Constraints on neutrino mass from Cosmic Microwave Background and Large Scale Structure

Our tightest upper limit on the sum of neutrino mass eigenvalues $M_{\nu }$ comes from cosmological observations that will improve substantially in the near future, enabling a detection. The combination of the Baryon Acoustic Oscillation feature measured from the Dark Energy Spectroscopic Instrument and a Stage-IV Cosmic Microwave Background experiment has been forecasted to achieve $\sigma (M_{\nu })<1\mathrm{/}3$ of the lower limit on $M_{\nu }$ from atmospheric and solar neutrino oscillations \citep{2013arXiv1309.5383A,2012PhRvD…86a3012F}. Here we examine in detail the physical effects of neutrino mass on cosmological observables that make these constraints possible. We also consider how these constraints would be improved to ensure at least a $5\sigma$ detection.