Kinematic lensing with high-resolution spectroscopic surveys. A unique opportunity for transformative cosmology at high redshifts in the 2040s

We present a science case to perform high-redshift cosmic shear surveys for cosmology with next-generation spectroscopic instruments, such as the proposed MegaMapper and Wide-field Spectroscopic Telescope. We argue that by using the novel technique called 'kinematic lensing' (KL) it will be possible to obtain shear catalogues at redshifts between 2 and 5. We show that the signal-to-noise ratio of KL at such high redshifts is on average twice as much that expected from current weak lensing (WL) surveys such as Euclid or LSST, and several times that of the previous generation of WL surveys like DES and KiDS, even with very conservative assumptions about the fraction of spectroscopically-detected sources for which KL shear estimates will be available. This will allow cosmologists to perform joint galaxy clustering-cosmic shear analyses over unprecedented cosmic volumes and to probe the growth of structures deep in the matter-dominated era and across the onset of dark-energy domination, offering a unique opportunity to unveil the mystery of cosmic acceleration.