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Register a new userThe effects of structure anisotropy on lensing observables in an exact general relativistic setting for precision cosmology
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The study of relativistic, higher order and nonlinear effects has become necessary in recent years in the pursuit of precision cosmology. We develop and apply here a framework to study gravitational lensing in exact models in general relativity that are not restricted to homogeneity and isotropy, and where full nonlinearity and relativistic effects are included. We apply the framework to a specific, anisotropic galaxy cluster model which is based on a modified NFW halo density profile and described by the Szekeres metric. We examine the effects of increasing levels of anisotropy in the galaxy cluster on lensing observables like the convergence and shear for various lensing geometries, finding a strong nonlinear response in both the convergence and shear for rays passing through anisotropic regions of the cluster. Deviation from the expected values in a spherically symmetric structure are asymmetric with respect to path direction and thus will persist as a statistical effect when averaged over some ensemble of such clusters. The resulting relative difference in various geometries can be as large as approximately 2%, 8%, and 24% in the measure of convergence for levels of anisotropy of 5%, 10%, and 15%, respectively, as a fraction of total cluster mass. For the total magnitude of shear, the relative difference can grow near the center of the structure to be as large as 15%, 32%, and 44% for the same levels of anisotropy, averaged over the two extreme geometries. The convergence is impacted most strongly for rays which pass in directions along the axis of maximum dipole anisotropy in the structure, while the shear is most strongly impacted for rays which pass in directions orthogonal to this axis, as expected. These effects due to anisotropic structures will affect lensing measurements and must be fully examined in an era of precision cosmology.
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We study the effects and implications of anisotropies at the scale of galaxy clusters by building an exact general relativistic model of a cluster using the inhomogeneous and anisotropic Szekeres metric. The model is built from a modified Navarro-Frenk-White (NFW) density profile. We compare this to a corresponding spherically symmetric structure in the Lemaitre-Tolman (LT) model and quantify the impact of introducing varying levels of anisotropy. We examine two physical measures of gravitational infall -- the growth rate of density and the velocity of the source dust in the model. We introduce a generalization of the LT dust velocity profile for the Szekeres metric and demonstrate its consistency with the growth rate of density. We find that the growth rate of density in one substructure increases by 0.5%, 1.5%, and 3.75% for 5%, 10%, and 15% levels of introduced anisotropy, which is measured as the fractional displaced mass relative to the spherically symmetric case. The infall velocity of the dust is found to increase by 2.5, 10, and 20 km/s (0.5%, 2%, and 4.5%), respectively, for the same three levels of anisotropy. This response to the anisotropy in a structure is found to be strongly nonlinear with respect to the strength of anisotropy. These relative velocities correspond to an equivalent increase in the total mass of the spherically symmetric structure of 1%, 3.8%, and 8.4%, indicating that not accounting for the presence of anisotropic mass distributions in cluster models can strongly bias the determination of physical properties like the total mass.
Weak gravitational lensing, the deflection of light by mass, is one of the best tools to constrain the growth of cosmic structure with time and reveal the nature of dark energy. I discuss the sources of systematic uncertainty in weak lensing measurements and their theoretical interpretation, including our current understanding and other options for future improvement. These include long-standing concerns such as the estimation of coherent shears from galaxy images or redshift distributions of galaxies selected based on photometric redshifts, along with systematic uncertainties that have received less attention to date because they are subdominant contributors to the error budget in current surveys. I also discuss methods for automated systematics detection using survey data of the 2020s. The goal of this review is to describe the current state of the field and what must be done so that if weak lensing measurements lead toward surprising conclusions about key questions such as the nature of dark energy, those conclusions will be credible.
Advances in upcoming weak lensing surveys pose new challenges for an accurate modeling of the lensing observables. With their large sky coverage, common approximations based on a flat-sky geometry cannot be used anymore to evaluate all measurable angular scales. Moreover, additional relativistic effects manifest themselves on large scales and thus need to be accounted for. In particular, the lensing magnification cannot be correctly described by the standard lensing convergence only. We present the analytical solutions for the fully-relativistic weak lensing angular power spectra, including the contribution from primordial gravitational waves. We compare the results obtained by using the Limber approximation with the precise all-sky calculations using spherical harmonics. Our numerical evaluations show that general relativistic corrections are one order-of-magnitude below cosmic variance at small scales ($lgeq 10$). At large scales ($l<10$), however, neglecting them leads to more significant errors, especially when combined with the Limber approximation. Hence, a precise, fully-relativistic modeling is necessary at these largest scales.
We study the imprints of an effective dark energy fluid in the large scale structure of the universe through the observed angular power spectrum of galaxies in the relativistic regime. We adopt the phenomenological approach that introduces two parameters ${Q,eta}$ at the level of linear perturbations and allow to take into account the modified clustering (or effective gravitational constant) and anisotropic stress appearing in models beyond $Lambda$CDM. We characterize the effective dark energy fluid by an equation of state parameter $w=-0.95$ and various sound speed cases in the range $10^{-6}leq c^2_sleq 1$, thus covering K-essence and quintessence cosmologies. We calculate the angular power spectra of standard and relativistic effects for these scenarios under the ${Q,eta}$ parametrization, and we compare these relative to a fiducial $Lambda$CDM cosmology. We find that, overall, deviations relative to $Lambda$CDM are stronger at low redshift since the behavior of the dark energy fluid can mimic the cosmological constant during matter domination era but departs during dark energy domination. In particular, at $z=0.1$ the matter density fluctuations are suppressed by up to $sim3%$ for the quintessence-like case, while redshift-space distortions and Doppler effect can be enhanced by $sim15%$ at large scales for the lowest sound speed scenario. On the other hand, at $z=2$ we find deviations of up to $sim5%$ in gravitational lensing, whereas the Integrated Sachs-Wolfe effect can deviate up to $sim17%$. Furthermore, when considering an imperfect dark energy fluid scenario, we find that all effects are insensitive to the presence of anisotropic stress at low redshift, and only the Integrated Sachs-Wolfe effect can detect this feature at $z=2$ and very large scales.
We review the general construction of distribution functions for gases of fermions and bosons (photons), emphasizing the similarities and differences between both cases. The central object which describes polarization for photons is a tensor-valued distribution function, whereas for fermions it is a vector-valued one. The collision terms of Boltzmann equations for fermions and bosons also possess the same general structure and differ only in the quantum effects associated with the final state of the reactions described. In particular, neutron-proton
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