arxiv: 2604.09400 · v1 · submitted 2026-04-10 · ✦ hep-th · gr-qc

Recognition: 2 theorem links

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Space- vs Time-dependence in taming the infrared instability of projectable Hov{r}ava Gravity

Jury Radkovski, Sergey Sibiryakov, Shinji Mukohyama

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Pith reviewed 2026-05-10 17:42 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords projectable Hořava gravityinfrared instabilityMinkowski spacetimehigher-derivative termsplanar symmetrystatic solutionsmodulated phases

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The pith

Higher-derivative terms produce no static inhomogeneous solutions that could end the infrared instability of Minkowski spacetime in projectable Hořava gravity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates whether higher-derivative corrections can resolve the infrared instability of flat spacetime in projectable Hořava gravity by creating static, modulated configurations with planar symmetry that might act as stable endpoints. It exhaustively classifies all static homogeneous isotropic solutions and all planar-symmetric ones, then demonstrates that none of these configurations can serve as such an endpoint. This rules out one proposed resolution and directs attention toward time-dependent effects that might conceal the instability instead. A reader cares because the instability threatens the theory's ability to recover standard cosmology and particle physics at low energies unless it is either hidden or redirected into an acceptable final state.

Core claim

The central claim is that the presence of higher-derivative terms does not allow the existence of static, inhomogeneous (quasi-)periodic solutions with planar symmetry in projectable Hořava gravity. The authors reach this conclusion by classifying all static homogeneous and isotropic solutions together with all solutions possessing planar symmetry, showing that every candidate either reduces to Minkowski space or carries average curvature too high to function as a low-curvature endpoint for the instability's evolution.

What carries the argument

Exhaustive classification of static solutions under planar symmetry, which constrains possible modulated phases and shows that none can terminate the instability.

If this is right

The infrared instability cannot be resolved by relaxation to any static inhomogeneous configuration.
Viability of the theory then requires that time-dependent processes, such as cosmic expansion or Jeans collapse, conceal the instability.
This imposes a constraint on the infrared renormalization-group flow of the theory.
Further analysis must focus on the actual time evolution rather than static alternatives.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar classification arguments might apply to other higher-derivative gravity theories that exhibit flat-space instabilities.
Numerical evolution of the instability could reveal whether it grows into oscillations or is cut off by nonlinearities not captured in the static sector.
If time-dependent hiding works, the theory's low-energy parameters must be tuned to ensure the instability timescale exceeds the Hubble time.

Load-bearing premise

That every possible endpoint of the instability must be static and at most planar-symmetric, and that the higher-derivative terms permit a complete listing of all such solutions.

What would settle it

An explicit construction, analytic or numerical, of a time-dependent solution starting from Minkowski spacetime that settles into a non-flat, static, planar-symmetric configuration with low average curvature would falsify the non-existence claim.

Figures

Figures reproduced from arXiv: 2604.09400 by Jury Radkovski, Sergey Sibiryakov, Shinji Mukohyama.

read the original abstract

Minkowski spacetime exhibits infrared instability in projectable Ho\v rava gravity in (3+1) dimensions. To be phenomenologically viable, the instability should be either hidden by other time-dependent processes such as the Hubble expansion of the universe and the Jeans instability, or evolve into another static solution with low average curvature. While the former scenario leads to a phenomenological constraint on the infrared properties of the renormalization group flow, this paper explores the latter possibility. We study if the presence of higher derivative terms in the action can lead to existence of static, inhomogeneous (quasi-) periodic solutions with planar symmetry, similar to modulated phases in magnetic materials. We find that such solutions do not exist. In doing so, we classify all static homogeneous and isotropic solutions and solutions with planar symmetry. We provide arguments that none of them can serve as an endpoint for the evolution of the Minkowski instability. This motivates further study of the scenario where the instability is concealed by time evolution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper delivers a clean classification showing no static planar-symmetric solutions exist to end the Minkowski IR instability in projectable Hořava gravity, even with higher derivatives.

read the letter

The main thing to know is that higher-derivative terms do not produce static inhomogeneous solutions with planar symmetry that could act as endpoints for the infrared instability of Minkowski space in projectable Hořava gravity. The authors classify all static homogeneous isotropic solutions plus the planar-symmetric ones and argue none of them can terminate the instability's evolution. This is a direct no-go within the static sector under the model's symmetries and action assumptions. It extends prior work by making the classification explicit and tying it to the question of phenomenological viability. The arguments stay grounded in the equations of motion without parameter fitting or circular steps, and the paper is upfront that this leaves the time-dependent route open. That honesty is useful. The classification itself looks thorough for the symmetries considered, and the link to modulated phases in other systems is a reasonable analogy without overstretch. The soft spot is exactly the one the stress-test flags: everything rests on the idea that any endpoint must be static and classifiable under planar symmetry. If the instability instead settles into a bounded but explicitly time-dependent state, such as oscillations or quasi-periodic behavior, the no-go does not apply. The authors acknowledge this gap and point to studying time evolution next, which keeps the claim proportionate. The planar symmetry choice is a practical starting point but could miss other geometries. This paper is for people already working inside the Hořava gravity program who need to see the static option ruled out. A reader focused on no-go results in modified gravity will get concrete value from the classification and the clear motivation for the next step. It deserves peer review because the result is narrowly scoped, the math is direct, and referees can verify the completeness of the listed solutions without needing broad new technology.

Referee Report

0 major / 2 minor

Summary. The paper investigates the infrared instability of Minkowski spacetime in projectable Hořava gravity in (3+1) dimensions. It explores whether higher-derivative terms can produce static inhomogeneous (quasi-)periodic solutions with planar symmetry that could serve as endpoints for the instability. The authors classify all static homogeneous/isotropic solutions and all planar-symmetric solutions, concluding that none can terminate the instability, and therefore motivate further study of time-dependent processes to conceal it.

Significance. If the classification is complete, the result is significant because it provides a concrete no-go for space-dependent static resolutions of the instability, even after including higher-derivative terms. This narrows viable phenomenological scenarios to time-dependent mechanisms (e.g., Hubble expansion or Jeans instability) that can hide the instability, thereby constraining the infrared renormalization-group flow. The explicit classification of solutions under the stated symmetries is a useful, falsifiable contribution. The stress-test concern that the paper assumes every endpoint must be static does not land: the manuscript explicitly frames its negative result as motivation for studying the time-dependent alternative rather than claiming static solutions are required.

minor comments (2)

[Introduction and §2] The precise form of the higher-derivative terms in the action should be stated explicitly (or referenced to a standard expression) in the introduction or §2 to make the classification self-contained.
[Classification section] A short appendix listing the reduced ordinary differential equations solved for the planar-symmetric case would improve verifiability of the claimed completeness of the classification.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. The referee's summary correctly reflects our focus on classifying static solutions under the relevant symmetries and our conclusion that none serve as endpoints for the Minkowski infrared instability, thereby motivating time-dependent mechanisms. We appreciate the recognition that our negative result is framed as motivation rather than an assumption that static endpoints are required.

Circularity Check

0 steps flagged

Direct classification of static solutions from equations of motion; no reduction to inputs

full rationale

The paper derives its central no-go result by classifying all static homogeneous/isotropic and planar-symmetric solutions directly from the projectable Hořava gravity equations of motion (including higher-derivative terms) and showing none can terminate the Minkowski instability. This is an exhaustive case analysis under explicit symmetry assumptions rather than any redefinition, parameter fit, or self-citation that bears the load. No step reduces a claimed prediction or uniqueness result to the input data or prior ansatz by construction. The argument is self-contained against the stated dynamical assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard projectable Hořava action with higher spatial derivatives, the assumption that any stable endpoint must be static, and the restriction to homogeneous-isotropic or planar-symmetric ansätze. No new free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption The infrared instability of Minkowski spacetime in projectable Hořava gravity is governed by the equations derived from the given higher-derivative action.
Invoked when stating that the instability should evolve into another static solution.
ad hoc to paper Any endpoint of the instability must be a static solution with either full homogeneity/isotropy or planar symmetry.
Used to limit the search space for possible endpoints.

pith-pipeline@v0.9.0 · 5476 in / 1348 out tokens · 68009 ms · 2026-05-10T17:42:07.998391+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear
We find that such solutions do not exist. [...] none of them can serve as an endpoint for the evolution of the Minkowski instability.

Reference graph

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