What this research found
The temperature power spectrum of the cosmic microwave background carries a train of acoustic peaks left by sound waves in the primordial plasma, and their spacing and heights encode the geometry and contents of the early universe. Working from the Planck 2018 binned temperature-temperature spectrum, the first three peaks were located without assuming any cosmological model, by smoothing the binned measurements with a cubic spline. The resulting acoustic scale — the characteristic spacing between consecutive peaks — is 298.3 ± 3.4 in multipole moment.
- The first and dominant acoustic peak sits at multipole 224.0 ± 4.1, with a temperature power of 5800 ± 85 squared microkelvin.
- The second peak falls at multipole 535.9 ± 5.8 with a power of 2601 ± 23 squared microkelvin, and the third at 820.6 ± 5.3 with 2525 ± 20. The second and third are nearly equal in height, in contrast to the steep drop from the first peak to the second.
- The acoustic scale, the characteristic spacing between successive peaks, is 298.3 ± 3.4 in multipole moment.
- Because the peaks were found as maxima of a spline through the binned data rather than by fitting a cosmological model to it, the three positions and the acoustic scale are properties measured from the spectrum itself.
How it was done
The published Planck 2018 binned temperature-temperature power spectrum was taken as input, expressed as multipole-weighted power in squared microkelvin with a 1 sigma error on each bin, and covering multipoles from roughly 50 to just above 1000 — enough to contain the first three acoustic peaks and the troughs between them. A cubic spline was fitted through the binned points to give a smooth curve, whose maxima located each peak in both position and amplitude with an attached uncertainty. The spacings between consecutive peak positions were then combined into a single acoustic-scale estimate, and the peaks, the smoothed curve, and the binned data were plotted together.
Data sources
- Planck 2018 binned temperature-temperature power spectrum, multipoles from about 50 to just above 1000
How this research was produced
K-Dense Web planned and ran this astronomy investigation end to end — gathering the sources, carrying out the analysis, producing the figures, and drafting the report. The full session transcript, including every intermediate step, is available to view.
