When galaxy formation started in the history of the Universe remains unclear. Studies of the cosmic microwave background indicate that the Universe, after initial cooling (following the Big Bang), was reheated and reionized by hot stars in newborn galaxies at a redshift in the range 6 < z < 14 (ref. 1). Though several candidate galaxies at redshift z > 7 have been identified photometrically, galaxies with spectroscopically confirmed redshifts have been confined to z < 6.6 (refs 4-8). Here we report a spectroscopic redshift of z = 6.96 (corresponding to just 750 Myr after the Big Bang) for a galaxy whose spectrum clearly shows Lyman-alpha emission at 9,682 A, indicating active star formation at a rate of approximately 10M(o) yr(-1), where M(o) is the mass of the Sun. This demonstrates that galaxy formation was under way when the Universe was only approximately 6 per cent of its present age. The number density of galaxies at z approximately 7 seems to be only 18-36 per cent of the density at z = 6.6.

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Long-duration γ-ray bursts are associated with the explosions of massive stars and are accordingly expected to reside in star-forming regions with molecular gas (the fuel for star formation). Previous searches for carbon monoxide (CO), a tracer of molecular gas, in burst host galaxies did not detect any emission. Molecules have been detected as absorption in the spectra of γ-ray burst afterglows, and the molecular gas is similar to the translucent or diffuse molecular clouds of the Milky Way. Absorption lines probe the interstellar medium only along the line of sight, so it is not clear whether the molecular gas represents the general properties of the regions where the bursts occur. Here we report spatially resolved observations of CO line emission and millimetre-wavelength continuum emission in two galaxies hosting γ-ray bursts. The bursts happened in regions rich in dust, but not particularly rich in molecular gas. The ratio of molecular gas to dust (<9-14) is significantly lower than in star-forming regions of the Milky Way and nearby star-forming galaxies, suggesting that much of the dense gas where stars form has been dissipated by other massive stars.

Nature of dark energy remains unknown. Especially, to constrain the time variability of the dark-energy, a new, standardisable candle that can reach more distant Universe has been awaited. Here we propose a new distance measure using fast radio bursts (FRBs), which are a new emerging population of ∼ ms time scale radio bursts that can reach high-z in quantity. We show an empirical positive correlation between the time-integrated luminosity (L ν ) and rest-frame intrinsic duration (w int,rest ) of FRBs. The L ν − w int,rest correlation is with a weak strength but statistically very significant, i.e., Pearson coefficient is ∼ 0.5 with p-value of ∼0.038, despite the smallness of the current sample. This correlation can be used to measure intrinsic luminosity of FRBs from the observed w int,rest . By comparing the luminosity with observed flux, we measure luminosity distances to FRBs, and thereby construct the Hubble diagram. This FRB cosmology with the L ν − w int,rest relation has several advantages over SNe Ia, Gamma-Ray Burst (GRB), and well-known FRB dispersion measure (DM)-z cosmology; (i) access to higher redshift Universe beyond the SNe Ia, (ii) high event rate that is ∼ 3 order of magnitude more frequent than GRBs, and (iii) it is free from the uncertainty from intergalactic electron density models, i.e., we can remove the largest uncertainty in the well-debated DM-z cosmology of FRB. Our simulation suggests that the L ν − w int,rest relation provides us with useful constraints on the time variability of the dark energy when the next generation radio telescopes start to find FRBs in quantity.