The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg² of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

We show, considering a specific f (R)-gravity model, that the Jordan frame and the Einstein frame could be physically non-equivalent, although they are connected by a conformal transformation which yields a mathematical equivalence. Calculations are performed analytically and this non-equivalence is shown in an unambiguous way. However this statement strictly depends on the considered physical quantities that have to be carefully selected. © 2010 Elsevier B.V. All rights reserved.PMM gratefully acknowledges the financial support provided by the I3P framework of CSIC and the European Social Fund.Peer Reviewe

We consider a non-static evolving version of the regular ‘black-bounce’/traversable wormhole geometry recently introduced in Simpson and Visser (2019 J. Cosmol. Astropart. Phys . JCAP02(2019)042). We first re-write the static metric using Eddington–Finkelstein coordinates, and then allow the mass parameter m to depend on the null time coordinate ( à la Vaidya ). The spacetime metric is Here denotes suitably defined null time coordinates; representing time, while, (at least for ), we allow . This spacetime is still simple enough to be tractable, and neatly interpolates between Vaidya spacetime, a black-bounce, and a traversable wormhole. We show how this metric can be used to describe several physical situations of particular interest, including a growing black-bounce, a wormhole to black-bounce transition, and the opposite black-bounce to wormhole transition.

We show that dust matter–dark energy combined phases can be achieved by the exact solution derived from a power law f(R) cosmological model. This example answers the query by which a dust-dominated decelerated phase, before dark-energy accelerated phase, is needed in order to form large scale structures