Description
Rescale a distance modulus under inverse-Hubble distance scaling.
Cosmology uses several distance measures and often expresses the expansion rate in mixed astronomical units. Scale-factor relations, inverse-Hubble scales and relativistic velocity composition answer different questions; units and the distinction between local algebra and an integrated expansion history are essential.
Rescale a distance modulus under inverse-Hubble distance scaling.
When to use this tool
Use Distance Modulus Hubble Rescale Term when checking one explicit cosmological distance, redshift-factor or unit convention.
How to use the tool and how it works
- Enter oldHubble, newHubble, oldModulus. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read distanceFactor, modulusShift, newModulus. Use the output convention below.
Rescale a distance modulus under inverse-Hubble distance scaling. Require positive oldHubble/newHubble; distanceFactor = old/new, modulusShift = 5*log10(factor), newModulus adds that shift.1
Cosmological distance, volume and lookback-time relations require the appropriate expansion-rate and distance conventions; local factors do not replace integration.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| oldHubble | Old Hubble | Required. Finite number; strictly above 0. |
| newHubble | New Hubble | Required. Finite number; strictly above 0. |
| oldModulus | Old Modulus | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| distanceFactor | Distance Factor | Required. Finite number. |
| modulusShift | Modulus Shift | Required. Finite number. |
| newModulus | New Modulus | Required. Finite number. |
{
"input": {
"oldHubble": 70,
"newHubble": 140,
"oldModulus": 40
},
"output": {
"distanceFactor": 0.5,
"modulusShift": -1.505149978319906,
"newModulus": 38.494850021680094
}
}Limitations and assumptions
- This holds other model assumptions fixed; it is not a general recomputation of cosmological distances.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete cosmological distance/time calculation and the appropriate observation model when an actual source distance, age or velocity is required.
References
-
Calculation and input contract: cosmology/distance-modulus-hubble-rescale-term — tool.io
-
Distance measures in cosmology — David W. Hogg
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