## 6 Future Instruments for Astrophysics and Fundamental Physics Research
### Instruments for Particle-Physics And Cosmology  
While astrophysics has been, historically, the main driver to develop TESs as sensitive thermometers in imaging spectrometers, more and more projects in other fields of particle physics and cosmology [174] are already employing or becoming interested in arrays of TESs for their very sensitive instruments. It happens thanks to the growing matureness of the TES technology, which is moving from the single pixel development phase to the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mission** & **F.o.V.** & **Angular Resolution** & **Number of Pixels** & **Energy** & **dE** & **Eff. Area** \\
**(Instrument)** & **arc min** & **arc sec** & & **(eV)** & **(eV)** & **(m\({}^{2}\)) @ 1 keV** \\ \hline Athena (XIFU) & 5 & 5 & \(\sim\)3800 & 0.2–8 keV & 2–2.5 eV & 1.4 \\ HUBS & 60 & \(\sim\)60 & \(\sim\)3600 & 0.2–2 & 0.8–2 & \(\sim\)0.05 \\ Super DIOS & \(>\)30 & 0–15 & \(\sim\)30,000 & 0.2–2 & \(<\)2 eV & \(>\)0.1 \\ Lynx (LXM) & 1–5 & 0.5–1 & \(\sim\)100,000 & 0.2–7 & 0.3–3 & 0.2–2 \\ CWE & 60 & 5 & \(\sim\)1 M & 0.1–3 & 0.3 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of the characteristic of the TES-based instruments planned for the future X-ray space observatories. Athena is currently in the ESA Phase-A study. The other missions are still in the selection or proposal phase. design and construction phase of complex instrumentations with larger and larger arrays of pixels. In this section, we consider the development of TES-based photon and power detectors for particle-physics and cosmology projects, like the ground-base experiments for (i) the direct detection of the neutrino mass, (ii) the detection of solar axions, and (iii) the search of signature of the primordial gravitational waves with space missions. (i) The absolute values of the masses of the three neutrino flavors, discovered with neutrino oscillation experiments, are unknown. An upper limit of 1.1 eV to the absolute mass scale has been set in Spring 2019 by the Karlsruhe Tritium Neutrino experiment KATRIN [175]. A precise measurement of the neutrino mass is one of the important ingredients toward the physics beyond the Standard Model. One way to directly probe the neutrino mass scale in the laboratory is by performing calorimetric measurement of the energy released in electron capture decay of holmium(\({}^{163}\)Ho). The HOLMES and ECHO projects [8,176,177] employ, respectively, arrays of low temperature TES X-ray calorimeters and metallic magnetic calorimeters to detect the spectrum of \({}^{163}\)Ho between 0 and 3 keV, with an energy resolution better than 3 eV. What makes these experiments unique is the fact that the radioactive source is embedded into the absorber. This means that the total energy of the decay process, except for the fraction taken away from the neutrino, is entirely released into the detector. This approach minimize the systematic uncertainties from energy calibration and gain instability correction, and is neutrino-model independent. The goal for these middle-scale experiments, employing an array of \(\sim\)1000 pixels, is to achieve a neutrino mass statistical sensitivity below 2 eV and develop the technology for a future megapixels detector [8]. As for X-IFU, and the other low temperature instruments for the future space mission, to meet the challenging requirement set for the neutrino mass experiment, cutting edge technology is required both for the detector and the readout. High energy resolution, \(\Delta E_{FWHM}\sim 1\) eV, and high statistics (exceeding 10\({}^{13}\) decays) are desired for a competitive experiment. One of the most critical limiting factor to the sensitivity comes from the intrinsic background from unresolved pile-up, as a results of the fact that the \({}^{163}\)Ho decay generates a signal with finite time resolution. The fraction of unresolved pile-up is given approximately by the product of the detector time resolution \(\tau_{res}\) with the source activity in the absorber.