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Naturalness in the Past from a Time-Dependent Supersymmetry Scale

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Tony Gherghetta, Kunio Kaneta, Wenqi Ke

High Energy Physics - Phenomenology · Submitted 9 Nov 2026 · 39 references

Pith's verdict: A clever framework with a load-bearing assumption that is left unsubstantiated.

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arXiv ID2611.12363 (version 1)
Pith IDGMDWPD4Z, Pith's permanent record of this paper and its review
CitationKunio Kaneta, Tony Gherghetta, Wenqi Ke. "Naturalness in the Past from a Time-Dependent Supersymmetry Scale." arXiv:2611.12363 (2026). https://pith.science/paper/GMDWPD4Z
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The paper

The paper claims

In no-scale supergravity, a rolling modulus can control the supersymmetry-breaking scale, allowing superpartners to be much lighter in the early universe while remaining heavy today, with fifth-force and varying-constant effects…

The reading

This paper argues that electroweak naturalness may be epoch-dependent. In no-scale supergravity, a modulus field that serves as both the quintessence field and the dominant source of supersymmetry breaking can roll, causing the gravitino mass—and hence the superpartner spectrum—to vary with cosmic time. The authors show that if the modular weights in the matter Kähler metrics and the exponents of modulus-dependent Yukawa couplings are chosen appropriately, the leading couplings of the rolling modulus to visible matter cancel, suppressing fifth forces and time variation of constants. However, the quintessence potential requires an additional independent tuning of field-dependent radiative corrections to remain stable. The result is an effective theory in which superpartners could have been light during the early universe—modifying phase transitions, relic abundances, and gravitational-wave signals—while being heavy (∼100 TeV) today, so that present-day collider bounds do not conflict with naturalness in the past.

What carries the argument

The machinery is the no-scale supergravity framework with a modulus T that has a double-exponential quintessence potential V_Q ∝ $e^{{λ_1 σ/M_P}}$ + $e^{{λ_2 σ/M_P}}$ derived from a superpotential with small deformations ϵ, ϵ'. The modulus sets the gravitino mass via m_{3/2} ∝ $e^{{-√6 σ/M_P}}$, and its rolling is governed by the equations of motion with kination and slow-roll phases. The visible-sector Kähler metrics are twisted by modular weights n_I, and the superpotential Yukawa couplings have modulus exponents κ_f. Together these parameters determine how particle masses scale with m_{3/2}, and the conditions d_m = d_e = d_g = 0 are algebraic equations that relate n_I and κ_f to the present-day logarithmic derivatives of the Higgs VEV.

Extended reading notes

Core claim

The central claim is that in no-scale supergravity, a quintessence modulus that also breaks supersymmetry can produce a time-dependent supersymmetry-breaking scale, making the naturalness of the electroweak scale epoch-dependent. The gravitino mass m_{3/2} sets the overall soft-mass scale. By choosing modular weights n_I and holomorphic Yukawa exponents κ_f such that the first-order variations of light-fermion masses, α_EM, and Λ_QCD vanish at the present field value, the leading scalar charges d_{m_u,d,s,e}, d_g, and d_e are zero. This suppresses composition-dependent and universal fifth forces. The early universe can then have a much lighter spectrum (m_{3/2} as low as ∼0.3 MeV in the bare-potential trajectory), while today m_{3/2,0}=100 TeV, explaining the absence of superpartners at colliders without sacrificing naturalness in the past.

Load-bearing premise

The paper assumes that the renormalized field-dependent loop and threshold corrections to the quintessence potential are tuned sufficiently small to preserve its value, slope, and curvature (sentence b58); this tuning is not derived from any mechanism and is independent of the modular-weight conditions.

Editorial extensions

If this is right

  • If the central claim is correct, electroweak naturalness is not a time-independent problem: superpartners were light in the early universe, so the weak scale was naturally small then, and the present heaviness is a cosmological accident.
  • The superpartner spectrum was much lighter before BBN, modifying the electroweak and QCD phase transitions, potentially producing a stochastic gravitational-wave background with a nanohertz-to-microhertz peak.
  • Fifth-force and varying-constant bounds are satisfied only for specific correlated values of modular weights and Yukawa exponents, making the framework testable through improved equivalence-principle experiments and searches for time variation of fundamental constants.
  • The gravitino mass is predicted to increase extremely slowly in the future (≈20 meV over 34 billion years), implying negligible present-day variation of particle masses.
  • The framework opens the possibility that the superpartner spectrum observed at colliders is not a fundamental input but a snapshot of a rolling scalar, shifting the naturalness debate from parameter fine-tuning to cosmological timing.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The assumption that field-dependent loop and threshold corrections to the quintessence potential are tuned sufficiently small (sentence b58) is the weakest link; without a dynamical mechanism (e.g., landscape selection or a symmetry) this tuning merely reinterprets the fine-tuning problem rather than solving it.
  • The modular-weight and Yukawa-exponent conditions required for vanishing scalar charges are highly non-generic; they may be realizable only in specific string compactifications (e.g., with particular brane configurations or fluxes), providing a concrete target for UV-completion efforts.
  • If early-universe kination or modified phase transitions are generic in these models, the predicted gravitational-wave spectrum (nHz–μHz) could be falsified by LISA or pulsar-timing arrays if no signal is found at the expected frequencies.
  • The model relies on a no-scale structure that is itself not generic in supergravity; if higher-order corrections or nonperturbative effects stabilize the modulus before it can roll sufficiently, the entire scenario collapses.
Original abstract

We consider the possibility that electroweak naturalness may be epoch dependent. In no-scale supergravity, a rolling quintessence modulus can control the supersymmetry-breaking scale, allowing superpartners to be much lighter in the early universe while remaining heavy today. Fifth-force and varying-constant effects can be suppressed via correlated modular weights in the visible-sector K\"ahler metric and modulus-dependent superpotential Yukawa couplings, while radiative stability of the quintessence potential requires additional tuning of the field-dependent vacuum energy. The resulting effective theory has distinctive implications for early-universe phase transitions, relic abundances, and gravitational waves.

Figures
Figure 1. FIG. 1. The evolutions of
Figure 2. FIG. 2. The evolutions of the total equation of state
Figure 3. FIG. 3. The zero-temperature evolution of the matched
Figure 4. FIG. 4. Present-day MSSM spectrum for the parameters of
Figure 5. FIG. 5. Present-day NMSSM spectrum for Eqs. (
Figure 7. FIG. 7. The evolution of
Figure 8. FIG. 8. The evolution of

Showing 7 of the paper's 8 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2611.12363 by the authors.

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