# Learner lab record: Vacuum cutoff and curvature-mismatch ledger

Course: Vacuum energy and the cosmological constant

Name: ____________________  Date: ____________________  Group: ____________________

## Investigation question

How does a regulated zero-point estimate depend on cutoff, and how is that formal scale compared with observed gravitational curvature?

## Setup

Use the vacuum-scale explorer. Sweep the hard cutoff by decades, keep units explicit, and compare the regulator-dependent quartic term with the declared observed dark-energy scale.

## Variables

| Variable | Role | Unit |
| --- | --- | --- |
| Ultraviolet cutoff | regulator input | energy |
| Field multiplicity/sign | model input | count |
| Regulated vacuum density | formal dependent | energy/volume |
| Observed curvature-equivalent density and mismatch | comparison diagnostic | energy/volume and decades |

## Predict before changing controls

1. Predict the density change for one decade of cutoff increase.

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2. Predict whether changing regulators alone fixes the renormalized cosmological constant.

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## Observation table

| cutoff | fields/sign | regulated density | observed density | ratio | decade mismatch | scheme note |
| --- | --- | --- | --- | --- | --- | --- |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |

## Analyze

1. Does the numerical result show quartic scaling?

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2. Which term is bare or scheme-dependent?

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3. What measurement fixes the renormalized gravitational parameter?

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4. Why is a large formal mismatch not a direct energy-extraction measurement?

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## Evidence-bounded conclusion

Raising cutoff from ___ to ___ changed the regulated term by ___ orders; the comparison with observed curvature is ___, while the physical renormalized claim remains ___.

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