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Space vs time dependence in taming the infrared instability of projectable Hořava gravity

Shinji Mukohyama1,2,3,*, Jury Radkovski4,5,†, and Sergey Sibiryakov4,5,‡

  • *Contact author: shinji.mukohyama@yukawa.kyoto-u.ac.jp
  • †Contact author: jradkovski@perimeterinstitute.ca
  • ‡Contact author: ssibiryakov@perimeterinstitute.ca
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Phys. Rev. D 114, 024039 – Published 15 July, 2026

DOI: https://doi.org/10.1103/qnhx-mpjq

Abstract

Minkowski spacetime exhibits infrared instability in projectable Hořava 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 the 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.

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Phys. Rev. D 114, 024039– Published 15 July, 2026
  • Received 14 April 2026
  • Accepted 9 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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