Refined Bounds on MeV-scale Thermal Dark Sectors from BBN and the CMB
  New light states thermally coupled to the Standard Model plasma alter the
expansion history of the Universe and impact the synthesis of the primordial
light elements. In this work, we carry out an exhaustive and precise analysis
of the implications of MeV-scale BSM particles in Big Bang Nucleosynthesis
(BBN) and for Cosmic Microwave Background (CMB) observations. We find that, BBN
observations set a lower bound on the thermal dark matter mass of $m_\chi >
0.4\,\text{MeV}$ at $2\sigma$. This bound is independent of the spin and number
of internal degrees of freedom of the particle, of the annihilation being
s-wave or p-wave, and of the annihilation final state. Furthermore, we show
that current BBN plus CMB observations constrain purely electrophilic and
neutrinophilic BSM species to have a mass, $m_\chi > 3.7\,\text{MeV}$ at
$2\sigma$. We explore the reach of future BBN measurements and show that
upcoming CMB missions should improve the bounds on light BSM thermal states to
$m_\chi > (10-15)\,\text{MeV}$. Finally, we demonstrate that very light BSM
species thermally coupled to the SM plasma are highly disfavoured by current
cosmological observations.
