Fitting the Nonlinear Matter Bispectrum by the Halofit Approach

Takahashi, Ryuichi; Nishimichi, Takahiro; Namikawa, Toshiya; Taruya, Atsushi; Kayo, Issha; Osato, Ken; Kobayashi, Yosuke; Shirasaki, Masato

doi:10.3847/1538-4357/ab908d

Cited by 54 publications

(89 citation statements)

References 132 publications

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“…These expressions are valid in the linear regime, where l 1 ; l 2 ; l 3 < 100 (see e.g., [27]). In order to be able to accurately capture the behavior of the bispectrum beyond this range, we must obtain fitting formulas from N-body simulations [28][29][30]. In this work, we use the fitting formula of [28], to allow consistent comparison with the results of [11].…”

Section: F the Convergence Bispectrummentioning

confidence: 99%

Post-Limber weak lensing bispectrum, reduced shear correction, and magnification bias correction

Deshpande

Kitching

2020

Phys. Rev. D

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The significant increase in precision that will be achieved by Stage IV cosmic shear surveys means that several currently used theoretical approximations may cease to be valid. An additional layer of complexity arises from the fact that many of these approximations are interdependent; the procedure to correct for one involves making another. Two such approximations that must be relaxed for upcoming experiments are the reduced shear approximation and the effect of neglecting magnification bias. Accomplishing this involves the calculation of the convergence bispectrum; typically subject to the Limber approximation. In this work, we compute the post-Limber convergence bispectrum, and the post-Limber reduced shear and magnification bias corrections to the angular power spectrum for a Euclid-like survey. We find that the Limber approximation significantly overestimates the bispectrum when any side of the bispectrum triangle, l i < 60. However, the resulting changes in the reduced shear and magnification bias corrections are well below the sample variance for l ≤ 5000. We also compute a worst-case scenario for the additional biases on w 0 w a CDM cosmological parameters that result from the difference between the post-Limber and Limber approximated forms of the corrections. These further demonstrate that the reduced shear and magnification bias corrections can safely be treated under the Limber approximation for upcoming surveys.

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Section: F the Convergence Bispectrummentioning

confidence: 99%

Post-Limber weak lensing bispectrum, reduced shear correction, and magnification bias correction

Deshpande

Kitching

2020

Phys. Rev. D

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“…In this paper, we have examined the validity of the reduced shear approximation when applying k-cut cosmic shear to Stage IV cosmic shear experiments, and a hypothetical kinematic lensing survey. We first compared the reduced shear correction calculated using two different models for the matter bispectrum: the fitting formulas of [31], and the BIHALOFIT model [33]. Despite the differences between the two approaches, we found that their resulting reduced shear corrections were not significantly different, and that accordingly the reduced shear correction was robust to the choice of bispectrum model.…”

Section: Discussionmentioning

confidence: 98%

“…Cosmological parameter biases predicted if the reduced shear correction is neglected for two different matter bispectrum models. The SC model uses the fitting formulas of [31], while BH is the BIHALOFIT model [33]. The difference between the two approaches is also stated, and is not significant.…”

Section: B K-cut Cosmic Shear and Reduced Shear For Stage IV Surveysmentioning

confidence: 94%

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Accessing the high- ℓ frontier under the reduced shear approximation with k -cut cosmic shear

2020

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The precision of Stage IV cosmic shear surveys will enable us to probe smaller physical scales than ever before, however, model uncertainties from baryonic physics and non-linear structure formation will become a significant concern. The k-cut method-applying a redshift-dependent l-cut after making the Bernardeau-Nishimichi-Taruya transform-can reduce sensitivity to baryonic physics; allowing Stage IV surveys to include information from increasingly higher l-modes. Here we address the question of whether it can also mitigate the impact of making the reduced shear approximation; which is also important in the high-κ, small-scale regime. The standard procedure for relaxing this approximation requires the repeated evaluation of the convergence bispectrum, and consequently can be prohibitively computationally expensive when included in Monte Carlo analyses. We find that the k-cut cosmic shear procedure suppresses the w 0 w a CDM cosmological parameter biases expected from the reduced shear approximation for Stage IV experiments, when l-modes up to 5000 are probed. The maximum cut required for biases from the reduced shear approximation to be below the threshold of significance is at k ¼ 5.37 h Mpc −1 . With this cut, the predicted 1σ constraints increase, relative to the case where the correction is directly computed, by less than 10% for all parameters. This represents a significant improvement in constraints compared to the more conservative case where only l-modes up to 1500 are probed [A. Blanchard et al., (Euclid Collaboration), arXiv:1910.09273], and no k-cut is used. We also repeat this analysis for a hypothetical, comparable kinematic weak lensing survey. The key parts of code used for this analysis are made publicly available.

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“…The matter bispectrum required by Eq. ( 30) is computed via the BIHALOFIT model [35] and package [36]. In order to calculate the IA contributions at both the two-point and three-point levels, we use the following values for the NLA model: A IA ¼ 1.72 and C IA ¼ 0.0134 [14].…”

Section: Methodsmentioning

confidence: 99%

Cosmological parameter biases from Doppler-shifted weak lensing in stage IV experiments

Deshpande

Kitching

2021

Phys. Rev. D

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The advent of stage IV weak lensing surveys will open up a new era in precision cosmology. These experiments will offer more than an order-of-magnitude leap in precision over existing surveys, and we must ensure that the accuracy of our theory matches this. Accordingly, it is necessary to explicitly evaluate the impact of the theoretical assumptions made in current analyses on upcoming surveys. One effect typically neglected in present analyses is the Doppler shift of the measured source comoving distances. Using Fisher matrices, we calculate the biases on the cosmological parameter values inferred from a Euclidlike survey, if the correction for this Doppler shift is omitted. We find that this Doppler shift can be safely neglected for stage IV surveys.

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Fitting the Nonlinear Matter Bispectrum by the Halofit Approach

Cited by 54 publications

References 132 publications

Post-Limber weak lensing bispectrum, reduced shear correction, and magnification bias correction

Post-Limber weak lensing bispectrum, reduced shear correction, and magnification bias correction

Accessing the high- ℓ frontier under the reduced shear approximation with k -cut cosmic shear

Cosmological parameter biases from Doppler-shifted weak lensing in stage IV experiments

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