Will it ever be possible to observe the cosmic neutrino background? Is there any foreseeable technology which would facilitate the direct observation of the cosmic neutrino background?
Would the ability to warp spacetime have any application here?
 A: There are several ideas for observing the cosmic neutrino background (C$\nu$B), but only one probably has any chance of working in the not-too-distant future.
The best prospect was first suggested in 1962 by Steven Weinberg who wondered if cosmic background neutrinos could be detected by their capture by $\beta$ unstable nuclei such as tritium.
$$\mathrm{\nu}_e + \mathrm{^3H} \rightarrow \mathrm{^3He} + e^-$$
Aside from the very low expected rate, there is a huge background from regular tritium decays, but the electrons produced by cosmic neutrino capture can in principle be identified because they will produce an almost monoenergetic line in the electron energy spectrum just above the tritium decay endpoint. The PTOLEMY Collaboration is developing an experiment that might detect a few events per year from a 100 g tritium sample.
Other ideas include:

*

*Detecting the force exerted on macroscopic objects as the Earth moves through the cosmic neutrino background, either by coherent neutral current scattering (Opher 1974) or by the C$\nu$B splitting atomic electron spin states (Stokolsky 1975). This requires an improvement of 11 orders of magnitude in our ability to detect very small forces or torques, and there are currently no workable proposals for this method.


*Observing a dip in the energy spectrum of ultra-high energy cosmic ray neutrinos because of resonant $Z^0$ bosons via $\nu\bar{\nu} \rightarrow Z^0$ interactions with the C$\nu$B (Weiler 1982).  Unfortunately, this requires that the ultra-high energy cosmic ray neutrinos spectrum extends to energies beyond $10^{21}\,\textrm{eV}$, but the spectrum observed by the best current detector, IceCube, only extends up to about  $10^{16}\,\textrm{eV}$.


*A related idea is to look for resonant absorption of neutrinos on heavy ions in a storage ring (Bauer & Sherwood 2021), but this is beyond any current or near-future ring.  For example, seeing 1 event per year for the resonant bound beta decay process
$${}^{157} \textrm{Gd} + \nu_e \rightarrow {}^{157} \textrm{Tb} + e^-\textrm{(bound)}$$
would require an energy per nucleon E/A=101.95 TeV and $2.65 \times 10^{23}$ ions stored in the beam.  The closest current accelerator is the LHC in heavy ion mode which has E/A=2.76 TeV and $2 \times 10^{11}$ stored ions.


*Finally, any process that emits low energy neutrinos can have its phase space suppressed by the Pauli Exclusion Principle if cosmic background neutrinos already occupy some of the process’s possible neutrino final states. In particular, this could happen for radiative emission of neutrino pairs from metastable excited atoms (Yoshimura, Sasao, and Tanaka 2015).  This idea requires much work to decide if it has a chance of ever working.
I am not aware of any idea for C$\nu$B detection that involves warping spacetime.
