Camille Bonvin

What galaxy surveys really measure

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 observer velocities but they can be used for non-linear matter power spectra. We shall see that the complications due to the fact that we only observe on our background lightcone and that we do not truly know the distance of the observed galaxy, but only its redshift is not only an additional difficulty, but even more a new opportunity for future galaxy surveys.

Can primordial magnetic fields be the origin of the BICEP2 data

If the B-mode signal in the cosmic microwave background polarization seen by the BICEP2 experiment is confirmed, it has dramatic implications for models of inflation. The result is also in tension with Planck limits on standard inflationary models. It is, therefore, important to investigate whether this signal can arise from alternative sources. If so, this could lessen the pressure on inflationary models and the tension with Planck data. We investigate whether vector and tensor modes from primordial magnetic fields can explain the signal. We find that, in principle, magnetic fields generated during inflation can indeed produce the required B mode, for a suitable range of energy scales of inflation. In this case, the primordial gravitational wave amplitude is negligible, so that there is no tension with Planck and no problems posed for current inflationary models. However, the simplest magnetic model is in tension with Planck limits on non-Gaussianity in the trispectrum. It may be possible to fine tune the magnetogenesis model so that this non-Gaussianity is suppressed. Alternatively, a weaker magnetic field can pass the non-Gaussianity constraints and allow the primordial tensor mode to be reduced to r ≃ 0.09, thus removing the tension with Planck data and alleviating the problems with simple inflationary models.

Asymmetric galaxy correlation functions

We study the two-point cross-correlation function between two populations of galaxies: for instance a bright population and a faint population. We show that this cross-correlation is asymmetric under the exchange of the line-of-sight coordinate of the galaxies, i.e. that the correlation is different if the bright galaxy is in front of, or behind, the faint galaxy. We give an intuitive, quasi-Newtonian derivation of all the effects that contribute to such an asymmetry in large-scale structure: gravitational redshift, Doppler shift, lensing, light-cone, evolution and Alcock-Paczynski effects – interestingly, the gravitational redshift term is exactly canceled by some of the others, assuming geodesic motion. Most of these effects are captured by previous calculations of general relativistic corrections to the observed galaxy density fluctuation; the asymmetry arises from terms that are suppressed by the ratio (H/k) – H is the Hubble constant and k is the wavenumber – which are more readily observable than the terms suppressed by (H/k) 2 . Some of the contributions to the asymmetry, however, arise from terms that are generally considered ’Newtonian’ – the lensing and evolution – and thus represent a contaminant in the search for general relativistic corrections. We propose methods to disentangle these different contributions. A simple method reduces the contamination to a level of ∼ < 10% for redshifts z ∼ < 1. We also clarify the relation to recent work

Magnetic fields from inflation: the transition to the radiation era

We compute the contribution to the scalar metric perturbations from large-scale magnetic fields which are generated during inflation. We show that apart from the usual passive and compensated modes, the magnetic fields also contribute to the constant mode from inflation. This is different from the causal (post inflationary) generation of magnetic fields where such a mode is absent and it might lead to significant, non-Gaussian CMB anisotropies.

Cosmic shear bispectrum from second-order perturbations in General Relativity

Future lensing surveys will be nearly full-sky and reach an unprecedented depth, probing scales closer and closer to the Hubble radius. This motivates the study of the cosmic shear beyond the small-angle approximation and including general relativistic corrections that are usually suppressed on sub-Hubble scales. The complete expression of the reduced cosmic shear at second order including all relativistic effects was derived in [1]. In the present paper we compute the resulting cosmic shear bispectrum when all these effects are properly taken into account and we compare it to primordial non-Gaussianity of the local type. The new general relativistic effects are generically smaller than the standard non-linear couplings. However, their relative importance increases at small multipoles and for small redshifts of the sources. The dominant effect among these non standard corrections is due to the inhomogeneity of the source redshift. In the squeezed limit, its amplitude can become of the order of the standard couplings when the redshift of the sources is below 0.5. Moreover, while the standard non-linear couplings depend on the angle between the short and long mode, the relativistic corrections do not and overlap almost totally with local type non-Gaussianity. We find that they can contaminate the search for a primordial local signal by f_NL>10.

Do we care about the distance to the CMB?:clarifying the impact of second-order lensing

It has recently been shown that second-order corrections to the background distance-redshift relation can build up significantly at large redshifts, due to an aggregation of gravitational lensing events. This shifts the expectation value of the distance to the CMB by 1%. In this paper we show that this shift is already properly accounted for in standard CMB analyses. We clarify the role that the area distance to the CMB plays in the presence of second-order lensing corrections.

Measurement of the dipole in the cross-correlation function of galaxies

It is usually assumed that in the linear regime the two-point correlation function of galaxies contains only a monopole, quadrupole and hexadecapole. Looking at cross-correlations between different populations of galaxies, this turns out not to be the case. In particular, the cross-correlations between a bright and a faint population of galaxies contain also a dipole. In this paper we present the first attempt to measure this dipole. We discuss the four types of effects that contribute to the dipole: relativistic distortions, evolution effect, wide-angle effect and large-angle effect. We show that the first three contributions are intrinsic anti-symmetric contributions that do not depend on the choice of angle used to measure the dipole. On the other hand the large-angle effect appears only if the angle chosen to extract the dipole breaks the symmetry of the problem. We show that the relativistic distortions, the evolution effect and the wide-angle effect are too small to be detected in the LOWz and CMASS sample of the BOSS survey. On the other hand with a specific combination of angles we are able to measure the large-angle effect with high significance. We emphasise that this large-angle dipole does not contain new physical information, since it is just a geometrical combination of the monopole and the quadrupole. However this measurement, which is in excellent agreement with theoretical predictions, validates our method for extracting the dipole from the two-point correlation function and it opens the way to the detection of relativistic effects in future surveys like e.g. DESI.

A ROBUST MEASURE OF COSMIC STRUCTURE BEYOND THE POWER SPECTRUM: COSMIC FILAMENTS AND THE TEMPERATURE OF DARK MATTER

We discover that the mass of dark matter particles m DM is imprinted in phase correlations of the cosmic density field more significantly than in the two-point correlation. In particular, phase correlations trace m DM out to scales about five times larger than the two-point correlation. This result relies on a new estimator ?(r) of pure phase information in Fourier space, which can be interpreted as a parameter-free and scale-invariant tracer of filament-like structure. Based on simulated density fields, we show how m DM can, in principle, be measured using ?(r), given a suitably reconstructed density field.

Optimising the measurement of relativistic distortions in large-scale structure

It has been shown recently that relativistic distortions generate a dipolar modulation in the two-point correlation function of galaxies. To measure this relativistic dipole it is necessary to cross-correlate different populations of galaxies with for example different luminosities or colours. In this paper, we construct an optimal estimator to measure the dipole with multiple populations. We show that this estimator increases the signal-to-noise of the dipole by up to 35 percent. Using 6 populations of galaxies, in a survey with halos and number densities similar to those of the millennium simulation, we forecast a cumulative signal-to-noise of 4.4. For the main galaxy sample of SDSS at low redshift z<0.2 our optimal estimator predicts a cumulative signal-to-noise of 2.4. Finally we forecast a cumulative signal-to-noise of 7.4 in the upcoming DESI survey. These forecasts indicate that with the appropriate choice of estimator the relativistic dipole should be detectable in current and future surveys.

Cosmological ensemble and directional averages of observables

We show that at second order, ensemble averages of observables and directional averages do not commute due to gravitational lensing -- observing the same thing in many directions over the sky is not the same as taking an ensemble average. In principle this non-commutativity is significant for a variety of quantities that we often use as observables and can lead to a bias in parameter estimation. We derive the relation between the ensemble average and the directional average of an observable, at second order in perturbation theory. We discuss the relevance of these two types of averages for making predictions of cosmological observables, focusing on observables related to distances and magnitudes. In particular, we show that the ensemble average of the distance in a given observed direction is increased by gravitational lensing, whereas the directional average of the distance is decreased. For a generic observable, there exists a particular function of the observable that is not affected by second-order lensing perturbations. We also show that standard areas have an advantage over standard rulers, and we discuss the subtleties involved in averaging in the case of supernova observations.