Description
Apply the supplied multipole weighting to an angular-power value.
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.
Apply the supplied multipole weighting to an angular-power value.
When to use this tool
Use CMB Bandpower Ell Weight when you already have multipole, angularPower and need to apply the supplied multipole weighting to an angular-power value.
How to use the tool and how it works
- Enter multipole, angularPower. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read weightedBandpower. Use the output convention below.
Require multipole a nonnegative safe integer; return ell*(ell+1)/(2π)*angularPower.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| multipole | Multipole | Required. Safe integer; minimum 0. |
| angularPower | Angular Power | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weightedBandpower | multipole*(multipole+1)*angularPower/(2π); a local D_l-style weighting, without bin averaging or spectral-density normalization. | Required. Finite number. |
{
"input": {
"multipole": 2,
"angularPower": 3
},
"output": {
"weightedBandpower": 2.864788975654116
}
}Limitations and assumptions
- The amplitude unit follows angularPower and values may be signed. This is one convention transformation, not a measured spectrum, bin average, sky analysis or cosmological fit; large multipoles lose integer precision in intermediate products.
- 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
- Primordial Spectrum Pivot Amplitude Term
Scale a supplied primordial spectrum amplitude from a pivot wavenumber.
- Weak Lensing Reduced Shear Scalar
Calculate one scalar reduced-shear component from supplied shear and convergence.