Non-Quantized Gravity Models

Updated 31 March 2026

Non-Quantized Gravity Models are frameworks where gravity remains classical even when interacting with quantum matter, challenging traditional quantization approaches.
They employ techniques like nonlocal modifications, unimodular approaches, and stochastic methods to address cosmological issues such as dark energy and the cosmological constant problem.
Experimental implications include tabletop tests and decoherence measurements that probe the interplay between classical gravitational fields and quantum effects.

Non-quantized gravity models encompass a diverse set of theoretical frameworks in which the gravitational field is not elevated to a quantum operator but retains classical or “semiclassical” status, even when coupled to quantum matter. These models challenge the prevailing assumption that gravity must be quantized and provide distinct alternatives ranging from nonlocal modifications inspired by renormalization group flow, classical metric theories with reduced symmetry, stochastic semiclassical coupling paradigms, to more radical departures where the dichotomy between “classical” and “quantum” is itself emergent. The physical motivations include addressing cosmological phenomena (such as dark energy or the cosmological constant problem), constructing ultraviolet-complete or infrared-modified theories, and probing the experimental boundaries of gravitationally mediated quantum effects.

1. Motivations and Foundational Structures

Non-quantized gravity models arise from fundamentally different theoretical and phenomenological motivations:

Limitations of quantization: The lack of experimental evidence for gravitons or quantum spacetime fluctuations motivates reconsideration of quantization. Certain models seek to avoid the mathematical difficulties or conceptual paradoxes (e.g., singularities, black hole information loss) that plague quantized gravity (Hossenfelder, 2012).
IR modifications and cosmological challenges: Nonlocal models are motivated by the possibility that quantum gravity effects manifest as nonlocalities in the infrared, producing effective dark energy and resolving the cosmic acceleration issue without an explicit cosmological constant (Amendola et al., 2017, Barvinsky, 2011).
Unimodular and reduced-symmetry gravity: Violations or modifications of general covariance, e.g., unimodular gravity, offer avenues to address aspects of the cosmological constant problem or provide alternative cosmological fits (Jain et al., 2011).
Semiclassical and stochastic paradigms: These models retain a classical gravitational field but couple it to quantum matter nontrivially—either at the mean field (Møller–Rosenfeld), via classical measurement-feedback channels, or through stochastic collapse-type effects (Diósi, 2 Nov 2025, Tilloy, 2019, Donadi et al., 2022).
Non-quantized, non-classical gravity: Some frameworks propose that the “quantum/classical” divide itself is dynamical and phase-dependent, with quantization emerging via spontaneous symmetry breaking (Hossenfelder, 2012).

2. Nonlocal and Infrared-Modified Classical Gravity

A leading class of non-quantized models are nonlocal gravity theories, in which the gravitational action contains nonlocal (typically inverse d'Alembertian) operators inspired by renormalization group running of coupling constants or effective action resummation:

Nonlocal Effective Actions: For example, in the “ $\Box^{-2}R$ ” model, Newton’s constant $G$ in the Einstein–Hilbert action is replaced by its functional running $G(\Box) \simeq G[1 - c_\zeta (\zeta^2\Box)^{-1/(2\nu)} + \cdots]$ , which leads to an effective action

$S = \frac{1}{16\pi G}\int d^4x\sqrt{-g}[R - \frac{M^4}{6}\Box^{-2}R] + S_\mathrm{matter}$

with $M^4\sim\mathcal{O}(H_0^4)$ the IR scale set by cosmology (Amendola et al., 2017).

Localization by Auxiliary Fields: The nonlocal structure is made tractable by introducing auxiliary scalar fields $U, S, Q, L$ satisfying nested $\Box$ -type equations, yielding local but higher-derivative field equations for both the metric and scalars.
Phenomenology: These models generically yield a late-time acceleration phase with dynamical, nontrivial dark energy equation of state parameters $w_{\rm DE}(z)$ deviating from $-1$ , and are compatible with solar-system constraints provided the scale $M$ is chosen appropriately.
Stability and Covariance: Covariant generalizations involve nonlocal operators acting on Ricci scalar, Ricci tensor, or even the full Einstein tensor, with care taken to ensure absence of ghost/tachyonic pathologies. Specific stability conditions on the curvature-dependent operator coefficients appear, ensuring that propagating degrees of freedom remain purely tensorial (two polarizations) and massless in the GR limit (Barvinsky, 2011).
Hamiltonian Structure and Degrees of Freedom: A systematic Hamiltonian formalism reveals an extended constraint structure, with infinite towers of auxiliary fields controlling the nonlocality, and guarantees the preservation of diffeomorphism invariance at the classical level, provided the nonlocal corrections are constructed with appropriate care (Joshi et al., 2019).

3. Modified Classical Metric Theories

Alternative non-quantized models involve changing the symmetry structure or coupling of gravity without introducing nonlocalities:

Unimodular Gravity: The metric is decomposed as $g_{\mu\nu} = \chi^2 \bar g_{\mu\nu}$ with fixed determinant $\det \bar g_{\mu\nu}$ , and dynamics are reparametrized in terms of a conformal scalar $\chi$ . The action, variational analysis, and cosmological evolution depend on a parameter $\xi$ controlling the degree of violation of full general covariance. Modifications in the matter sector—altering powers of $\chi$ in matter couplings—are necessary for cosmological consistency. These models fit high- $z$ supernova data comparably well to $\Lambda$ CDM without explicit dark energy (Jain et al., 2011).
Conformal Superspace and Reduced-Symmetry Models: Approaches where the group of invariance is limited to spatial diffeomorphisms and conformal rescalings (excluding refoliation invariance), with the configuration space as conformal superspace. The models retain only two physical gravitational degrees of freedom, possess nontrivial supermetric structure in field space, and admit couplings to matter (electromagnetism) that ensure hyperbolic propagation in the constructed “emergent” spacetime (Gomes, 2016).
Extensions in $f(R)$ and Scalar–Tensor Theories: Non-quantized modifications may include $f(R)$ , $f(G)$ , and scalar–tensor actions, engineered to produce desired cosmic histories, avoid future singularities, or undergo cosmological phase transitions (Nojiri et al., 2010). Viability heavily depends on stability conditions (e.g., $f''(R)>0$ ), compatibility with Solar-System tests, and the ability to match cosmological reconstructions.

4. Semiclassical and Stochastic Gravity Models

Models retaining a classical gravitational field but coupling it to quantum matter are categorized into mean-field, stochastic, and measurement-feedback frameworks:

Semiclassical Mean-Field Theories: The Møller–Rosenfeld prescription yields the Schrödinger–Newton (SN) equation for matter whereby the Newtonian potential is sourced by the expectation value of quantum energy density. This nonlinearity leads to conceptual issues: it permits superluminal signaling, violates the Born rule, and in the mean-field setting, fails to mediate entanglement between spatially separated quantum subsystems (Diósi, 2 Nov 2025).
Stochastic / Measurement-Feedback Models: Stochastic semiclassical models replace deterministic field sourcing by monitoring the quantum matter sector with noise (e.g., continuous position measurements or spontaneous GRW-type “flashes”) and feeding the measurement outcomes back into the Newton potential. The resulting averaged dynamics is linear and master-equation-like, preserving no-signalling and precluding superluminal communication or “hidden nonlocalities” (Tilloy, 2019).
Decoherence and Collapse Models: Physically, all consistent classical-quantum gravity models unavoidably inject noise and decoherence into the quantum sector if they are to avoid entanglement. The “minimal noise” threshold necessary to maintain consistency has been quantified, and experimental protocols aiming to measure below this threshold effectively serve as direct tests of gravitational quantization (Fabiano et al., 27 Mar 2026, Donadi et al., 2022).
Experimental Implications: Tabletop mechanical oscillator experiments, hybrid systems, and mass-superposition interferometry are now approaching sensitivities sufficient to constrain broad classes of non-quantized models by measuring force-noise or decoherence rates (Fabiano et al., 27 Mar 2026).

5. Emergent Quantum/Classical Phase Models

A more radical path is the postulate that the status of gravity (and perhaps matter sectors) as “classical” or “quantum” is not fundamental, but an emergent phase resulting from spontaneous symmetry breaking in a novel field:

Dynamical $\hbar$ Frameworks: The Planck constant itself is promoted to a massless scalar field $h(x)$ whose vacuum expectation value determines whether fields are quantized ( $\langle h\rangle\neq0$ ) or classical ( $\langle h\rangle=0$ ). The metric, matter, and $h$ -field sectors are all coupled in the total action. In high-temperature or high-curvature regimes, the unquantized “symmetric phase” nullifies commutators and decouples gravity ( $G\to0$ ), dynamically resolving standard singularities and information paradoxes. The broken phase recovers quantum field theory and general relativity phenomenology. The precise form of the symmetry-breaking potential for $h$ and its coupling to matter require further investigation (Hossenfelder, 2012).

6. Quantum Matter and Entanglement Tests

The interplay of quantum matter with non-quantized or semiclassical gravity is a critical diagnostic for the underlying structure:

No Entanglement from Classical Gravity: Exact field-theoretic calculations demonstrate that any classical ( $c$ -number) gravitational field, determined solely by the expectation value of the quantum stress-energy, cannot mediate entanglement between separated quantum systems. Only a quantum channel—i.e., propagating gravitons—permits gravitationally-induced entanglement. This result underpins the ongoing experimental focus on observing gravitational entanglement as smoking-gun evidence for the quantization of gravity (Diósi, 2 Nov 2025, Fabiano et al., 27 Mar 2026).
Minimal Decoherence Bounds: The requirement that classical or measurement-feedback gravity does not entangle quantum objects imposes a strict quantitative lower bound on the gravitationally-induced noise. Any observed noise below this “minimal noise” threshold excludes all non-quantized gravity models in the Newtonian regime (Fabiano et al., 27 Mar 2026).

7. Comparative Table of Non-Quantized Gravity Models

Model Class	Key Features	Phenomenological Targets / Constraints
Nonlocal IR-Modified Models	Nonlocal $\Box^{-n}R$ terms, dynamical dark energy	Cosmological acceleration, solar-system bounds
Unimodular / Reduced-Symmetry Models	Modify coordinate invariance, novel scalar sector	Cosmological constant problem, supernova fit, GR limit
Semiclassical Mean-Field	$g_{\mu\nu}$ classical, quantum matter, no entanglement	No gravitational entanglement, consistency at low energy
Stochastic/Feedback (CSL/DP/KTM/TD)	Classical gravity, noisy feedback from quantum sector	Decoherence, minimal noise threshold, non-entangling
Emergent $\hbar$ (Hossenfelder)	Spontaneous graviton quantization, dynamical phase	Singularity avoidance, unification of QFT/GR

These frameworks collectively demonstrate that viable non-quantized gravity models are increasingly restricted either by internal consistency, compatibility with quantum matter coupled dynamics, or by emerging experimental capabilities targeting their unique signatures. As the sensitivity of quantum gravitational tests improves, empirical falsifiability of broad non-quantized classes becomes a realistic prospect.

References: (Amendola et al., 2017, Barvinsky, 2011, Hossenfelder, 2012, Diósi, 2 Nov 2025, Gomes, 2016, Calcagni et al., 2010, Fabiano et al., 27 Mar 2026, Nojiri et al., 2010, Jain et al., 2011, Tilloy, 2019, Donadi et al., 2022, Joshi et al., 2019)