Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification. II - Derivation

Abstract

We present a derivation of the cosmological distance-redshift relation up to second order in perturbation theory. In addition, we find the observed redshift and the lensing magnification to second order. We do not require that the density contrast is small, we only that the metric potentials and peculiar velocities are small. Thus our results apply into the nonlinear regime, and can be used for most dark energy models. We present the results in a form which can be readily computed in an N-body simulation. This paper accompanies arXiv:1207.2109, where the key results are summarised in a physically transparent form and applications are discussed.

25 pages, 1 figure. v2 has presentational changes and minor corrections. To appear in CQG

References in corpus (11)

• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• xPert: Computer algebra for metric perturbation theory
• The value of H_0 in the inhomogeneous Universe
• Do stochastic inhomogeneities affect dark-energy precision measurements?
• Anti-lensing: the bright side of voids
• Cosmology with Doppler Lensing
• Vector modes generated by primordial density fluctuations
• Vector and Tensor Contributions to the Luminosity Distance
• Late time anisotropy as an imprint of cosmological backreaction
• Brane Inflation After WMAP Three Year Results

Cited by in corpus (44)

• Galaxy number counts to second order and their bispectrum
• On the Bias of the Distance-Redshift Relation from Gravitational Lensing
• How does the cosmic large-scale structure bias the Hubble diagram?
• Do we care about the distance to the CMB? Clarifying the impact of second-order lensing
• Safely smoothing spacetime: backreaction in relativistic cosmological simulations
• A new approach to the propagation of light-like signals in perturbed cosmological backgrounds
• Gauge-Invariance and Infrared Divergences in the Luminosity Distance
• Does small scale structure significantly affect cosmological dynamics?
• Cosmological ensemble and directional averages of observables
• Unified Treatment of the Luminosity Distance in Cosmology
• Light propagation in inhomogeneous and anisotropic cosmologies
• Non-linear general relativistic effects in the observed redshift
• The theory of stochastic cosmological lensing
• General and consistent statistics for cosmological observations
• Lensing convergence in galaxy clustering in LambdaCDM and beyond
• General relativistic corrections and non-Gaussianity in large scale structure
• Relativistic cosmological large scale structures at one-loop
• Nonlinear modulation of the HI power spectrum on ultra-large scales. I
• Cosmic variance of $H_0$ in light of forthcoming high-redshift surveys
• Second-order gauge-invariant formalism for the cosmological observables: Complete verification of their gauge-invariance
• Towards detection of relativistic effects in galaxy number counts using kSZ Tomography
• Scalar perturbations in cosmological models with dark energy - dark matter interaction
• On the relationship between mean observations, spatial averages and the Dyer-Roeder approximation in Einstein-Straus models
• Imprint of non-linear effects on HI intensity mapping on large scales
• Tetrad formalism for exact cosmological observables
• Testing the equivalence principle on cosmological scales using the odd multipoles of galaxy cross-power spectrum and bispectrum
• The skewness of the distance-redshift relation in $\Lambda$CDM
• The halo bias for number counts on the light cone from relativistic N-body simulations
• Consequences of using a smooth cosmic distance in a lumpy universe: I
• Galaxy number counts at second order: an independent approach
• Full-sky weak lensing: a nonlinear post-Friedmann treatment
• Hubble flow variations as a test for inhomogeneous cosmology
• Non-perturbative results for the luminosity and area distances
• The art of building a smooth cosmic distance ladder in a perturbed universe
• Accurately computing weak lensing convergence
• Emergence of smooth distance and apparent magnitude in a lumpy Universe
• Perturbative treatment of the luminosity distance
• 1+1+2 covariant formulation of light propagation in spacetime
• Cosmological Simulations of Number Counts
• Precision Cosmology and Hubble tension in the era of LSS surveys
• The Cosmological Consistency Relation in a Universe with Structure
• A Light-Cone Approach to Higher-Order Cosmological Observables
• How Dark is Dark Energy? A Lightcones Comparison Approach
• Galaxy number counts at second order in perturbation theory: a leading-order term comparison