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Register a new userJacobi Mapping Approach for a Precise Cosmological Weak Lensing Formalism
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Cosmological weak lensing has been a highly successful and rapidly developing research field since the first detection of cosmic shear in 2000. However, it has recently been pointed out in Yoo et al. that the standard weak lensing formalism yields gauge-dependent results and, hence, does not meet the level of accuracy demanded by the next generation of weak lensing surveys. Here, we show that the Jacobi mapping formalism provides a solid alternative to the standard formalism, as it accurately describes all the relativistic effects contributing to the weak lensing observables. We calculate gauge-invariant expressions for the distortion in the luminosity distance, the cosmic shear components and the lensing rotation to linear order including scalar, vector and tensor perturbations. In particular, the Jacobi mapping formalism proves that the rotation is fully vanishing to linear order. Furthermore, the cosmic shear components contain an additional term in tensor modes which is absent in the results obtained with the standard formalism. Our work provides further support and confirmation of the gauge-invariant lensing formalism needed in the era of precision cosmology.
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We show how LIGO is expected to detect coalescing binary black holes at $z>1$, that are lensed by the intervening galaxy population. Gravitational magnification, $mu$, strengthens gravitational wave signals by $sqrt{mu}$, without altering their frequencies, which if unrecognised leads to an underestimate of the event redshift and hence an overestimate of the binary mass. High magnifications can be reached for coalescing binaries because the region of intense gravitational wave emission during coalescence is so small ($sim$100km), permitting very close projections between lensing caustics and gravitational-wave events. Our simulations incorporate accurate waveforms convolved with the LIGO power spectral density. Importantly, we include the detection dependence on sky position and orbital orientation, which for the LIGO configuration translates into a wide spread in observed redshifts and chirp masses. Currently we estimate a detectable rate of lensed events rateEarly{}, that rises to rateDesign{}, at LIGOs design sensitivity limit, depending on the high redshift rate of black hole coalescence.
In the next decades, the gravitational-wave (GW) standard siren observations and the neutral hydrogen 21 cm intensity mapping (IM) surveys, as two promising non-optical cosmological probes, will play an important role in precisely measuring cosmological parameters. In this work, we make a forecast for cosmological parameter estimation with the synergy between the GW standard siren observations and the 21 cm IM surveys. We choose the Einstein Telescope (ET) and the Taiji observatory as the representatives of the GW detection projects and choose the Square Kilometre Array (SKA) phase I mid-frequency array as the representative of the 21 cm IM experiments. We find that the synergy of the GW standard siren observations and the 21 cm IM surveys could break the cosmological parameter degeneracies. The joint ET+Taiji+SKA data give $sigma(H_0)=0.28 {rm km s^{-1} Mpc^{-1}}$ in the $Lambda$CDM model, $sigma(w)=0.028$ in the $w$CDM model, which are better than the results of $Planck$+BAO+SNe, and $sigma(w_0)=0.077$ and $sigma(w_a)=0.295$ in the CPL model, which are comparable with the results of $Planck$+BAO+SNe. In the $Lambda$CDM model, the constraint accuracies of $H_0$ and $Omega_{rm m}$ are less than or rather close to 1%, indicating that the magnificent prospects for non-optical precision cosmology are worth expecting.
We introduce the skew-spectrum statistic for weak lensing convergence $kappa$ maps and test it against state-of-the-art high-resolution all-sky numerical simulations. We perform the analysis as a function of source redshift and smoothing angular scale for individual tomographic bins. We also analyse the cross-correlation between different tomographic bins. We compare the numerical results to fitting-functions used to model the bispectrum of the underlying density field as a function of redshift and scale. We derive a closed form expression for the skew-spectrum for gravity-induced secondary non-Gaussianity. We also compute the skew-spectrum for the projected $kappa$ inferred from Cosmic Microwave Background (CMB) studies. As opposed to the low redshift case we find the post-Born corrections to be important in the modelling of the skew-spectrum for such studies. We show how the presence of a mask and noise can be incorporated in the estimation of a skew-spectrum.
In this manuscript of the habilitation `a diriger des recherches (HDR), the author presents some of his work over the last ten years. The main topic of this thesis is cosmic shear, the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure. I review the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then I give an overview of weak-lensing measurements, and present observational results from the Canada-France Hawaii Lensing Survey (CFHTLenS), as well as the implications for cosmology. I conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations.
We present a full-sky derivation of weak lensing observables in the Post-Friedmann (PF) formalism. Weak lensing has the characteristic of mixing small scales and large scales since it is affected by inhomogeneities integrated along the photon trajectory. With the PF formalism, we develop a modelling of lensing observables which encompasses both leading order relativistic effects and effects that are due to the fully non-linear matter distribution at small scales. We derive the reduced shear, convergence and rotation up to order $1/c^4$ in the PF approximation, accounting for scalar, vector and tensor perturbations, as well as galaxies peculiar velocities. We discuss the various contributions that break the Kaiser-Squires relation between the shear and the convergence at different orders. We pay particular attention to the impact of the frame-dragging vector potential on lensing observables and we discuss potential ways to measure this effect in future lensing surveys.
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