Bachelor Project seminar: Jeffrey Dijkstra

Title:
Early Dark Energy and Rayleigh Scattering in the CMB

Abstract:
Early- and late-universe observations of the Hubble constant $H_0$ show a systematic difference between the two inferred values, termed the Hubble tension. The inclusion of Early Dark Energy (EDE) to the early universe acting as a cosmological constant before quickly decaying away can resolve this tension as it increases $H_0$ inferred from the cosmic microwave background (CMB). Here is studied the inclusion of Rayleigh scattering to Fisher forecasts of a three parameter EDE extension to the $\Lambda$CDM model. Rayleigh scattering is a secondary anisotropy of the CMB caused by the additional scattering of neutral species produced during recombination with a unique frequency dependency ($\propto \nu^4$). EDE Fisher forecasts show benefits when including the Rayleigh signal as it peaks a short time after recombination, tightening constraints on the local expansion history. For this work the Python branch of the Boltzmann hierarchy solver \mintinline{text}{CAMB} was modified to calculate, for a singe frequency, the total Thomson $+$ Rayleigh power spectrum. The implementation is consistent with the older Fortran Rayleigh branch of \mintinline{text}{CAMB} to sub-percentile level. The auto $RR$ and cross $TR$ spectra are calculated indirectly from the total spectra. Both spectra are accurate except for $RR$ at the lowest $\ell$. The EDE parameter forecast, including PICO noise levels, give an improvement ranging 54 to 90$\%$ (depending on the parameter) for the Rayleigh signal compared to the Thomson primary. This improvement is too high compared to previous studies, particularly $\Omega_c h^2$, $H_0$ and $f_{\text{EDE}}$. The missing cross-correlation terms in the covariance matrices is the possible error. However, the individual parameter errors are slightly worse than other studies due to excluding polarization effects. Upcoming development in the code, primarily including multi-frequency correlated Rayleigh signals, should clarify whether the forecasts are accurate or correct them to only show minor improvements, demonstrating the real constraining power of Rayleigh effects on EDE.