Description
Return a local lookback-time increment.
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.
Return a local lookback-time increment.
When to use this tool
Use Cosmological Lookback Time Local Increment when checking one explicit cosmological distance, redshift-factor or unit convention.
How to use the tool and how it works
- Enter redshift, redshiftIncrement, hubbleAtRedshift. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lookbackIncrement. Use the output convention below.
Return a local lookback-time increment. Require z > -1 and hubbleAtRedshift > 0; increment = redshiftIncrement/((1+z)*H(z)).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 |
|---|---|---|
| redshift | Dimensionless redshift z; the stated scaling formulas require z > -1. | Required. Finite number; strictly above -1. |
| redshiftIncrement | Redshift Increment | Required. Finite number. |
| hubbleAtRedshift | Hubble At Redshift | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lookbackIncrement | Signed differential lookback-time contribution in inverse-Hubble time units; not a finite integral. | Required. Finite number. |
{
"input": {
"redshift": 1,
"redshiftIncrement": 0.1,
"hubbleAtRedshift": 2
},
"output": {
"lookbackIncrement": 0.025
}
}Limitations and assumptions
- H sets inverse-time units; this differential step is not a finite-bin integral or a complete universe-age calculation.
- 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
Similar or alternative tools
- Hubble Time Gigayear Supplied Unit Factor
Convert a supplied Hubble parameter into inverse time.
- Hubble Distance Hunit Factor
Return Hubble distance under a supplied unit conversion.