Distortion of the CMB spectrum by the first molecules of the Dark Ages

Astronomical Observatory of Ivan Franko National University of Lviv, Kyryla i Methodia Str., 8, Lviv 79005, Ukraine

^⋆ Corresponding author: yuriy.kulinich@lnu.edu.ua

Received: 26 October 2024
Accepted: 21 March 2025

Abstract

Context. The formation of the first stars and galaxies at Cosmic Dawn was preceded by primordial chemistry reactions during the Dark Ages, generating the first molecules, H₂, HD, and HeH⁺, which were critical for the emergence of the first stars. These molecules absorb and scatter cosmic microwave background (CMB) quanta leading to distortion of the CMB spectrum.

Aims. We aimed to estimate how much bound-bound transitions between the rovibrational levels of H₂, HD, and HeH⁺ molecules contribute to the distortion of the CMB spectrum in the standard ΛCDM cosmology.

Methods. We modelled the formation kinetics of the first molecules using a system of 166 chemical reactions involving 20 reagents. We solved the differential equations governing the processes of spontaneous and collisional transitions between rovibrational levels of H₂, HD, and HeH⁺ molecules. The populations of rovibrational levels and the optical thickness of the gas in transition lines between these levels were used to estimate the differential brightness produced by the first molecules on the CMB.

Results. The signal from the first molecules in the standard ΛCDM cosmology takes the form of an absorption profile in the CMB spectrum and originates from the Dark Ages. The H₂ absorption profile features multiple peaks, reaching a maximum of ∼10⁻³ Jy/sr within the frequency range of ∼50 GHz to ∼120 GHz. The major contribution to absorption originates at redshifts 300 > z > 200. The HD absorption profile features double peaks, reaching a maximum of ∼10⁻⁵ Jy/sr within the frequency range from ∼40 GHz to ∼70 GHz, with the dominant absorption contribution originating at redshifts 300 > z > 30. The absorption profile of HeH⁺ ion-molecule has no features, reaching a maximum of ∼10⁻⁷ Jy/sr within the frequency range of ∼200 GHz to ∼800 GHz, and absorption comes mainly from redshifts 100 > z > 4.