Theory 09/Physics, Cosmos & Matter /Fundamental physics
Vacuum Energy Depends on Topology
The cosmological constant problem is stated as a magnitude. It may be a sign problem first.
The sign of the vacuum energy contribution is set by the topology of the compact dimensions rather than by the field content, so two theories with identical particles can predict opposite cosmological constants.
01The evidence
Calculations of vacuum energy in compactified theories give contributions that depend on the boundary conditions, with both signs appearing.
02The tension
The problem is framed as a fine-tuning of magnitude, and the sign dependence on topology is treated as a technical detail rather than as the organising fact.
03The mechanism
A field on a compact space has a spectrum set by the boundary conditions. Summing the zero-point energies gives a result whose sign depends on whether the lightest modes are bosonic or fermionic under the compactification.
That makes the sign a topological question, and predicts that theories differing only in compactification should differ in the sign of their vacuum energy.
04What this is not
That framing asks why the number is small. This asks why it has the sign it does, which is a different and more constrained question.
05Predictions
- P1Sign should track compactification topology.
- P2Theories with identical content should differ in sign.
- P3Boundary conditions should control the result.
06Refutation
Sign independent of topology would leave the magnitude framing intact.
07What it changes
It would restate the cosmological constant problem.