Description
Return normalized scale factor and its redshift derivatives.
Cosmological redshift relates emitted and observed scales through a declared normalization. Density components, lengths and temperatures follow different model-dependent powers of the expansion factor, so matching symbols or dimensions does not make their physical meanings interchangeable.
Return normalized scale factor and its redshift derivatives.
When to use this tool
Use Scale Factor Redshift Log Derivative when evaluating the stated redshift scaling under its explicit normalization and component assumptions.
How to use the tool and how it works
- Enter redshift. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read scaleFactor, derivative, logDerivative. Use the output convention below.
Return normalized scale factor and its redshift derivatives. Require redshift > -1; scaleFactor = 1/(1+z), derivative = -1/(1+z)² and logDerivative = -1/(1+z).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| redshift | Dimensionless redshift z; the stated scaling formulas require z > -1. | Required. Finite number; strictly above -1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| scaleFactor | Scale Factor | Required. Finite number. |
| derivative | Derivative | Required. Finite number. |
| logDerivative | d(ln a)/dz = -1/(1+z), under a0=1. | Required. Finite number. |
{
"input": {
"redshift": 1
},
"output": {
"scaleFactor": 0.5,
"derivative": -0.25,
"logDerivative": -0.5
}
}Limitations and assumptions
- Normalization is present-day a=1; logDerivative means d(ln a)/dz, not d(a)/d(ln z).
- 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 model with justified parameters for expansion histories, component evolution and observational inference.
References
Similar or alternative tools
- Redshift Scale Factor Gap
Compare a supplied scale factor with normalized redshift scaling.
- Cosmic Scale Factor Reference Gap
Compare scale factor under an explicit normalization.