We analytically derive the spectrum of gravitational waves due to magneto-hydrodynamical turbulence generated by bubble collisions in a first-order phase transition. In contrast to previous studies, we take into account the fact that turbulence and magnetic fields act as sources of gravitational waves for many Hubble times after the phase transition is completed. This modifies the gravitational wave spectrum at large scales. We also model the initial stirring phase preceding the Kolmogorov cascade, while earlier works assume that the Kolmogorov spectrum sets in instantaneously. The continuity in time of the source is relevant for a correct determination of the peak position of the gravitational wave spectrum. We discuss how the results depend on assumptions about the unequal-time correlation of the source and motivate a realistic choice for it. Our treatment gives a similar peak frequency as previous analyses but the amplitude of the signal is reduced due to the use of a more realistic power spectrum for the magneto-hydrodynamical turbulence. For a strongly first-order electroweak phase transition, the signal is observable with the space interferometer LISA.

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.

Liquid crystals are remarkably useful for laboratory exploration of the dynamics of cosmologically relevant defects. They are convenient to work with, they allow the direct study of the "scaling solution" for a network of strings, and they provide a model for the evolution of monopoles and texture. Experiments described here support the simple "one-scale" model for cosmic string evolution, as well as some qualitative predictions of string statistical mechanics. The structure of monopoles and their apparent cylindrical but not spherical symmetry is discussed. A particular kind of defect known as texture is described and is shown to have a dynamical instability—it can decay into a monopole-antimonopole pair. This decay process has been observed occurring in the liquid crystal, and studied with numerical simulations.

In this paper we compute the quantity which is truly measured in a large galaxy survey. We take into account the effects coming from the fact that we actually observe galaxy redshifts and sky positions and not true spatial positions. Our calculations are done within linear perturbation theory for both the metric and the source velocities but they can be used for nonlinear matter power spectra. We shall see that the complications due to the fact that we only observe on our background light cone, and that we do not truly know the distance of the observed galaxy but only its redshift, not only cause an additional difficulty, but provide even more a new opportunity for future galaxy surveys.

Gravitational wave production from bubble collisions was calculated in the early 1990s using numerical simulations. In this paper, we present an alternative analytic estimate, relying on a different treatment of stochasticity. In our approach, we provide a model for the bubble velocity power spectrum, suitable for both detonations and deflagrations. From this, we derive the anisotropic stress and analytically solve the gravitational wave equation. We provide analytical formulas for the peak frequency and the shape of the spectrum which we compare with numerical estimates. In contrast to the previous analysis, we do not work in the envelope approximation. This paper focuses on a particular source of gravitational waves from phase transitions. In a companion article, we will add together the different sources of gravitational wave signals from phase transitions: bubble collisions, turbulence and magnetic fields and discuss the prospects for probing the electroweak phase transition at LISA.