The ESA Euclid telescope launched July 1, 2023 to study dark energy and dark matter in space.
NASA’s Roman Space Telescope is designed to study dark energy , matter, exoplanets, and infrared astrophysics.
Are there others?
Before you start looking for something using telescopes, you need to understand what exactly you are looking for. Dark energy and dark matter are the constituent media that carry light energy in space. This medium has density. The value of this density is contained in the “Planck constant”. It can be obtained both theoretically and (indirectly) experimentally:
https://www.researchgate.net/publication/372725587_ON_RADIATION_ENERGY_CONSTANT_EQUIVALENCE_OF_MASS_AND_ENERGY_AND_DENSITY_OF_THE_ETHER_UNIVERSUM_ENVIRONMENT?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaX JlY3QiLCJwYWdlIjoicHJvZmlsZSIsInBvc2l0aW9uIjoicGFnZUNvbnRlbnQifX0
Robert Shour, 'How many dark energy space telescopes are currently planned or operating?'
Dark matter cannot be seen, but its presence can be inferred from its interactions with normal matter. Examples observed by the Hubble Space Telescope include evidence of dark matter separation in galactic collisions, the rotation rates in the outer parts of galaxies which indicate they have dark matter halos, and the ongoing mapping of the Cosmic Web which has shown that the voids between its strands are open and interconnected, like those of a sponge, rather than closed bubble-like hollows. In theory any telescope could make such observations, but in practise the larger and more versatile the instruments are, the more comprehensive the results will be.
So there is no such thing as a 'dark matter telescope'. If dark matter can be detected directly, it will be with instruments on Earth or in nearby space. There is an Alpha Magnetic Spectrometer on the International Space Station which hopes to detect dark matter particles, but has yet to do so as far as I know, and there is a very large neutrino detector being built which may also be able to detect the still weaker interactions of dark matter with ordinary matter that it passes through.
Similarly a 'dark energy telescope' cannot exist because dark energy is not a 'thing' which can be observed. It is an unknown force which permeates the Universe, which acts in opposition to gravity and is causing the Universe to expand at an increasing rate, We can only measure its effect by observations of the behaviour of ordinary matter over large volumes of space. In theory, again, any telescope could contribute to that, but the larger the instrument and the more frequencies it can access the better the results will be. At present they are inconsistent when different techniques are used.
That said, the University of Michigan has a Dark Energy Spectroscopic Instrument (DESI) under construction for first use in 2018, and it will be deployed on the Mayall Telescope on Kitt Peak. It will compile optical spectra for millions of galaxies out to 11 billion light-years, to analyse the effects of dark energy on them using techniques such as baryon acoustic oscillations, and before you ask, I don't know what they are either! But I hope that information is all helpful.
With best wishes,
Duncan.
The Nancy Grace Roman Space Telescope, formerly named the Wide Field Infrared Survey Telescope (WFIRST), is set to launch in the mid-2020s with the primary goal of studying dark energy. Additionally, the European Space Agency's Euclid mission is another telescope working to explore both dark energy and dark matter. These missions represent ongoing efforts to deepen our understanding of these cosmic mysteries
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