, $w \equiv \frac{p}{\rho}$0 for $w \equiv \frac{p}{\rho}$1, and $w \equiv \frac{p}{\rho}$2 for $w \equiv \frac{p}{\rho}$3. The “Phantom Crossing DGP” model remedies this by promoting $w \equiv \frac{p}{\rho}$4 to $w \equiv \frac{p}{\rho}$5, with $w \equiv \frac{p}{\rho}$6 the scale factor and $w \equiv \frac{p}{\rho}$7 constant, so that the effective DGP equation of state crosses the phantom divide when $w \equiv \frac{p}{\rho}$8. Its modified Friedmann equation is

$w \equiv \frac{p}{\rho}$9

The best-fit parameters reported are $w<-1$0 and $w<-1$1, implying a crossing redshift $w<-1$2. In the SNIa+CMB+BAO comparison quoted there, the Phantom Crossing DGP model gives $w<-1$3, $w<-1$4, and $w<-1$5, compared with $w<-1$6, $w<-1$7, $w<-1$8 for the Dvali–Turner model and $w<-1$9, $w=-1$0, $w=-1$1 for the original DGP model (Hirano et al., 2010).

A second class of constructions uses two effective degrees of freedom. Quintom models combine one quintessence-like field and one phantom-like field so that the total equation of state can cross $w=-1$2 smoothly while each field stays on its own side of the divide. The recent two-scalar quintom study represented here emphasizes hill-top and hyperbolic-tangent “cliff-face” potentials bound from above, and reports that the hyperbolic-tangent form can reproduce the desired phantom crossing suggested by DESI BAO, although with significant fine-tuning of initial conditions and potential parameters (Goh et al., 15 Sep 2025).

Other late-time models exploit bounded potentials and sign-switching vacuum structure. The “Ph-$w=-1$3CDM” construction uses a phantom scalar with

$w=-1$4

to generate a smooth mirror AdS-to-dS transition in the late-time dark-energy density, with a de Sitter attractor rather than a Big Rip. In its mirror case, the paper reports $w=-1$5 for the potential sign switch and $w=-1$6 for the density sign switch (Akarsu et al., 9 Jun 2026). A related proposal realizes a low-redshift phantom crossing from Standard Model fermion condensation plus GR backreaction from nonlinear structure formation; for $w=-1$7, its CPL fit gives $w=-1$8, $w=-1$9, and $w=-1$0, consistent with combined DESI+CMB+SNIa analyses quoted there (Liu et al., 9 Jul 2026).

3. Stability bounds, singularities, and effective reinterpretations

The modern stability analysis represented here makes the status of the phantom divide highly nontrivial. In a broad class of single-field effective scalar cosmologies minimally coupled to Einstein gravity, with background energy conservation, $w=-1$1, and $w=-1$2, one has

$w=-1$3

with equality only when $w=-1$4. In the Hubble-modulated models treated there, the hypersurface $w=-1$5 is an invariant manifold: trajectories approach $w=-1$6 asymptotically, but continuous ghost-free evolution cannot cross into $w=-1$7 (Sahoo, 25 Jan 2026). This result sharply separates stable single-field evolution from phenomenological phantom-crossing models that require extra degrees of freedom, modified gravity, or a reinterpretation of the dark sector.

The singularity literature then asks what persistent phantom behavior does at the level of cosmic evolution. The review on phantom singularities surveys Big Rip, Big Freeze, sudden singularities, Type IV singularities, Little Rip, and the Little Sibling of the Big Rip, emphasizing that phantom fields typically lead to singular late-universe behavior in GR. It also reviews Wheeler–DeWitt and loop quantum cosmology analyses in which several such singularities are avoided in the quantum theory, either through vanishing wave functions on singular configurations or through effective bounce dynamics (Bouhmadi-López et al., 2019). Another misconception is therefore that $w=-1$8 automatically implies an unavoidable Big Rip. The bounded-potential and stability-protected constructions represented here instead give de Sitter-like late-time attractors or prevent any stable entry into the phantom regime at all (Akarsu et al., 9 Jun 2026).

Coupled-quintessence models provide a third path: they keep canonical scalar kinetics but redefine the observational dark-energy sector. With matter and possibly radiation coupled through scalar-dependent prefactors, the effective dark-energy density becomes

$w=-1$9

and $-1<w<-\tfrac13$0 can become phantom even though $-1<w<-\tfrac13$1. In that framework, steep exponential potentials

$-1<w<-\tfrac13$2

can fit current observations and reproduce the phantom regime. The same study further argues that poles in $-1<w<-\tfrac13$3, appearing when $-1<w<-\tfrac13$4, may occur at recent times $-1<w<-\tfrac13$5, and that an Early-Dark-Energy-like feature appears systematically in the models considered (Andriot, 15 May 2025).

4. Phantom sectors in defects and black holes

Outside background cosmology, phantom sectors are used to modify defects, black holes, and strong-field observables. In the domain-wall setting, the model with two real scalar fields described in “Phantom Domain Walls” admits phantom domain wall solutions whose tension grows with cosmic time because of the evolution of a phantom scalar field. This yields an additional damping term in the wall equation of motion,

$-1<w<-\tfrac13$6

and the macroscopic analysis concludes that extended phantom defects whose tension varies on a cosmological timescale cannot be the dark energy (Avelino et al., 2017).

In black-hole physics, “phantom” often means a scalar or electromagnetic field with a wrong-sign kinetic term. In Einstein–(anti-)Maxwell–(anti-)dilaton theory, the strong-deflection lensing analysis shows that phantom scalar and/or phantom electromagnetic fields produce considerable changes in the angular position, brightness, and separation of relativistic images relative to ordinary black holes (Gyulchev et al., 2012). The three-dimensional analog in “Phantom BTZ black holes” treats an anti-Maxwell field in BTZ-(A)dS geometry and reports that phantom BTZ black holes have a single horizon whose radius increases with charge, exist for $-1<w<-\tfrac13$7, $-1<w<-\tfrac13$8, and $-1<w<-\tfrac13$9, satisfy the first law of thermodynamics, and possess larger local and global stability regions than Maxwell BTZ black holes (Panah et al., 2024).

Accretion studies provide another strong-field manifestation. For phantom energy accretion onto the Schwarzschild–de Sitter black hole, the conserved energy and mass fluxes imply that the black-hole mass decreases because $w<-1$0. The analysis finds two critical points lying in the exterior of the black-hole and cosmological horizons, and recovers the Schwarzschild result in the limit $w<-1$1 (Sharif et al., 2011). In this setting, “phantom” is not merely a label on the equation of state; it changes the sign of the accretion effect.

5. Phantom in instrumentation and robotic design

In atomic force microscopy, the “phantom force” is a specific, current-induced modification of the electrostatic tip–sample force. In combined STM / FM-AFM, the frequency shift can be written empirically as

$w<-1$2

with positive phantom-force slope $w<-1$3 corresponding to a less negative, apparently repulsive force signal as the tunneling current increases. The resistive model underlying the effect assumes a local voltage drop

$w<-1$4

under the tip, caused by the high areal current density of tunneling. This reduces the electrostatic attraction and produces current-correlated “repulsive” contrast. The study shows that the effect occurs not only on Si(111)-$w<-1$5 but also on H/Si(100), that a metallic surface state does not suppress it, and that the local resistance $w<-1$6 strongly affects its magnitude (Wutscher et al., 2012).

In robotics, “Phantom Twist” denotes a low-visibility single-propeller UAV designed to exploit high-speed spinning and motion blur. The vehicle spins at around 15–25 rotations per second, and its geometry is optimized by a two-stage automated pipeline that places batteries, a control PCB, a motor-propeller assembly, and counterweights so as to minimize a human-aligned perceptual metric, LPIPS, subject to inertial and aerodynamic constraints. The paper reports that the optimized design produces stable, controllable flight and significantly reduced visual perceptibility compared with conventional quadcopters, with gradient refinement reducing average visibility by 12% and the best design reaching an LPIPS visibility score of 0.0104 (Wang et al., 11 May 2026). In this usage, “phantom” no longer refers to $w<-1$7; it denotes engineered visual inconspicuity.

6. PHANTOM as dataset, software, and protective framework

Several papers use PHANTOM as the formal name of a research resource. The term then functions as an acronym or system name rather than as a physical descriptor. The three examples represented here occupy machine learning, computational cosmology, and privacy-preserving vision.

The multimodal safety dataset PHANTOM is a large-scale, open-source collection of pre-generated adversarial attacks for vision-LLMs. It contains 47,524 adversarial samples generated from 7,826 intents, organized into 10 high-level categories and 55 subcategories of harmful intent, and is intended to support systematic robustness evaluation, attack-generation research, and the stress-testing of defensive guardrails (Gallivanone et al., 23 Jun 2026). The cosmology toolbox phantom—“Profile and Halo Analysis for Numerous Theoretical dark Matter Observables”—is a public MATLAB toolbox and Octave package that connects the linear density field to halo observables; its abstract reports sub-percent agreement with the Python packages colossus, hmf, and halomod across shared models for distances, power spectra, variance, correlation functions, halo mass functions, and density profiles (Chowdhury, 17 Jun 2026). The face-swap protection framework Phantom jointly constrains perturbations in latent and spatial domains, synthesizes identity-shifted yet attribute-preserving targets, and masks perturbations to semantically relevant facial regions; it improves dodging protection success rates by 27.8%, 25.6%, and 16.6% on UniFace, INSwapper, and SimSwap, respectively, and improves impersonation protection by up to 10.2% while improving perceptual fidelity (Kim et al., 30 Jun 2026).

PHANTOM system	Domain	Reported scope
PHANTOM (Gallivanone et al., 23 Jun 2026)	VLM safety	47,524 attacks; 7,826 intents; 10 categories; 55 subcategories
phantom (Chowdhury, 17 Jun 2026)	Computational cosmology	MATLAB/Octave toolbox linking linear density fields to halo observables
Phantom (Kim et al., 30 Jun 2026)	Deepfake protection	Latent and spatial constraints for proactive face-swap defense

These uses illustrate the full semantic spread of the term. In one branch of the literature, “phantom” names a cosmological regime defined by $w<-1$8, along with its crossing, stability, and singularity structure. In another, it labels experimentally observed forces, low-visibility robots, adversarial datasets, numerical software, and privacy-preserving defenses. The convergence is linguistic rather than theoretical: the same word persists, but its technical content is discipline-specific and must be inferred from context.