We study the physics potential of the detection of the Cosmic Neutrino Background via neutrino capture on tritium , taking the proposed PTOLEMY experiment as a case study .
With the projected energy resolution of \Delta \sim 0.15 eV , the experiment will be sensitive to neutrino masses with degenerate spectrum , m _ { 1 } \simeq m _ { 2 } \simeq m _ { 3 } = m _ { \nu } \gtrsim 0.1 eV .
These neutrinos are non-relativistic today ; detecting them would be a unique opportunity to probe this unexplored kinematical regime .
The signature of neutrino capture is a peak in the electron spectrum that is displaced by 2 m _ { \nu } above the beta decay endpoint .
The signal would exceed the background from beta decay if the energy resolution is \Delta \lesssim 0.7 ~ { } m _ { \nu } .
Interestingly , the total capture rate depends on the origin of the neutrino mass , being \Gamma ^ { D } \simeq 4 and \Gamma ^ { M } \simeq 8 events per year ( for a 100 g tritium target ) for unclustered Dirac and Majorana neutrinos , respectively .
An enhancement of the rate of up to \mathcal { O } ( 1 ) is expected due to gravitational clustering , with the unique potential to probe the local overdensity of neutrinos .
Turning to more exotic neutrino physics , PTOLEMY could be sensitive to a lepton asymmetry , and reveal the eV-scale sterile neutrino that is favored by short baseline oscillation searches .
The experiment would also be sensitive to a neutrino lifetime on the order of the age of the universe and break the degeneracy between neutrino mass and lifetime which affects existing bounds .