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Abstract The intergalactic helium became fully ionized by the end of cosmic noon (z∼ 2).Similarly to the reionization of hydrogen, helium reionization is expected to be patchy, driven by luminous quasars that ionize the intergalactic gas in their surrounding environment.Probing the morphology of ionized electrons during this epoch can provide crucial information about early structure formation, including the clustering and luminosities of quasars, the accretion rates, variability, and lifetimes of active galactic nuclei, as well as the growth and evolution of supermassive black holes.In this study, we present how measurements of the cosmic microwave background (CMB) can be used to reconstruct the optical-depth fluctuations resulting from patchy helium reionization.As helium reionization occurred at lower redshifts, upcoming probes of large-scale structure surveys will present a significant opportunity to enhance the prospects of probing this epoch by their combined analysis with the CMB.Using a joint information-matrix analysis of hydrogen and helium reionization, we show that near-future galaxy and CMB surveys will have enough statistical power to detect optical-depth fluctuations due to doubly-ionized helium, providing a way of measuring the redshift and duration of helium reionization to high significance.We also show that modeling uncertainties in helium reionization can impact the measurement precision of parameters characterizing hydrogen reionization. 

Abstract Astrometry, the precise measurement of star motions, offers an alternative avenue to investigate low-frequency gravitational waves through the spatial deflection of photons, complementing pulsar timing arrays reliant on timing residuals. Upcoming data from Gaia, Theia, and Roman can not only cross-check pulsar timing array findings but also explore the uncharted frequency range bridging pulsar timing arrays and LISA. We present an analytical framework to evaluate the feasibility of detecting a gravitational wave background, considering measurement noise and the intrinsic variability of the stochastic background. Furthermore, we highlight astrometry's crucial role in uncovering key properties of the gravitational wave background, such as spectral index and chirality, employing information-matrix analysis. Finally, we simulate the emergence of quadrupolar correlations, commonly referred to as the generalized Hellings-Downs curves.