117 research outputs found
Propagating photo- uncertainties: a functional derivative approach
Photometric redshifts are a key ingredient in the analysis and interpretation
of large-scale structure (LSS) surveys. The accuracy and precision of these
redshift estimates are directly linked to the constraining power of photometric
surveys. It is hence necessary to define precision and accuracy requirements
for the redshift calibration \revision{to not} infer biased results in the
final analysis. For weak gravitational lensing of the LSS, the photometry
culminates in the estimation of the source redshift distribution (SRD) in each
of the tomographic bins used in the analysis. The focus has been on shifts of
the mean of the SRDs and how well the calibration must be able to recover
those. Since the estimated SRDs are usually given as a normalized histogram
with corresponding errors, it would be advantageous to propagate these
uncertainties accordingly to see whether the requirements of the given survey
are indeed fulfilled. Here we propose the use of functional derivatives to
calculate the sensitivity of the final observables, e.g. the lensing angular
power spectrum, with respect to the SRD at a specific redshift. This allows the
propagation of arbitrarily shaped small perturbations to the SRD, without
having to run the whole analysis pipeline for each realization again. We apply
our method to an EUCLID survey and demonstrate it with SRDs of the KV450 data
set, recovering previous results. Lastly, we note that the moments of the SRD
of order larger than two will probably not be relevant when propagating
redshift uncertainties in cosmic shear analysis.Comment: 10 pages, 9 figures, matches accepted version in MNRA
Shear and vorticity in the spherical collapse of dark matter haloes
Traditionally the spherical collapse of objects is studied with respect to a
uniform background density, yielding the critical over-density
as key ingredient to the mass function of virialized
objects. Here we investigate the shear and rotation acting on a peak in a
Gaussian random field. By assuming that collapsing objects mainly form at those
peaks, we use this shear and rotation as external effects changing the dynamics
of the spherical collapse, which is described by the Raychaudhuri equation. We
therefore assume that the shear and rotation have no additional dynamics on top
of their cosmological evolution and thus only appear as inhomogeneities in the
differential equation.Comment: 8 pages, 5 figures, MNRAS accepte
Cosmological Covariance of Fast Radio Burst Dispersions
The dispersion of fast radio bursts (FRBs) is a measure of the large-scale
electron distribution. It enables measurements of cosmological parameters,
especially of the expansion rate and the cosmic baryon fraction. The number of
events is expected to increase dramatically over the coming years, and of
particular interest are bursts with identified host galaxy and therefore
redshift information.
In this paper, we explore the covariance matrix of the dispersion measure
(DM) of FRBs induced by the large-scale structure, as bursts from a similar
direction on the sky are correlated by long wavelength modes of the electron
distribution. We derive analytical expressions for the covariance matrix and
examine the impact on parameter estimation from the FRB dispersion measure -
redshift relation. The covariance also contains additional information that is
missed by analysing the events individually. For future samples containing over
FRBs with host identification over the full sky, the covariance needs
to be taken into account for unbiased inference, and the effect increases
dramatically for smaller patches of the sky. Also forecasts must consider these
effects as they would yield too optimistic parameter constraints. Our procedure
can also be applied to the DM of the afterglow of Gamma Ray Bursts.Comment: 8 pages, 5 figures, accepted by MNRAS, matches final submitted
versio
Consistent Constraints on the Equivalence Principle from localised Fast Radio Bursts
Fast Radio Bursts (FRBs) are short astrophysical transients of extragalactic
origin. Their burst signal is dispersed by the free electrons in the
large-scale-structure (LSS), leading to delayed arrival times at different
frequencies. Another potential source of time delay is the well known Shapiro
delay, which measures the space-space and time-time metric perturbations along
the line-of-sight. If photons of different frequencies follow different
trajectories, i.e. if the universality of free fall guaranteed by the weak
equivalence principle (WEP) is violated, they would experience an additional
relative delay. This quantity, however, is not an observable on the background
level as it is not gauge independent, which has led to confusion in previous
papers. Instead, an imprint can be seen in the correlation between the time
delays of different pulses. In this paper, we derive robust and consistent
constraints from twelve localised FRBs on the violation of the WEP in the
energy range between 4.6 and 6 meV. In contrast to a number of previous
studies, we consider our signal to be not in the model, but in the covariance
matrix of the likelihood. To do so, we calculate the covariance of the time
delays induced by the free electrons in the LSS, the WEP breaking terms, the
Milky Way and host galaxy. By marginalising over both host galaxy contribution
and the contribution from the free electrons, we find that the parametrised
post-Newtonian parameter characterising the WEP violation must be
constant in this energy range to 1 in at 68 confidence. These
are the tightest constraints to-date on in this low energy
range.Comment: 8 pages, 4 figures, accepted by MNRAS, matches final submitte
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