Cosmological forecasts on thermal axions, relic neutrinos and light
  elements
  One of the targets of future Cosmic Microwave Background and Baryon Acoustic
Oscillation measurements is to improve the current accuracy in the neutrino
sector and reach a much better sensitivity on extra dark radiation in the Early
Universe. In this paper we study how these improvements can be translated into
constraining power for well motivated extensions of the Standard Model of
elementary particles that involve axions thermalized before the quantum
chromodynamics (QCD) phase transition by scatterings with gluons. Assuming a
fiducial $\Lambda$CDM cosmological model, we simulate future data for Stage-IV
CMB-like and Dark Energy Spectroscopic Instrument (DESI)-like surveys and
analyze a mixed scenario of axion and neutrino hot dark matter. We further
account also for the effects of these QCD axions on the light element
abundances predicted by Big Bang Nucleosynthesis. The most constraining
forecasted limits on the hot relic masses are $m_{\rm a} \lesssim 0.92$ eV and
$\sum m_\nu\lesssim 0.12$ eV at 95 per cent Confidence Level, showing that
future cosmic observations can substantially improve the current bounds,
supporting multi-messenger analyses of axion, neutrino and primordial light
element properties.
