Table 1.
List of higher-order correction terms to the shear angular power spectrum resulting from relaxing approximations.
| Correction | Reference | Percentage of sample variance |
||
|---|---|---|---|---|
| ℓ = 10 | ℓ = 100 | ℓ = 1000 | ||
| Source-lens clustering | Yu et al. (2015) | N/A | 6.0 | 57.2 |
| Reduced shear + magnification bias | Deshpande et al. (2020a) | 0.4 | 1.8 | 15.3 |
| Post-Limber reduced shear | Deshpande & Kitching (2020) | 0.2 | 0.6 | 1.9 |
| Non-linear ellipticity-shear relation | Krause & Hirata (2010) | 0.2 | 0.6 | 1.9 |
| Limber + flat-sky | Kitching et al. (2017) | 9.8 | 3.0 | 1.0 |
| Local Universe effects | Hall (2020) | 7.8 | 24.2 | N/A |
| Higher-order reduced shear | Krause & Hirata (2010) | O(ϕ4) | O(ϕ4) | O(ϕ4) |
| Time delay-lens coupling | Bernardeau et al. (2010) | O(ϕ4) | O(ϕ4) | O(ϕ4) |
| Deflection-deflection coupling | Bernardeau et al. (2010) | O(ϕ4) | O(ϕ4) | O(ϕ4) |
| Born approximation | Cooray & Hu (2002) | O(ϕ4) | O(ϕ4) | O(ϕ4) |
| Lensing by dark energy pressure | Simpson et al. (2010) | O(ϕ4) | O(ϕ4) | O(ϕ4) |
| Second-order speed-of-light | Cuesta-Lazaro et al. (2018) | < 0.01 | < 0.01 | < 0.01 |
| Temporal-Born approximation | Cuesta-Lazaro et al. (2018) | < 0.01 | < 0.01 | < 0.01 |
| Finite-beam corrections | Fleury et al. (2019) | < 0.01 | < 0.01 | < 0.01 |
| Doppler-shift | Deshpande & Kitching (2021) | < 0.01 | < 0.01 | < 0.01 |
| Unequal-time correlators | Kitching & Heavens (2017) | < 0.01 | < 0.01 | < 0.01 |
| Sachs-Wolfe effect | Cuesta-Lazaro et al. (2018) | < 0.01 | < 0.01 | < 0.01 |
| Integrated Sachs-Wolfe effect | Cuesta-Lazaro et al. (2018) | < 0.01 | < 0.01 | < 0.01 |
| Flexion correction | Schneider & Er (2008) | N/A | N/A | N/A |
| Flat-geometry assumption | Taylor et al. (2018b) | −2.0 | −6.0 | −19.1 |
| Source obscuration | Hartlap et al. (2011) | −2.0 | −6.0 | −19.1 |
| Spatially-varying survey depth | Heydenreich et al. (2020) | −5.9 | −18.1 | −57.2 |
Notes. To illustrate their typical sizes and facilitate comparison, the values of these correction terms at redshift z ∼ 1 are also stated here. These are provided for ℓ-modes 10, 100, and 1000, and as a percentage of sample variance i.e. 100δCℓ/(sample variance). Sample variance here is calculated using the definition of Kaiser (1992), see Eq. (61). These values are taken from the available literature for the case of Stage IV cosmic shear experiments. Unavailable values are represented by ‘N/A’. Corrections which have a functional form that is fourth-order in lensing potential, and therefore sub-dominant, are denoted by O(ϕ4). The references provided refer to the values stated where available, or to the work describing the correction where explicit values are not available. For the case where the absolute value of an effect is more than four orders of magnitude smaller than the sample variance, it is denoted by < 0.01. The sign denotes whether the effect is to decrease the power (a negative sign) or to increase (no sign). The rows are ordered in decreasing amplitude for ℓ = 1000. These numbers were read from graphs published in the referenced papers, due to the inherent inaccuracy of this approach we quote only one decimal place; in the case that only correlation functions were provide these were converted to power spectrum results using a Hankel transform over the quoted angular range. We note that the Table is ordered by the magnitude of the impact of the effects at ℓ = 1000, not the absolute value of the impact, therefore those effects that cause a negative change to the power spectra are at the bottom of the Table. The effects in bold are those whose approximations are investigated in this paper. Where values are the same this is due to rounding and limitations of transcribing values from plots in papers; hence, these values should only be taken as indicative of the amplitude of the effects.
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