An arXiv preprint reports that coupling a generic perfect fluid to “freezing gravity” preserves the model’s separation between the cosmic background and its perturbations, while the scalar sector still freezes on large scales at linear order. In the matter-inclusive formulation, F(t) and G(t) control background density, pressure and the equation of state, whereas effective-field-theory and matter quantities control perturbations. The result is conditional: whether this infrared freezing survives at nonlinear orders without strong coupling remains unresolved.
The work is a theoretical modeling study built around cosmological perturbations. Its matter component is a relativistic perfect fluid minimally coupled to freezing gravity through the Schutz–Sorkin action. The perturbation setup is restricted to scalar modes; vector and tensor perturbations are neglected. From that system, the authors derive analytic conditions for ghost and gradient stability, including a no-ghost test that does not rely on a high-wavenumber approximation.
The cutoff depends on the parameter branch
The no-ghost condition—the paper’s test for an allowed kinetic sector—is expressed through bounds on the model parameters. With αL > −1 and αA > 0, the no-ghost region is defined by Q(k) > 0 and Ξ(k) > 0. The criterion is scale-dependent, so the analysis tracks these quantities rather than reducing the result to a single parameter-free statement.
One of the clearest matter-inclusive results concerns the cutoff. For the branch −1 < αL < 0, the matter-corrected cutoff kc is lower than the vacuum reference cutoff kb. The comparison is specific to that negative-αL branch and is not presented as a result that applies across every parameter choice.
Across the parameter regions examined, the analytic conditions allow two broad outcomes: some regions have a finite ghost cutoff, while others remain ghost-free throughout the effective field theory’s validity range—the range in which that description is intended to apply. Which outcome occurs depends on the chosen parameters.
Frozen at large scales, active at small ones
The scalar’s behavior changes with scale. At linear order, large-scale kinetic degeneracy leaves the freezing-gravity scalar non-propagating. On sufficiently small scales, however, the same scalar remains dynamical and has a local sound speed. The calculation therefore allows different propagation behavior in different regimes.
The gradient-stability test is also tied to the regime being analyzed. In the WKB, or wave-based, treatment, stability requires the discriminant D² − detKdetG to be nonnegative and the propagation eigenvalues c²± to be positive. The high-k limit is applicable on the αL > 0 branch.
For the high-wavenumber branch with αL > 0 and αA > 0, the gravity-sector condition is (1 + αH)² > [αA/2](1 + αT) > 0, together with a positive tensor-speed condition, c²T = 1 + αT > 0. These are analytic restrictions on the effective-field-theory parameters, not measured quantities.
A narrower picture emerges for cosmic growth
The study then specializes to cold dark matter, or CDM, in a restricted quasi-static regime used for its structure-growth formulas. There, the effective friction keeps its standard form, while any change to structure growth is encoded in Gcdm. In the gradient-stable region, the calculation gives Gcdm > 0, which the authors interpret as an attractive effective interaction in that stated regime.
The same quasi-static treatment gives a compact result for gravitational slip, the quantity used to compare the model’s two gravitational potentials: η = (1 + αT)/(1 + αH). The expression depends only on the beyond-Horndeski parameter αH and the tensor-speed parameter αT, making them the controls of slip within this approximation.
Those conclusions about CDM growth and gravitational slip belong to the restricted quasi-static calculation. They do not extend automatically to the full scale range or to matter models beyond the CDM specialization used for the structure-growth interpretation.
What the calculation still cannot answer
The most important unresolved issue is nonlinear behavior. The linear analysis finds large-scale freezing, but the paper does not establish whether that property persists at nonlinear orders or avoids strong coupling. It identifies nonlinear perturbation theory or a full Hamiltonian analysis as the work needed to settle that question.
The range of the stability claims also matters. The negative-αL branch has a matter-corrected cutoff, while the gradient analysis is framed through WKB conditions and, on the high-k branch, through additional parameter inequalities. The growth and slip formulas are separately confined to the quasi-static treatment.
The perturbation calculation covers scalar modes only, leaving vector and tensor perturbations outside its setup. Taken together, the preprint presents a conditional analytic framework: matter preserves the background–perturbation separation, linear infrared freezing remains, stability depends on the effective-theory branch, and scalar dynamics reappears on small scales. Its conclusions stop short of resolving the model beyond those analytic limits.
Paper data and sources
Original title: Effective Field Theory for Freezing Gravity with Minimally Coupled Matter
Authors: Zhibang Yao
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text