Dark Energy Spectroscopic Instrument/ESA/NASA/Roman Space Telescope/ESA Euclid

A Pre-Announced, Testable Forecast on Redshift-Dependent σ₈ Deviations

Prediction Statement

I present a pre-announced, testable forecast regarding redshift-dependent deviations in the linear growth amplitude σ₈(z), intended for direct comparison with upcoming large-scale structure observations.

The forecast is model-agnostic at the phenomenological level and does not rely on post-hoc fitting.

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Testable Forecast Table (σ₈ Deviations)

Testable Forecast Table (σ₈ Deviations)

Redshift (z) | σ₈ᵉᶠᶠ / σ₈^ΛCDM | Relative deviation (%) | Observable probes / Datasets

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

0.2. | 0.978 – 0.990. | –1.0% to –2.2% | Low-redshift weak lensing

0.5. | 0.970 – 0.985. | –1.5% to –3.0% | Weak lensing / clusters

0.8. | 0.964 – 0.978. | –2.2% to –3.6% | Euclid forecast

1.0. | 0.960 – 0.974. | –2.6% to –4.0% | Current tension range

1.5. | 0.952 – 0.968. | –3.2% to –4.8% | High-z growth trend

At z = 0.2, the effective σ₈ is predicted to be 0.978 – 0.990 of the ΛCDM value,

corresponding to a −1.0% to −2.2% deviation, testable via low-redshift weak lensing.

At z = 0.5, the predicted ratio is 0.970 – 0.985 (−1.5% to −3.0%),

accessible through weak lensing and cluster measurements.

At z = 0.8, the deviation increases to −2.2% to −3.6%,

within the forecast sensitivity of Euclid.

At z = 1.0, the deviation reaches −2.6% to −4.0%,

corresponding to the current LSS tension regime.

At z = 1.5, the predicted suppression is −3.2% to −4.8%,

probing high-redshift growth behavior.

Shape Constraint (Qualitative)

The deviation follows a smooth, single-peaked redshift dependence:

• Approaches zero at low redshift

• Reaches a mild maximum around intermediate redshift

• No oscillatory or discontinuous behavior

This shape is designed to be falsifiable by near-term weak lensing and cluster measurements.

Scope and Disclosure

• This post intentionally does not specify the underlying microphysical model

• No assumptions are made about the ultimate nature of dark matter or dark energy

• The purpose is prior disclosure of observable consequences only

• All statements are made before data release

Author

Manway Leo

Independent researcher

(Date + platform timestamp serves as prior disclosure)