arXiv subjects

Ruth Durrer

Publications and source records attributed to Ruth Durrer.

At least 73 records · Page 4Linked to original sources

arXiv2018

Safely smoothing spacetime: backreaction in relativistic cosmological simulations

A persistent theme in the study of dark energy is the question of whether it really exists or not. It is often claimed hat we are mis-calculating the cosmological model by neglecting the effects associated with averaging over large-scale structures. In the Newtonian approximation this is clear: there is no effect. Within the full relativistic picture this remains an important open question however, owing to the complex mathematics involved. We study this issue using particle numerical simulations which account for all relevant relativistic effects without any problems from shell crossing. In this context we show for the first time that the backreaction from structure can differ by many orders of magnitude depending upon the slicing of spacetime one chooses to average over. In the worst case, where smoothing is carried out in synchronous spatial surfaces, the corrections can reach ten percent and more. However, when smoothing on the constant time hypersurface of the Newtonian gauge, backreaction contributions remain 3-5 orders of magnitude smaller.

astro-ph.CO↗

arXiv2018

Polarization of a stochastic gravitational wave background through diffusion by massive structures

The geometric optics approximation traditionally used to study the propagation of gravitational waves on a curved background, breaks down in the vicinity of compact and extended astrophysical objects, where wave-like effects like diffusion and generation of polarization occur. We provide a framework to study the generation of polarization of a stochastic background of gravitational waves propagating in an inhomogeneous universe. The framework is general and can be applied to both cosmological and astrophysical gravitational wave backgrounds in any frequency range. We derive an order of magnitude estimate of the amount of polarization generated for cosmological and astrophysical backgrounds, in the frequency range covered by present and planned gravitational wave experiments. For an astrophysical background in the PTA and LISA band, the amount of polarization generated is suppressed by a factor $10^{-4}$ $(10^{-5})$ with respect to anisotropies. For a cosmological background we get an additional $10^{-2}$ suppression. We speculate on using our approach to map the distribution of (unresolvable) structures in the Universe.

astro-ph.CO↗

arXiv2018

The Generation of Vorticity in Cosmological N-body Simulations

Clustering of a perfect fluid does not lead to the generation of vorticity. It is the collisionless nature of dark matter, inducing velocity dispersion and shell crossing, which is at the origin of cosmological vorticity generation. In this paper we investigate the generation of vorticity during the formation of cosmological large scale structure using the public relativistic N-body code $\textit{gevolution}$. We test several methods to compute the vorticity power spectrum and we study its convergence with respect to the mass and grid resolution of our simulations. We determine the power spectrum, the spectral index on large-scales, the amplitude of the peak position and their time evolution. We also compare the vorticity extracted from our simulations with the vector perturbations of the metric. Our results are accompanied by resolution studies and compared with previous studies in the literature.

astro-ph.CO↗

arXiv2018

Statistical Properties of Scale-Invariant Helical Magnetic Fields and Applications to Cosmology

We investigate the statistical properties of isotropic, stochastic, Gaussian distributed, helical magnetic fields characterized by different shapes of the energy spectra at large length scales and study the associated realizability condition. We discuss smoothed magnetic fields that are commonly used when the primordial magnetic field is constrained by observational data. We are particularly interested in scale-invariant magnetic fields that can be generated during the inflationary stage by quantum fluctuations. We determine the correlation length of such magnetic fields and relate it to the infrared cutoff of perturbations produced during inflation. We show that this scale determines the observational signatures of the inflationary magnetic fields on the cosmic microwave background. At smaller scales, the scale-invariant spectrum changes with time. It becomes a steeper weak-turbulence spectrum at progressively larger scales. We show numerically that the critical length scale where this happens is the turbulent-diffusive scale, which increases with the square root of time.

astro-ph.CO↗

arXiv2018

Intensity mapping of the 21cm emission: lensing

In this paper, we study lensing of 21cm intensity mapping (IM). Like in the cosmic microwave background (CMB), there is no first order lensing in intensity mapping. The first effects in the power spectrum are therefore of second and third order. Despite this, lensing of the CMB power spectrum is an important effect that needs to be taken into account, which motivates the study of the impact of lensing on the IM power spectrum. We derive a general formula up to third order in perturbation theory including all the terms with two derivatives of the gravitational potential, i.e. the dominant terms on sub-Hubble scales. We then show that in intensity mapping there is a new lensing term which is not present in the CMB. We obtain that the signal-to-noise of 21 cm lensing for futuristic surveys like SKA2 is about 10. We find that surveys probing only large scales, lmax < 700, can safely neglect the lensing of the intensity mapping power spectrum, but that otherwise this effect should be included.

astro-ph.CO↗

arXiv2018

CMB-lensing beyond the leading order: temperature and polarization anisotropies

We investigate the weak lensing corrections to the CMB temperature and polarization anisotropies. We consider all the effects beyond the leading order: post-Born corrections, LSS corrections and, for the polarization anisotropies, the correction due to the rotation of the polarization direction between the emission at the source and the detection at the observer. We show that the full next-to-leading order correction to the B-mode polarization is not negligible on small scales and is dominated by the contribution from the rotation, this is a new effect not taken in account in previous works. Considering vanishing primordial gravitational waves, the B-mode correction due to rotation is comparable to cosmic variance for $\ell \gtrsim 3500$, in contrast to all other spectra where the corrections are always below that threshold for a single multipole. Moreover, the sum of all the effects is larger than cosmic variance at high multipoles, showing that higher-order lensing corrections to B-mode polarization are in principle detectable.

astro-ph.CO↗

arXiv2018

Redshift-space distortions from vector perturbations II: Anisotropic signal

We study the impact on the galaxy correlation function of the presence of a vector component in the tracers' peculiar velocities, in the case in which statistical isotropy is violated. We present a general framework - based on the bipolar spherical harmonics expansion - to study this effect in a model independent way, without any hypothesis on the origin or the properties of these vector modes. We construct six new observables, that can be directly measured in galaxy catalogs in addition to the standard monopole, quadrupole and hexadecapole, and we show that they completely describe any deviations from isotropy. We then perform a Fisher analysis in order to quantify the constraining power of future galaxy surveys. As an example, we show that the SKA2 would be able to detect anisotropic rotational velocities with amplitudes as low as 1% of that of the vorticity generated during shell-crossing in standard dark matter scenarios.

astro-ph.CO↗

arXiv2018

COFFE: a code for the full-sky relativistic galaxy correlation function

We present a public version of the code COFFE (COrrelation Function Full-sky Estimator) available at https://github.com/JCGoran/coffe. The code computes the galaxy two-point correlation function and its multipoles in linear perturbation theory, including all relativistic and wide angle corrections. COFFE also calculates the covariance matrix for two physically relevant estimators of the correlation function multipoles. We illustrate the usefulness of our code by a simple but relevant example: a forecast of the detectability of the lensing signal in the multipoles of the two-point function. In particular, we show that lensing should be detectable in the multipoles of the two-point function, with a signal-to-noise larger than 10, in future surveys like Euclid or the SKA.

astro-ph.CO↗

arXiv2018

Note on the Kaiser-Peacock paper regarding gravitational lensing effects

This paper revisits the controversy concerning whether gravitational lensing effects make a significant difference to estimation of distance to the Cosmic Microwave Background last scattering surface in cosmology. A recent paper by Kaiser and Peacock supports a previous paper by Weinberg stating that such affects average to zero because of energy conservation. In this note, problems are pointed out in the Kaiser and Peacock analysis related to their choice of endpoint of integration, and to the `wrinkly surface' argument.

gr-qc↗

arXiv2018

General Relativistic corrections in density-shear correlations

We investigate the corrections which relativistic light-cone computations induce on the correlation of the tangential shear with galaxy number counts, also known as galaxy-galaxy lensing. The standard-approach to galaxy-galaxy lensing treats the number density of sources in a foreground bin as observable, whereas it is in reality unobservable due to the presence of relativistic corrections. We find that already in the redshift range covered by the DES first year data, these currently neglected relativistic terms lead to a systematic correction of up to 50% in the density-shear correlation function for the highest redshift bins. This correction is dominated by the the fact that a redshift bin of number counts does not only lens sources in a background bin, but is itself again lensed by all masses between the observer and the counted source population. Relativistic corrections are currently ignored in the standard galaxy-galaxy analyses, and the additional lensing of a counted source populations is only included in the error budget (via the covariance matrix). At increasingly higher redshifts and larger scales, these relativistic and lensing corrections become however increasingly more important, and we here argue that it is then more efficient, and also cleaner, to account for these corrections in the density-shear correlations.

astro-ph.CO↗

arXiv2018

The full-sky relativistic correlation function and power spectrum of galaxy number counts: I. Theoretical aspects

We derive an exact expression for the correlation function in redshift shells including all the relativistic contributions. This expression, which does not rely on the distant-observer or flat-sky approximation, is valid at all scales and includes both local relativistic corrections and integrated contributions, like gravitational lensing. We present two methods to calculate this correlation function, one which makes use of the angular power spectrum C_ell(z1,z2) and a second method which evades the costly calculations of the angular power spectra. The correlation function is then used to define the power spectrum as its Fourier transform. In this work theoretical aspects of this procedure are presented, together with quantitative examples. In particular, we show that gravitational lensing modifies the multipoles of the correlation function and of the power spectrum by a few percent at redshift z=1 and by up to 30% and more at z=2. We also point out that large-scale relativistic effects and wide-angle corrections generate contributions of the same order of magnitude and have consequently to be treated in conjunction. These corrections are particularly important at small redshift, z=0.1, where they can reach 10%. This means in particular that a flat-sky treatment of relativistic effects, using for example the power spectrum, is not consistent.

astro-ph.CO↗

arXiv2017

Redshift-space distortions from vector perturbations

We compute a general expression for the contribution of vector perturbations to the redshift-space distortion of galaxy surveys. We show that they contribute to the same multipoles of the correlation function as scalar perturbations and should thus in principle be taken into account in data analysis. We derive constraints for next-generation surveys on the amplitude of two sources of vector perturbations, namely non-linear clustering and topological defects. While topological defects leave a very small imprint on redshift-space distortions, we show that the multipoles of the correlation function are sensitive to vorticity induced by non-linear clustering. Therefore future redshift surveys such as DESI or the SKA should be capable of measuring such vector modes, especially with the hexadecapole which appears to be the most sensitive to the presence of vorticity.

astro-ph.CO↗

arXiv2017

Scale-invariant helical magnetic field evolution and the duration of inflation

We consider a scale-invariant helical magnetic field generated during inflation. We show that, if the mean magnetic helicity density of such a field is measured, it can be used to determine a lower bound on the duration of inflation. Upper bounds can be used to derive constraints on the minimal duration of inflation if one assumes that the magnetic field generated during inflation is helical. Using three-dimensional simulations, we show that an initially scale-invariant field develops, which is similar both with and without magnetic helicity. In the fully helical case, however, the magnetic field appears to have a more pronounced folded structure.

astro-ph.CO↗

arXiv2017

Relativistic N-body simulations with massive neutrinos

Some of the dark matter in the Universe is made up of massive neutrinos. Their impact on the formation of large scale structure can be used to determine their absolute mass scale from cosmology, but to this end accurate numerical simulations have to be developed. Due to their relativistic nature, neutrinos pose additional challenges when one tries to include them in N-body simulations that are traditionally based on Newtonian physics. Here we present the first numerical study of massive neutrinos that uses a fully relativistic approach. Our N-body code, gevolution, is based on a weak-field formulation of general relativity that naturally provides a self-consistent framework for relativistic particle species. This allows us to model neutrinos from first principles, without invoking any ad-hoc recipes. Our simulation suite comprises some of the largest neutrino simulations performed to date. We study the effect of massive neutrinos on the nonlinear power spectra and the halo mass function, focusing on the interesting mass range between 0.06 eV and 0.3 eV and including a case for an inverted mass hierarchy.

astro-ph.CO↗

arXiv2017

Gauge-Transformation Properties of Cosmological Observables and its Application to the Light-Cone Average

Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems. This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their theoretical description is verified by checking its gauge-invariance. We argue that cosmological observables are invariant scalars under diffeomorphisms and as a consequence their theoretical description is gauge-invariant, only at linear order in perturbations. Beyond linear order, they are usually not gauge-invariant, and we provide the general law for the gauge-transformation that the perturbation part of an observable does obey. We apply this finding to derive the second-order expression for the observational light-cone average in cosmology and demonstrate that our expression is indeed invariant under diffeomorphisms.

astro-ph.CO↗

arXiv2017

Impact of next-to-leading order contributions to CMB lensing

In this Letter we study the impact on cosmological parameter estimation, from present and future surveys, due to lensing corrections on CMB temperature and polarization anisotropies beyond leading order. In particular, we show how post-Born corrections, LSS effects and the correction due to the change in the polarization direction between the emission at the source and the detection at the observer, are non-negligible in the determination of the polarization spectra. They have to be taken into account for an accurate estimation of cosmological parameters sensitive to or even based on these spectra. We study in detail the impact of higher order lensing on the determination of the tensor-to-scalar ratio $r$ and on the estimation of the effective number of relativistic species $N_\text{eff}$. We find that neglecting higher order lensing terms can lead to misinterpreting these corrections as a primordial tensor-to-scalar ratio of about $\mathcal{O}(10^{-3})$. Furthermore, it leads to a shift of the parameter $N_\text{eff}$ by nearly two sigma considering the level of accuracy aimed by future S4 surveys.

astro-ph.CO↗

arXiv2017

Vorticity generation in the Universe: A perturbative approach

We compute the generation of vorticity from velocity dispersion in the dark matter fluid. For dark matter at zero temperature Helmholtz's theorem dictates that no vorticity is generated and we therefore allow the dark matter fluid to have a non-vanishing velocity dispersion. This implies a modification to the usual hydrodynamical system (continuity and Euler equations): we have to consider the Boltzmann hierarchy up to the second moment. This means that the Euler equation is modified with a source term that describes the effect of non-zero velocity dispersion. We write an equation for the Eulerian vorticity in Lagrangian coordinates and show that it has a growing mode already at second order in perturbation theory. We compute the power spectrum of the vorticity and the rotational velocity at second order in perturbation theory.

astro-ph.CO↗

arXiv2017

Higher order relativistic galaxy number counts: dominating terms

We review the number counts to second order concentrating on the terms which dominate on sub horizon scales. We re-derive the result for these terms and compare it with the different versions found in the literature. We generalize our derivation to higher order terms, especially the third order number counts which are needed to compute the 1-loop contribution to the power spectrum.

astro-ph.CO↗