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Aims. Classical Cepheids provide the foundation for the empirical extragalactic distance ladder. Milky Way Cepheids are the only stars in this class accessible to trigonometric parallax measurements. However, the parallaxes of Cepheids from the second Gaia data release (GDR2) are affected by systematics because of the absence of chromaticity correction, and occasionally by saturation. Methods. As a proxy for the parallaxes of 36 Galactic Cepheids, we adopt either the GDR2 parallaxes of their spatially resolved companions or the GDR2 parallax of their host open cluster. This novel approach allows us to bypass the systematics on the GDR2 Cepheids parallaxes that is induced by saturation and variability. We adopt a GDR2 parallax zero-point (ZP) of −0.046 mas with an uncertainty of 0.015 mas that covers most of the recent estimates. Results. We present new Galactic calibrations of the Leavitt law in the V, J, H, KS, and Wesenheit WH bands. We compare our results with previous calibrations based on non-Gaia measurements and compute a revised value for the Hubble constant anchored to Milky Way Cepheids. Conclusions. From an initial Hubble constant of 76.18 ± 2.37 km s−1 Mpc−1 based on parallax measurements without Gaia, we derive a revised value by adopting companion and average cluster parallaxes in place of direct Cepheid parallaxes, and we find H0 = 72.8 ± 1.9 (statistical + systematics) ±1.9 (ZP) km s−1 Mpc−1 when all Cepheids are considered and H0 = 73.0 ± 1.9 (statistical + systematics) ±1.9 (ZP) km s−1 Mpc−1 for fundamental mode pulsators only. [ABSTRACT FROM AUTHOR]

Aims. We investigated the degree of improvement in dark energy constraints that can be achieved by extending Type Ia supernova (SN Ia) samples to redshifts z > 1:5 with the Hubble Space Telescope (HST), particularly in the ongoing Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) and the Cluster Lensing and Supernova survey with Hubble (CLASH) multi-cycle treasury programs. Methods. Using the popular Chevalier-Polarski-Linder (CPL) parametrization of the dark energy w = w0 + wa(1 - a) we generated mock SN Ia samples that can be projected out to higher redshifts. The synthetic datasets thus generated were fitted to the CPL model, and we evaluated the improvements that a high-z sample can add to improve the statistical and systematic uncertainties on cosmological parameters. Results. In an optimistic but still very achievable scenario, we find that extending the HST sample beyond CANDELS+CLASH to reach a total of 28 SN Ia at z > 1:0 could improve the uncertainty in the wa parameter σwaby up to 21%. The corresponding improvement in the figure of merit (FoM) would be as high as 28%. Finally, we consider the use of high-redshift SN Ia samples to detect non-cosmological evolution in SN Ia luminosities with redshift, finding that these tests could be undertaken by future space-based infrared surveys using the James Webb Space Telescope (JWST). [ABSTRACT FROM AUTHOR]