Technical naturalness of the renormalised vacuum energy: stability of Λ under radiative corrections
Kept at the calibrated 90/7/56: the defining open problem of the field, probably needing quantum gravity, and the only non-mathematical problem in the 90s. Leverage 56 stays below dark matter (70) because few concrete results are stated conditionally on a solution. No practical application.
The problem
Why is the energy of empty space so small, and why does it stay small under quantum corrections?
- 1Quantum fields give empty space energy
- 2Gravity feels that energy as dark energy
- 3Predicted size far above what we observe
- 4Cancellations needed at every order
- 5No accepted mechanism explains this
The puzzle. In quantum field theory (QFT), every field has zero-point energy, and every massive particle contributes to the vacuum energy at every loop order in perturbation theory. Combined with gravity, the effective cosmological constant is the sum of a bare term and these corrections. The observed dark-energy density is about 10⁻¹²³ in Planck units.
Built from
earlier problems → this oneThe problems this one is built from: progress or tools it needs (builds on), special cases that come first (generalizes), and weaker results on the way (implies). On the right, what builds on it.
- Start with
- Step 2
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- Technical naturalness of the renormalised vacuum energy: stability of Λ under radiative correctionsThis problem
Path to understanding
foundations → problemThe research entries this problem rests on, in the order to read them. Each links to its explainer.
- Start with
- Step 2
- Step 3
- ΛCDM, the standard model of cosmologyTheory · host
- Then
- Technical naturalness of the renormalised vacuum energy: stability of Λ under radiative correctionsThe problem
State of the art
A Planck-scale cutoff gives a mismatch of about 10¹²⁰ (the power depends on the cutoff convention); the electroweak phase transition alone contributes roughly 10⁵⁵ times too much. Weinberg's 1989 review gives a no-go analysis of adjustment mechanisms and surveys five classes of proposals; Burgess's lectures (arXiv:1309.4133) explain why most later proposals fail or move the tuning elsewhere. Martin's review (arXiv:1205.3365) clarifies the order-by-order tuning formulation. The anthropic (landscape) argument predicted a small nonzero Λ of roughly the observed order (Weinberg 1987) but is not a mechanism and remains contested. Supersymmetry cancels contributions only where unbroken. DESI DR2's hint of evolving dark energy (2025, unresolved) would not by itself address the size of Λ. No proposed solution is accepted.
Realistic applications
There is no near-term practical application. Progress would reshape the interface of quantum field theory and gravity and the interpretation of dark-energy measurements.
What counts as solved
Resolved by a framework that predicts or explains the observed vacuum energy without order-by-order tuning, makes testable predictions, and is accepted by experts as satisfying Weinberg's no-go constraints (for example through a controlled quantum-gravity calculation).
How it gets verified
Expert reviewOnly expert review of the argument is possible today.
No measurement can settle it; a proposed framework must predict or explain the observed vacuum energy without order-by-order tuning, make testable predictions, and satisfy Weinberg's no-go constraints. Experts judge the argument, for example a controlled quantum-gravity calculation, and no Lean statement exists for it.
Claims under verification
+ add a claimNo claimed results on the Verification board for this problem yet.
Where the work is
The barrier is conceptual. A new framework is needed; data can only exclude evolution of Λ.
Bottlenecks
ranked by votes- #1TheoryWeinberg's no-go for adjustment mechanisms
Any Lorentz-invariant mechanism that relaxes Λ dynamically must evade the argument that the adjusting field settles at a value giving zero only by tuning.
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Connected problems
Progress
- Sep 17, 2013Burgess lecturessource
Review of why later proposals fail or relocate the tuning.
- May 14, 2012Martin's sharp formulationsource
The problem is stated as order-by-order tuning of the renormalised vacuum energy.
- Jan 1, 1989Weinberg's review and no-go theoremsource
Surveys adjustment mechanisms and shows that Lorentz-invariant ones fail.