Antigravity: Concepts, Models, and Cosmology

• Antigravity is a collection of theories encompassing repulsive cosmic dynamics driven by negative pressure, sign-changing gravitational coupling, and effective matter–antimatter repulsion.
• Models employ scalar–tensor frameworks, Weyl-invariant two-scalar cosmologies, and exact test-particle dynamics to delineate transitions between attractive and repulsive gravitational regimes.
• Empirical studies, including antihydrogen free-fall measurements and galaxy cluster analyses, help distinguish standard dark energy effects from more speculative antigravity proposals.

Antigravity denotes a family of non-equivalent concepts rather than a single theory. In relativistic cosmology it may refer to accelerated expansion when the effective source satisfies $\rho+3P<0$, most commonly through vacuum energy or dark energy. In scalar–tensor and Weyl-invariant frameworks it denotes a regime in which the coefficient of the Ricci scalar changes sign, so that the effective Newton coupling becomes negative. In antimatter literature it usually means gravitational repulsion between matter and antimatter, while in exact test-particle dynamics it can describe an effective outward force generated by spin–curvature coupling rather than a reversal of the source field itself. Other constructions invoke negative active gravitational mass, dual matter sectors, or vacancy-dominated geometries; outside fundamental gravity, the term is also used for load-managing bodily regulation against gravity rather than for repulsive gravitation in the field-theoretic sense (Dolgov, 2012, Oikonomou et al., 2014, Plyatsko et al., 2016, Klinkhamer et al., 2018, Wilkinson et al., 2023).

1. Conceptual scope and competing definitions

A primary distinction in the literature is between repulsive cosmological dynamics and repulsive pairwise interaction. In the former, general relativity permits accelerated expansion because pressure gravitates, with the acceleration equation written schematically as $\ddot a \sim -(\rho+3P)$; sufficiently negative pressure therefore yields cosmological “antigravity” without implying laboratory-scale shielding or propulsion (Dolgov, 2012). In the latter, antigravity is taken to mean that particular sectors of matter repel one another, as in matter–antimatter or ordinary–dual interactions.

A second distinction concerns the sign of the gravitational coupling. In scalar–tensor models of the Jordan-frame form

$$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$

the effective coupling is

$$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$

When $\varphi-\mathcal B<0$, the theory is said to enter an antigravity regime. This definition is operational and differs from matter–antimatter repulsion, because it concerns the sign of the coefficient multiplying $R$ rather than the interaction of two object classes (Oikonomou et al., 2014).

The term is also used more narrowly for effective repulsion in exact dynamics. In the Mathisson–Papapetrou treatment of a spinning test particle in Schwarzschild spacetime, “antigravity” refers to strong repulsive behavior caused by spin–curvature coupling in the highly relativistic regime; the background Schwarzschild field remains attractive, so the effect is explicitly not “true antigravity” in the sense of changing the source’s gravitational field (Plyatsko et al., 2016).

Outside fundamental gravity, the phrase acquires a different meaning. In developmental and sensorimotor theory, “antigravity homeostasis” is defined as the organism’s effortful regulation of body position, form, and action against gravity, with neutral buoyancy in utero proposed as the developmental set-point; this usage is biomechanical and homeostatic, not a claim about repulsive spacetime curvature or negative gravitational charge (Wilkinson et al., 2023).

2. Cosmological repulsion, vacuum energy, and local dark-energy dynamics

Within standard relativistic cosmology, antigravity appears most conservatively as the effect of a source with sufficiently negative pressure. Vacuum energy, with

$P_{\rm vac}=-\rho_{\rm vac},$

is the simplest case, and a vacuum-dominated universe expands exponentially. This is the framework in which dark energy is understood as a repulsive cosmic component. The observational motivation summarized in the literature includes Type Ia supernovae, the cosmic microwave background, large-scale structure, and the age of the universe, with the dark-energy component occupying roughly $75\%$ of the cosmic energy budget in the inventory quoted there (Dolgov, 2012).

A more localized application is the treatment of dark energy as an effective antigravity force on megaparsec scales. For the Virgo Cluster, a nonlinear spherical analytical model embeds a quasi-stationary central mass concentration in a uniform dark-energy background with density $\rho_\Lambda$ and equation of state $p_\Lambda=-\rho_\Lambda$. In Newtonian language, the vacuum contributes an outward acceleration

$\ddot a \sim -(\rho+3P)$0

because the GR-effective gravitating density is $\ddot a \sim -(\rho+3P)$1. The competition between this linearly growing term and the cluster’s $\ddot a \sim -(\rho+3P)$2 gravity defines the zero-gravity radius

$\ddot a \sim -(\rho+3P)$3

inside which gravity dominates and outside which antigravity dominates (Chernin et al., 2010).

For Virgo, using $\ddot a \sim -(\rho+3P)$4, the quoted estimate is $\ddot a \sim -(\rho+3P)$5, close to and slightly larger than the observed zero-velocity radius $\ddot a \sim -(\rho+3P)$6. The observed Hubble diagram of 761 galaxies displays a two-component structure: a central cluster region with velocities scattered around zero and an outer flow with positive recession velocities. Beyond roughly $\ddot a \sim -(\rho+3P)$7 Mpc, the flow becomes progressively more regular and approaches a linear relation $\ddot a \sim -(\rho+3P)$8, with the most accurate data lying near $\ddot a \sim -(\rho+3P)$9 with $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$0, and the asymptotic dark-energy-dominated law approaching $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$1 (Chernin et al., 2010).

This local analysis is presented as evidence that dark-energy antigravity is not merely a global background effect but a dynamical ingredient of the Virgo flow and, by scaling, of the Local Group outflow as well. The proposed “two-component” architecture—a bound central core plus an expanding dark-energy-dominated outskirts flow—therefore treats antigravity as an organizing principle of structure on $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$2 Mpc scales rather than as an exotic departure from $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$3CDM (Chernin et al., 2010).

3. Sign-changing gravity in scalar–tensor and Weyl-invariant theories

A large theoretical literature identifies antigravity with a sign flip of the effective Planck mass squared. In the $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$4-derived scalar–tensor and Brans–Dicke constructions, the sign of $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$5 determines whether $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$6 is positive or negative. A central result is that antigravity may appear in the Jordan-frame scalar–tensor counterpart even when the original $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$7 theory itself has no antigravity because $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$8; the transition occurs when $$S=\int d^4x\sqrt{-g}\,\Big[(\varphi-\mathcal B)R-U(\varphi)\Big]+S_m,$$9, and the transition is singular because $$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$0 there (Oikonomou et al., 2014).

In Weyl-invariant two-scalar cosmologies, the relevant coupling is

$$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$1

The sign of $$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$2 separates gravity and antigravity regions, and the Weyl-invariant quantity

$$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$3

is used to track evolution through Big Crunch/Big Bang transitions. In this framework, the Einstein-frame scale factor satisfies $$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$4, so the apparent Einstein-frame singularity corresponds to $$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$5. The geodesic-completion program argues that restricting the theory to $$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$6 is non-generic and that geodesic completeness requires extending field space to include $$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$7, where gravity is repulsive (Bars et al., 2011, Bars, 2012).

The cosmological consequence is a class of cyclic or bounce-like solutions in which contraction to zero size is followed by a brief antigravity interval and then a return to ordinary gravity. Anisotropy plays a decisive role: in the generic anisotropic case, an attractor mechanism forces trajectories through the origin of field space, making the antigravity loop unavoidable at the level of the classical effective theory. In this picture, antigravity is not an optional deformation but an intermediate sector of a geodesically complete cosmology (Bars, 2012).

The perturbative status of such models has been studied explicitly. For the Weyl-symmetric two-scalar action with opposite-sign conformal couplings, the deep antigravity limit yields a reduced second-order action with a positive kinetic coefficient for the relevant perturbation variable, and the resulting solution satisfies $$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$8 as the system approaches the maximal antigravity point. The conclusion drawn there is that, despite the wrong-signed kinetic term in the full action, the cosmological solutions studied are perturbatively stable at the scalar level in the antigravity regime analyzed (Oltean et al., 2014).

A related interpretive program treats antigravity regions as sectors beyond singularities rather than pathologies. In the Weyl-invariant Standard Model plus gravity, antigravity is the region where $$G_{\mathrm{eff}}=\frac{1}{16\pi(\varphi-\mathcal B)}.$$9, and observers confined to the gravity patch are said to access it only through in/out amplitudes, “like a spacetime black box.” A later Higgs-based proposal extends this idea by making the effective Newton coupling dynamical,

$\varphi-\mathcal B<0$0

so that $\varphi-\mathcal B<0$1 defines an antigravity domain; singularities then become transition surfaces between gravity and antigravity, with electroweak symmetry restored where the scalars vanish (Bars et al., 2015, Bars, 9 Sep 2025).

4. Matter–antimatter antigravity and related cosmologies

Matter–antimatter antigravity is a distinct research line. One symmetry-based proposal treats particle–antiparticle exchange as space-time inversion or, classically, as a formal mass inversion $\varphi-\mathcal B<0$2, and extends the Newtonian force law to

$\varphi-\mathcal B<0$3

with attraction for matter–matter and antimatter–antimatter, and repulsion for matter–antimatter. In that framework antigravity is a prediction of a generalized symmetry principle rooted in special relativity, CPT, and mass inversion rather than a consequence of standard general relativity alone (Ni et al., 2010).

A more recent reinterpretation argues that the phrase “antimatter gravitationally speaking” should not be equated with “anything containing an antiparticle.” Precision tests of the Weak Equivalence Principle are taken to show that binding energy acts like ordinary matter under gravity, while lattice-QCD proton mass decompositions are used to argue that roughly $\varphi-\mathcal B<0$4 of the proton, and hence of the antiproton by CPT invariance of QCD, is due to gluons. On this basis the antiproton is treated as mostly matter gravitationally speaking, leading in the antigravity scenario to the estimate

$\varphi-\mathcal B<0$5

for antihydrogen free fall, rather than the naive $\varphi-\mathcal B<0$6 prediction (Menary, 2024).

This mass-accounting viewpoint substantially alters the associated cosmology. One consequence is that antibaryons are “more matter than antimatter,” so a universe with equal baryon and antibaryon production need not be gravitationally symmetric. Related work then proposes a phenomenology with equal amounts of hydrogen and antihydrogen but far fewer antistars than stars, possible diffuse antihydrogen halos, antineutrino-rich cosmic voids, and MOND-like galaxy rotation curves. The same program treats the antiproton antimatter fraction as approximately $\varphi-\mathcal B<0$7, so antinucleon self-attraction is much weaker than nucleon self-attraction (Menary, 2024).

A different cosmological realization is the Dirac–Milne universe, a symmetric matter–antimatter cosmology in which matter has positive gravitational mass, antimatter negative gravitational mass, and the cosmic expansion is Milne-like or coasting. In that review, the model is presented as compatible with the age relation $\varphi-\mathcal B<0$8, with a Type Ia supernova luminosity-distance curve close to that of $\varphi-\mathcal B<0$9CDM, and with structure-formation simulations producing a characteristic comoving scale of about $R$0, identified with the observed BAO scale. Antigravity here is bound to the existence of negative gravitational mass and to gravitational polarization effects invoked as possible explanations of MOND-like behavior (Chardin et al., 2018).

5. Other mechanisms: defects, spin–curvature coupling, dual sectors, and vacancy geometry

Antigravity has also been constructed without invoking antimatter. One classical example is a spacetime defect embedded in Minkowski spacetime and supported by an $R$1 Skyrme field. The defect geometry is topologically nontrivial, the metric becomes degenerate at the defect surface $R$2, and the mass function can remain negative all the way to infinity. The resulting asymptotic ADM mass is then negative, which implies negative active gravitational mass and repulsion of distant test particles. In this usage, antigravity means repulsive acceleration generated by a negative-mass configuration within classical general relativity coupled to a classical Skyrme field (Klinkhamer et al., 2018).

A second mechanism is purely dynamical and test-body based. Using the exact Mathisson–Papapetrou equations for a spinning test particle in Schwarzschild spacetime, highly relativistic spin–curvature coupling can generate strong effective repulsion. Circular orbits become possible in the region $R$3, inside the usual geodesic circular-orbit boundary for spinless particles, and sufficiently large orbital velocity can make a spinning particle move outward where the corresponding spinless particle falls inward. The paper stresses, however, that this is not “true antigravity”: the Schwarzschild source remains attractive, and the effect disappears in the spinless limit (Plyatsko et al., 2016).

The theory of dual relativity introduces antigravity by postulating two matter sectors coupled to two metrics related by a duality condition. In the Newtonian limit, ordinary matter has positive inertial and gravitational mass, while dual matter has positive inertial mass but negative gravitational mass. The effective interaction energy between ordinary and dual particles is therefore positive,

$R$4

so the cross-sector interaction is repulsive, whereas ordinary–ordinary and dual–dual interactions remain attractive. The proposed mechanism is thus a sign difference in gravitational mass induced by the two-metric structure (Tselyaev, 30 Mar 2026).

At the most speculative end, a “ponderable” spacetime modeled on a Menger Sponge is argued to produce antigravity through vacancy-dominated geometry. The guiding intuition is a shift from “adding stuff” to “thinning out”: repeated removal of subcubes creates a geometry in which embedded observers experience shortened effective paths and negative curvature. The toy metric is built from a vacancy density $R$5, and the resulting Ricci-scalar and stress-energy analysis is interpreted as yielding effective negative mass or negative curvature behavior for $R$6. The proposal is explicitly described as a conceptual model rather than established physics (Svozil, 2024).

6. Critiques, experimental tests, and present evidential status

Because antigravity proposals are heterogeneous, criticism is often directed at specific mechanisms rather than at the abstract possibility of repulsive gravity. A prominent objection to CPT-based matter–antimatter antigravity argues that deriving antimatter motion in general relativity by applying CPT to the matter equation of motion “puts the cart before the horse.” The critique is methodological and ontological: CPT is treated there as a metalevel symmetry statement that should emerge from the object-level theory of gravitational interaction, while the ontology of general relativity contains one spacetime and one metric for both matter and antimatter. On that basis, the sign-flipped equation is judged “not acceptable in its current state of development” as a derivation of antigravity from GR (Cabbolet, 2011).

The Weyl-invariant cosmology program has likewise attracted direct criticism. For anisotropic solutions in the proposed “journey through antigravity,” the Weyl-invariant curvature observable

$R$7

was computed and shown to diverge at both the Big Crunch and the Big Bang. The conclusion drawn there is that the singularities are not physically resolved merely by lifting Einstein gravity to a Weyl-invariant model, because a genuine Weyl-invariant curvature scalar still blows up (Carrasco et al., 2013).

Direct experimental tests concentrate on antihydrogen. The three major CERN programs repeatedly emphasized in the literature are AEgIS, ALPHA-g, and Gbar. AEgIS targets a $R$8 measurement of antihydrogen gravitational deflection using a Moiré deflectometer; ALPHA-g aims first at a $R$9-$P_{\rm vac}=-\rho_{\rm vac},$0 sign determination for $P_{\rm vac}=-\rho_{\rm vac},$1 and later at $P_{\rm vac}=-\rho_{\rm vac},$2 sensitivity using vertically trapped antihydrogen; Gbar uses $P_{\rm vac}=-\rho_{\rm vac},$3 ions, with a few hundred annihilations expected to yield about $P_{\rm vac}=-\rho_{\rm vac},$4 precision in the first stage and later $P_{\rm vac}=-\rho_{\rm vac},$5, while longer-term ultracold methods are discussed as potentially reaching relative precision of $P_{\rm vac}=-\rho_{\rm vac},$6 or better (Chardin, 2022).

The most concrete recent benchmark cited in this literature is the ALPHA-g free-fall result

$P_{\rm vac}=-\rho_{\rm vac},$7

which suggests antihydrogen falls downward, not upward, but with large uncertainty. This measurement is already used as a discriminant among antigravity models: the gluon-dominated antiproton analysis treats its own $P_{\rm vac}=-\rho_{\rm vac},$8 prediction as disfavored but not ruled out, while broader antigravity cosmologies explicitly acknowledge that a precise relativistic formulation is still required for a fully predictive model (Menary, 2024, Menary, 2024).

The present literature therefore supports a sharply differentiated assessment. Cosmological antigravity in the form of accelerated expansion from negative-pressure sources is part of standard relativistic cosmology. By contrast, matter–antimatter antigravity, sign-changing gravity across singularities, negative-mass defects, dual-sector repulsion, and vacancy-geometry antigravity remain model-dependent proposals with active criticism, incomplete relativistic closure, or explicitly speculative status. The word “antigravity” thus functions less as the name of a settled theory than as a label for several distinct mechanisms by which gravitational repulsion, negative effective coupling, or effective outward motion may arise in otherwise very different theoretical settings.