Description
Scale a supplied primordial spectrum amplitude from a pivot wavenumber.
Cosmological quantities depend on scale factor, redshift, distance definition and the dimensionless Hubble parameter h. Proper and comoving distances differ at a specified epoch, and h-scaled units differ from the dimensional Hubble constant. A scalar rescaling or model contribution preserves supplied conventions without fitting a cosmology or inferring an observed distance.
Scale a supplied primordial spectrum amplitude from a pivot wavenumber.
When to use this tool
Use Primordial Spectrum Pivot Amplitude Term when you already have pivotAmplitude, waveNumber, pivotWaveNumber, spectralIndex and need to scale a supplied primordial spectrum amplitude from a pivot wavenumber.
How to use the tool and how it works
- Enter pivotAmplitude, waveNumber, pivotWaveNumber, spectralIndex. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read powerAmplitude. Use the output convention below.
Require pivotAmplitude>=0 and both wavenumbers positive/finite; return amplitude*(waveNumber/pivotWaveNumber)^(spectralIndex-1).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| pivotAmplitude | Pivot Amplitude | Required. Finite number; minimum 0. |
| waveNumber | Wave Number | Required. Finite number; strictly above 0. |
| pivotWaveNumber | Pivot Wave Number | Required. Finite number; strictly above 0. |
| spectralIndex | Exponent is spectralIndex-1; no spectral running or transfer function is included. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| powerAmplitude | Power Amplitude | Required. Finite number. |
{
"input": {
"pivotAmplitude": 2,
"waveNumber": 4,
"pivotWaveNumber": 2,
"spectralIndex": 2
},
"output": {
"powerAmplitude": 4
}
}Limitations and assumptions
- Wavenumber units and amplitude convention must match. This is a supplied pure power law, without running, transfer functions, parameter fitting or a complete matter spectrum.
- 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 the complete cosmological model and its parameter, epoch and unit definitions for a physical inference. Review redshift, distance, lensing and spectrum conventions before combining these local terms; they do not perform line-of-sight integration, parameter estimation or uncertainty analysis.
References
Similar or alternative tools
- CMB Bandpower Ell Weight
Apply the supplied multipole weighting to an angular-power value.
- Wave Number H Per Mpc Label
Remove the h factor from a supplied h/Mpc wavenumber.