Cosmological parameter constraints from the CMB power spectra alone suffer several well-known degeneracies. These degeneracies can be broken by numerical artefacts and also a variety of physical effects that become quantitatively important with high-accuracy data e.g. from the Planck satellite. We study degeneracies in models with flat and non-flat spatial sections, non-trivial dark energy and massive neutrinos, and investigate the importance of various physical degeneracy-breaking effects. We test the camb power spectrum code for numerical accuracy, and demonstrate that the numerical calculations are accurate enough for degeneracies to be broken mainly by true physical effects (the integrated Sachs-Wolfe effect, CMB lensing and geometrical and other effects through recombination) rather than numerical artefacts. We quantify the impact of CMB lensing on the power spectra, which inevitably provides degeneracy-breaking information even without using information in the non-Gaussianity. Finally we check the numerical accuracy of sample-based parameter constraints using camb and CosmoMC. In an appendix we document recent changes to camb's numerical treatment of massive neutrino perturbations, which are tested along with other recent improvements by our degeneracy exploration results.

We investigate the prospects for constraining alternative theories of gravity with a typical nearterm low-budget 21 cm intensity mapping experiment. We derive the 21 cm brightness temperature perturbation consistently in linear theory including all line-of-sight and relativistic effects. We uncover new terms that are a small correction on large scales, analogous to those recently found in the context of galaxy surveys. We then perform a Fisher matrix analysis of the B0 parametrization of f (R) gravity, where B0 is proportional to the square of Compton wavelength of the scalaron. We find that our 21 cm survey, in combination with CMB information from Planck, will be able to place a 95% upper limit of 7 × 10 −5 on B0 in flat models with a ΛCDM expansion history, improving on current cosmological constraints by several orders of magnitude. We argue that this constraint is limited by our ability to model the mildly non-linear regime of structure formation in modified gravity. We also perform a model-independent principal component analysis on the free functions introduced into the field equations by modified gravity, µ and Σ. We find that 20-30 modes of the free functions will be 'well-constrained' by our combination of observables, the lower and upper limits dependent on the criteria used to define the 'goodness' of the constraint. These constraints are found to be robust to uncertainties in the time-dependence of the bias. Our analysis reveals that our observables are sensitive primarily to temporal variations in Σ and scale variations in µ. We argue that the inclusion of 21 cm intensity maps will significantly improve constraints on any cosmological deviations from General Relativity in large-scale structure in a very cost-effective manner.

PRISM (Polarized Radiation Imaging and Spectroscopy Mission) was proposed to ESA in May 2013 as a large-class mission for investigating within the framework of the ESA Cosmic Vision program a set of important scientific questions that require high resolution, high sensitivity, full-sky observations of the sky emission at wavelengths ranging from millimeter-wave to the far-infrared. PRISM's main objective is to explore the distant universe, probing cosmic history from very early times until now as well as the structures, distribution of matter, and velocity flows throughout our Hubble volume. PRISM will survey the full sky in a large number of frequency bands in both intensity and polarization and will measure the absolute spectrum of sky emission more than three orders of magnitude better than COBE FIRAS. The data obtained will allow us to precisely measure the absolute sky brightness and polarization of all the components of the sky emission in the observed frequency range, separating the primordial and extragalactic components cleanly from the galactic and zodiacal light emissions. The aim of this Extended White Paper is to provide a more detailed overview of the highlights of the new science that will be made possible by PRISM, which include: (1) the ultimate galaxy cluster survey using the Sunyaev-Zeldovich (SZ) effect, detecting approximately 106 clusters extending to large redshift, including a characterization of the gas temperature of the brightest ones (through the relativistic corrections to the classic SZ template) as well as a peculiar velocity survey using the kinetic SZ effect that comprises our entire Hubble volume; (2) a detailed characterization of the properties and evolution of dusty galaxies, where the most of the star formation in the universe took place, the faintest population of which constitute the diffuse CIB (Cosmic Infrared Background); (3) a characterization of the B modes from primordial gravity waves generated during inflation and from gravitational lensing, as well as the ultimate search for primordial non-Gaussianity using CMB polarization, which is less contaminated by foregrounds on small scales than the temperature anisotropies; (4) a search for distortions from a perfect blackbody spectrum, which include some nearly certain signals and others that are more speculative but more informative; and (5) a study of the role of the magnetic field in star formation and its interaction with other components of the interstellar medium of our Galaxy. These are but a few of the highlights presented here along with a description of the proposed instrument.

We have calculated the detectable merger rate of primordial black holes, as a function of the redshift, as well as the binary's mass ratio, total mass and chirp mass (observables that have not previously been explored in great detail for PBHs). We consider both the current and design sensitivity of LIGO and five different primordial black hole mass functions, as well as showing a comparison to a predicted astrophysical black hole merger rate. We show that the empirical preference for nearly equal-mass binaries in current LIGO/Virgo data can be consistent with a PBH hypothesis once observational selection effects are taken into account. However, current data do exclude some PBH mass distributions, and future data may be able to rule out the possibility that all observed BH mergers had a primordial origin.

Lensing of the CMB is an important effect, and is usually modelled by remapping the unlensed CMB fields by a lensing deflection. However the lensing deflections also change the photon path so that the emission angle is no longer orthogonal to the background last-scattering surface. We give the first calculation of the emissionangle corrections to the standard lensing approximation from dipole (Doppler) sources for temperature and quadrupole sources for temperature and polarization. We show that while the corrections are negligible for the temperature and E-mode polarization, additional large-scale B-modes are produced with a white spectrum that dominates those from post-Born field rotation (curl lensing). On large scales about one percent of the total lensing-induced B-mode amplitude is expected to be due to this effect. However, the photon emission angle does remain orthogonal to the perturbed last-scattering surface due to time delay, and half of the largescale emission-angle B modes cancel with B modes from time delay to give a total contribution of about half a percent. While not important for planned observations, the signal could ultimately limit the ability of delensing to reveal low amplitudes of primordial gravitational waves. We also derive the rotation of polarization due to multiple deflections between emission and observation. The rotation angle is of quadratic order in the deflection angle, and hence negligibly small: polarization typically rotates by less than an arcsecond, orders of magnitude less than a small-scale image rotates due to post-Born field rotation (which is quadratic in the shear). The field-rotation B modes dominate the other effects on small scales.

Posterior samples from each of the sources in the O1O2 source catalogue, indicated in each panel. We show samples in the plane of redshifted chirp mass Mz and mass ratio q, marginalised over the other source parameters. Samples have been thinned by a factor of 16 for visual clarity.

We demonstrate that the intrinsic alignment of galaxies with large-scale tidal fields sources an extra contribution to the recently-detected cross-correlation of galaxy shear and weak lensing of the microwave background. The extra term is the analogy of the 'GI' term in standard cosmic shear studies, and results in a reduction in the amplitude of the cross-correlation. We compute the intrinsic alignment contribution in linear and non-linear theory, and show that it can be at roughly the 15% level for the CFHT Stripe 82 redshift distribution, if the canonical amplitude of intrinsic alignments is assumed. The new term can therefore potentially reconcile the apparently low value of the measured cross-correlation with standard ΛCDM. We discuss various small-scale effects in the signal and the dependence on the source-redshift distribution. We discuss the exciting possibility of self-calibrating intrinsic alignments with a joint analysis of cosmic shear and weak lensing of the microwave background.

We investigate the possibility of constraining the dark energy equation of state by measuring the ratio of Einstein radii in a strong gravitational lens system with two source planes. This quantity is independent of the Hubble parameter and directly measures the growth of angular diameter distances as a function of redshift. We investigate the prospects for a single doublesource plane system and for a forecast population of systems discovered by re-observing a population of single-source lenses already known from a photometrically selected catalogue such as Cambridge and Sloan survey of wide arcs in the sky or from a spectroscopically selected catalogue such as Sloan Lens ACS survey. We find that constraints comparable to current data sets (σ (w) ∼ 15 per cent) are possible with a handful of double-source plane systems. We also find that the method's degeneracy between M and w is almost orthogonal to that of cosmic microwave background and Baryon Acoustic Oscillations measurements, making this method highly complimentary to current probes.