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Fundamental Cosmology from Precision Spectroscopy: II. Synergies with supernovae

In previous work [Amendola {\it et al.}, Phys. Rev. D86 (2012) 063515], Principal Component Analysis based methods to constrain the dark energy equation of state using Type Ia supernovae and other low redshift probes were extended to spectroscopic tests of the stability fundamental couplings, which can probe higher redshifts. Here we use them to quantify the gains in sensitivity obtained by combining spectroscopic measurements expected from ESPRESSO at the VLT and the high-resolution ultra-stable spectrograph for the E-ELT (known as ELT-HIRES) with future supernova surveys. In addition to simulated low and intermediate redshift supernova surveys, we assess the dark energy impact of high-redshift supernovas detected by JWST and characterized by the E-ELT or TMT. Our results show that a detailed characterization of the dark energy properties beyond the acceleration phase (i.e., deep in the matter era) is viable, and may reach as deep as redshift 4.