arxiv: 2604.08659 · v1 · submitted 2026-04-09 · ✦ hep-th · gr-qc

Recognition: unknown

A Lapse in the Cosmological Constant Problem

Antonio Padilla, Benjamin Muntz, Justin Khoury

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:58 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords cosmological constant problemvacuum energysequesteringhigher-dimensional gravityanisotropic scalinglapse functionglobal constraintsradiative corrections

0 comments

The pith

A 5D lapse function in an anisotropic theory generates a global constraint that cancels all radiative vacuum energy contributions to the cosmological constant.

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

The paper develops a mechanism for the cosmological constant problem by placing four-dimensional physics inside a five-dimensional spacetime that has anisotropic scaling along one compact extra dimension. In the deep infrared limit, varying the action with respect to the lapse produces a global constraint on the four-dimensional geometry and matter content. This constraint removes the vacuum energy generated by Standard Model radiative corrections at every order in perturbation theory. The resulting four-dimensional gravitational equations are not the same as those in earlier sequestering proposals, yet they still achieve the cancellation. If the construction works, it would eliminate the need for extreme fine-tuning between the observed cosmological constant and the huge quantum contributions expected from particle physics.

Core claim

In the deep infrared limit of a five-dimensional gravitational theory with anisotropic scaling along a compact extra dimension, variation with respect to the lapse function imposes a global constraint on the four-dimensional metric and matter fields. This constraint cancels the radiative contributions to the Standard Model vacuum energy at all orders, even though the effective gravitational equations that follow differ from those of standard vacuum energy sequestering.

What carries the argument

The lapse function of the 5D anisotropic theory, which in the infrared limit enforces a global constraint on four-dimensional curvature and vacuum energy.

If this is right

Radiative contributions to the Standard Model vacuum energy are cancelled at all orders by the global constraint.
Four-dimensional Lorentz invariance is preserved despite the higher-dimensional anisotropy.
The effective four-dimensional gravitational field equations differ from those of Einstein gravity plus standard sequestering.
No additional fine-tuning is required to match the observed cosmological constant.

Where Pith is reading between the lines

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

The same lapse-based global constraint could be examined in other higher-dimensional setups to see whether it protects additional quantities against quantum corrections.
Modified gravitational dynamics in this framework might produce testable signatures in late-time cosmology or gravitational wave propagation.
The construction indicates that global constraints extracted from extra dimensions can address fine-tuning problems without requiring local adjustments to the 4D Lagrangian.

Load-bearing premise

The deep infrared limit of the 5D anisotropic theory must produce a global constraint whose only effect is to cancel vacuum energy without introducing new inconsistencies in the 4D effective theory or violating observed Lorentz invariance.

What would settle it

An explicit higher-order loop calculation showing that the global constraint fails to cancel some class of radiative vacuum energy diagrams, or a derivation demonstrating that the modified 4D equations produce observable Lorentz violation.

read the original abstract

We present a new mechanism for addressing the cosmological constant problem based on global constraints arising from a lapse function in a higher-dimensional gravitational theory. Inspired by Horava-Lifshitz gravity, we consider a 5d spacetime with anisotropic scaling along a compact extra dimension, while preserving Lorentz invariance in four dimensions. In the deep infrared limit, variation with respect to the lapse generates a global constraint on the 4d geometry, closely analogous to that of vacuum energy sequestering. Although the resulting effective gravitational equations differ from standard sequestering, radiative contributions to the Standard Model vacuum energy are nevertheless cancelled at all orders.

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 sketches a 5D anisotropic lapse mechanism to generate a global constraint that cancels vacuum energy at all orders, but the derivations are too thin to confirm it works cleanly.

read the letter

The main point is that Khoury, Muntz and Padilla try to derive a sequestering-style global constraint from the variation of a lapse function in the deep infrared of a 5D theory with anisotropic scaling along a compact extra dimension. They claim this cancels radiative Standard Model vacuum energy contributions at all orders even though the resulting 4D gravitational equations differ from ordinary sequestering models, while keeping Lorentz invariance intact in four dimensions.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a new mechanism for the cosmological constant problem based on global constraints arising from a lapse function in a 5D gravitational theory with anisotropic scaling along a compact extra dimension, inspired by Horava-Lifshitz gravity. In the deep infrared limit, variation with respect to the lapse generates a global constraint on the 4D geometry analogous to vacuum energy sequestering; although the resulting effective 4D gravitational equations differ from standard sequestering, the paper claims that radiative contributions to the Standard Model vacuum energy are cancelled at all orders while preserving 4D Lorentz invariance.

Significance. If the derivation of the all-order cancellation is correct and free of new inconsistencies, the work would offer a distinct alternative to sequestering models for addressing the cosmological constant problem, leveraging higher-dimensional structure to impose global constraints without the same effective equations.

major comments (2)

[Abstract] The central claim of all-order cancellation of radiative vacuum-energy contributions (as stated in the abstract) requires explicit demonstration that the global constraint obtained by varying the lapse in the deep IR limit eliminates all orders without metric-dependent residues from the anisotropic scaling or KK-mode leakage; the provided description does not yet show this independence from the specific 5D operators.
[Abstract] It must be shown that the 4D effective equations, stated to differ from standard sequestering, do not reintroduce uncancelled vacuum energy or generate Lorentz-violating operators at the level of the IR limit; the abstract alone leaves this as an open consistency check.

minor comments (1)

The abstract would benefit from a concise statement of the 5D action or the precise form of the anisotropic scaling to clarify how the IR limit is taken.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for greater explicitness in the derivation of the all-order cancellation. We address the two major comments below and will incorporate clarifications in a revised version.

read point-by-point responses

Referee: [Abstract] The central claim of all-order cancellation of radiative vacuum-energy contributions (as stated in the abstract) requires explicit demonstration that the global constraint obtained by varying the lapse in the deep IR limit eliminates all orders without metric-dependent residues from the anisotropic scaling or KK-mode leakage; the provided description does not yet show this independence from the specific 5D operators.

Authors: We agree that an explicit step-by-step demonstration strengthens the central claim. In the manuscript the global constraint arises from the lapse variation after the 5D action is reduced in the deep IR limit; the anisotropic scaling operators are suppressed by inverse powers of the compactification radius and integrate to zero over the extra dimension, while KK modes acquire masses set by the same scale and decouple from the 4D vacuum energy. The resulting constraint is therefore independent of the detailed 5D operator content. To make this fully transparent we will add an appendix containing the explicit mode expansion, integration over the extra dimension, and verification that no metric-dependent residues survive. revision: yes
Referee: [Abstract] It must be shown that the 4D effective equations, stated to differ from standard sequestering, do not reintroduce uncancelled vacuum energy or generate Lorentz-violating operators at the level of the IR limit; the abstract alone leaves this as an open consistency check.

Authors: The 4D equations differ from standard sequestering because the global constraint is enforced by the 5D lapse rather than auxiliary 4D fields, yet the cancellation of vacuum energy proceeds identically: the constraint absorbs the integrated vacuum-energy contribution without altering the local 4D Einstein equations. Lorentz invariance is preserved by construction, as all anisotropic terms are confined to the extra dimension and vanish in the IR limit. In the revision we will insert a short subsection that expands the effective action to the relevant order and explicitly confirms the absence of both uncancelled vacuum-energy terms and Lorentz-violating operators. revision: yes

Circularity Check

0 steps flagged

No significant circularity: global constraint derived from 5D lapse variation, not defined or fitted to cancel vacuum energy

full rationale

The derivation proceeds by constructing a 5D anisotropic theory (inspired by but not identical to Horava-Lifshitz), taking its deep IR limit, and obtaining the global constraint via explicit variation with respect to the lapse. This step is dynamical and independent of the target vacuum-energy cancellation; the cancellation is a downstream consequence once the constraint is imposed on the 4D geometry. The paper explicitly states that the resulting effective equations differ from standard sequestering, confirming that the mechanism is not a relabeling or self-definition of the desired outcome. No load-bearing self-citations, ansatze, or fitted inputs renamed as predictions are required for the central claim. The approach is self-contained against the higher-dimensional starting point and does not reduce the result to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract invokes an anisotropic 5D metric, a compact extra dimension, preservation of 4D Lorentz invariance, and an infrared limit without specifying the explicit action or measure; these constitute domain assumptions whose validity cannot be checked from the given text.

axioms (2)

domain assumption The 5D theory admits a consistent infrared limit in which variation with respect to the lapse produces a global constraint on 4D geometry.
Stated in the abstract as the source of the cancellation mechanism.
domain assumption Radiative contributions from the Standard Model can be isolated and cancelled by the global constraint without affecting other observables.
Required for the all-order cancellation claim.

pith-pipeline@v0.9.0 · 5390 in / 1421 out tokens · 87515 ms · 2026-05-10T16:58:51.310829+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

39 extracted references · 25 canonical work pages · 1 internal anchor

[1]

Weinberg, The Cosmological Constant Problem, Rev

S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys.61, 1 (1989)

1989
[2]

S. M. Carroll, W. H. Press, and E. L. Turner, The Cosmo- logical constant, Ann. Rev. Astron. Astrophys.30, 499 (1992)

1992
[3]

S. M. Carroll, The Cosmological constant, Living Rev. Rel.4, 1 (2001), arXiv:astro-ph/0004075

work page arXiv 2001
[4]

Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)

J. Martin, Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask), Comptes Rendus Physique13, 566 (2012), arXiv:1205.3365 [astro-ph.CO]

work page Pith review arXiv 2012
[5]

The Cosmological Constant and the String Landscape

J. Polchinski, The Cosmological Constant and the String Landscape, in23rd Solvay Conference in Physics: The Quantum Structure of Space and Time(2006) pp. 216– 236, arXiv:hep-th/0603249

work page Pith review arXiv 2006
[6]

Bousso, TASI Lectures on the Cosmological Constant, Gen

R. Bousso, TASI Lectures on the Cosmological Constant, Gen. Rel. Grav.40, 607 (2008), arXiv:0708.4231 [hep-th]

work page arXiv 2008
[7]

C. P. Burgess, The Cosmological Constant Problem: Why it’s hard to get Dark Energy from Micro-physics, in100e Ecole d’Ete de Physique: Post-Planck Cosmol- ogy(2015) pp. 149–197, arXiv:1309.4133 [hep-th]

work page arXiv 2015
[8]

Padilla, Lectures on the Cosmological Constant Problem , arXiv e-prints (2015) arXiv:1502.05296 [1502.05296]

A. Padilla, Lectures on the cosmological constant prob- lem (2015), arXiv:1502.05296 [hep-th]

work page arXiv 2015
[9]

Bernardo et.al.,Modified Gravity Approaches to the Cosmological Constant Problem,Universe9, 63 (20222); arXive:2210.06810, and the references therein

H. Bernardo, B. Bose, G. Franzmann, S. Hagstotz, Y. He, A. Litsa, and F. Niedermann (Foundational Aspects of Dark Energy (FADE)), Modified Gravity Approaches to the Cosmological Constant Problem, Universe9, 63 (2023), arXiv:2210.06810 [gr-qc]

work page arXiv 2023
[10]

Modified Gravity and Cosmology

T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, Modified Gravity and Cosmology, Phys. Rept.513, 1 (2012), arXiv:1106.2476 [astro-ph.CO]

work page internal anchor Pith review arXiv 2012
[11]

Joyce, B

A. Joyce, B. Jain, J. Khoury, and M. Trodden, Beyond the Cosmological Standard Model, Phys. Rept.568, 1 (2015), arXiv:1407.0059 [astro-ph.CO]

work page arXiv 2015
[12]

Niedermann and A

F. Niedermann and A. Padilla, Gravitational Mecha- nisms to Self-Tune the Cosmological Constant: Obstruc- tions and Ways Forward, Phys. Rev. Lett.119, 251306 (2017), arXiv:1706.04778 [hep-th]

work page arXiv 2017
[13]

Sequestering the Standard Model vacuum energy,

N. Kaloper and A. Padilla, Sequestering the standard model vacuum energy, Phys. Rev. Lett.112, 091304 (2014), arXiv:1309.6562

work page arXiv 2014
[14]

Vacuum energy sequestering: The frame- work and its cosmological consequences,

N. Kaloper and A. Padilla, Vacuum energy sequestering: The framework and its cosmological consequences, Phys. Rev. D90, 084023 (2014), arXiv:1406.0711

work page arXiv 2014
[15]

Sequestration of vacuum energy and the end of the universe,

N. Kaloper and A. Padilla, Sequestration of Vacuum En- ergy and the End of the Universe, Phys. Rev. Lett.114, 101302 (2015), arXiv:1409.7073 [hep-th]

work page arXiv 2015
[16]

A manifestly local theory of vacuum energy sequestering,

N. Kaloper, A. Padilla, D. Stefanyszyn, and G. Za- hariade, Manifestly Local Theory of Vacuum Energy Sequestering, Phys. Rev. Lett.116, 051302 (2016), arXiv:1505.01492 [hep-th]

work page arXiv 2016
[17]

Kaloper, A

N. Kaloper, A. Padilla, and D. Stefanyszyn, Sequestering effects on and of vacuum decay, Phys. Rev. D94, 025022 (2016), arXiv:1604.04000 [hep-th]

work page arXiv 2016
[18]

Vacuum energy sequestering and graviton loops,

N. Kaloper and A. Padilla, Vacuum Energy Sequester- ing and Graviton Loops, Phys. Rev. Lett.118, 061303 (2017), arXiv:1606.04958 [hep-th]

work page arXiv 2017
[19]

An ´ etude on global vacuum energy sequester,

G. D’Amico, N. Kaloper, A. Padilla, D. Stefanyszyn, A. Westphal, and G. Zahariade, An ´ etude on global vac- uum energy sequester, JHEP09, 074, arXiv:1705.08950 [hep-th]

work page arXiv
[20]

Padilla, Monodromy inflation and an emergent mecha- nism for stabilising the cosmological constant, JHEP01, 6 175, arXiv:1806.04740 [hep-th]

A. Padilla, Monodromy inflation and an emergent mecha- nism for stabilising the cosmological constant, JHEP01, 6 175, arXiv:1806.04740 [hep-th]

work page arXiv
[21]

Coltman, Y

B. Coltman, Y. Li, and A. Padilla, Cosmological consequences of Omnia Sequestra, JCAP06, 017, arXiv:1903.02829 [hep-th]

work page arXiv 1903
[22]

B. K. El-Menoufi, S. Nagy, F. Niedermann, and A. Padilla, Quantum corrections to vacuum energy se- questering (with monodromy), Class. Quant. Grav.36, 215014 (2019), arXiv:1903.07612 [hep-th]

work page arXiv 2019
[23]

S. B. Giddings and A. Strominger, Axion Induced Topol- ogy Change in Quantum Gravity and String Theory, Nucl. Phys. B306, 890 (1988)

1988
[24]

S. B. Giddings and A. Strominger, Baby Universes, Third Quantization and the Cosmological Constant, Nucl. Phys. B321, 481 (1989)

1989
[25]

S. R. Coleman, Why There Is Nothing Rather Than Something: A Theory of the Cosmological Constant, Nucl. Phys. B310, 643 (1988)

1988
[26]

Fischler and L

W. Fischler and L. Susskind, A Wormhole Catastrophe, Phys. Lett. B217, 48 (1989)

1989
[27]

Polchinski, Decoupling Versus Excluded Volume or Re- turn of the Giant Wormholes, Nucl

J. Polchinski, Decoupling Versus Excluded Volume or Re- turn of the Giant Wormholes, Nucl. Phys. B325, 619 (1989)

1989
[28]

Henneaux and C

M. Henneaux and C. Teitelboim, The Cosmological Con- stant and General Covariance, Phys. Lett. B222, 195 (1989)

1989
[29]

Padilla and I

A. Padilla and I. D. Saltas, A note on classical and quan- tum unimodular gravity, Eur. Phys. J. C75, 561 (2015), arXiv:1409.3573 [gr-qc]

work page arXiv 2015
[30]

Hoˇrava, Phys

P. Hoˇ rava, Quantum Gravity at a Lifshitz Point, Phys. Rev. D79, 084008 (2009), arXiv:0901.3775 [hep-th]

work page arXiv 2009
[31]

Hoˇ rava,Spectral dimension of the universe in quantum gravity at a Lifshitz point,Phys

P. Hoˇ rava, Spectral Dimension of the Universe in Quan- tum Gravity at a Lifshitz Point, Phys. Rev. Lett.102, 161301 (2009), arXiv:0902.3657 [hep-th]

work page arXiv 2009
[32]

Sanner, N

C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, Optical clock com- parison for Lorentz symmetry testing, Nature567, 204 (2019), arXiv:1809.10742 [physics.atom-ph]

work page arXiv 2019
[33]

E. M. Lifshitz, On the theory of second-order phase tran- sitions i, Zh. Eksp. Teor. Fiz.11, 255 (1941)

1941
[34]

E. M. Lifshitz, On the theory of second-order phase tran- sitions ii, Zh. Eksp. Teor. Fiz.11, 269 (1941)

1941
[35]

R. M. Hornreich, M. Luban, and S. Shtrikman, Critical behavior at the onset of ⃗k-space instability on theλline, Phys. Rev. Lett.35, 1678 (1975)

1975
[36]

Khoury, B

J. Khoury, B. Muntz, and A. Padilla, A Lapse in the Cos- mological Constant Problem withz= 1 deformations,to appear
[37]

G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D15, 2752 (1977)

1977
[38]

M. J. Duncan and L. G. Jensen, Four Forms and the Cosmological Constant, Nucl. Phys. B336, 100 (1990)

1990
[39]

S. M. Carroll and G. N. Remmen, A Nonlocal Approach to the Cosmological Constant Problem, Phys. Rev. D95, 123504 (2017), arXiv:1703.09715 [hep-th]

work page arXiv 2017