TY - JOUR

T1 - Quantifying the redshift space distortion of the bispectrum II

T2 - Induced non-Gaussianity at second-order perturbation

AU - Mazumdar, Arindam

AU - Bharadwaj, Somnath

AU - Sarkar, Debanjan

N1 - Publisher Copyright:
© 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.

PY - 2020/11/1

Y1 - 2020/11/1

N2 - The anisotrpy of the redshift space bispectrum Bsk1, k2, k3), which contains a wealth of cosmological information, is completely quantified using multipole moments Bmℓ(k1, μ, t), where k1, the length of the largest side, and (μ, t), respectively, quantify the size and the shape of the triangle k1 k2 k3). We present analytical expressions for all the multipoles that are predicted to be non-zero (≤ 8, m ≤ 6) at second-order perturbation theory. The multipoles also depend on β1, b1, and γ2, which quantify the linear redshift distortion parameter, linear bias and quadratic bias, respectively. Considering triangles of all possible shapes, we analyse the shape dependence of all of the multipoles holding k1=0.2, Mpc-1, β1=1, b1=1, and γ2 = 0 fixed. The monopole $\bar{B}^0_0$, which is positive everywhere, is minimum for equilateral triangles. $\bar{B}_0^0$ increases towards linear triangles, and is maximum for linear triangles close to the squeezed limit. Both $\bar{B}^0_{2}$ and $\bar{B}^0_4$ are similar to $\bar{B}^0_0$, however, the quadrupole $\bar{B}^0_2$ exceeds $\bar{B}^0_0$ over a significant range of shapes. The other multipoles, many of which become negative, have magnitudes smaller than $\bar{B}^0_0$. In most cases, the maxima or minima, or both, occur very close to the squeezed limit. $\mid \bar{B}^m_{\ell } \mid$ is found to decrease rapidly if or m are increased. The shape dependence shown here is characteristic of non-linear gravitational clustering. Non-linear bias, if present, will lead to a different shape dependence.

AB - The anisotrpy of the redshift space bispectrum Bsk1, k2, k3), which contains a wealth of cosmological information, is completely quantified using multipole moments Bmℓ(k1, μ, t), where k1, the length of the largest side, and (μ, t), respectively, quantify the size and the shape of the triangle k1 k2 k3). We present analytical expressions for all the multipoles that are predicted to be non-zero (≤ 8, m ≤ 6) at second-order perturbation theory. The multipoles also depend on β1, b1, and γ2, which quantify the linear redshift distortion parameter, linear bias and quadratic bias, respectively. Considering triangles of all possible shapes, we analyse the shape dependence of all of the multipoles holding k1=0.2, Mpc-1, β1=1, b1=1, and γ2 = 0 fixed. The monopole $\bar{B}^0_0$, which is positive everywhere, is minimum for equilateral triangles. $\bar{B}_0^0$ increases towards linear triangles, and is maximum for linear triangles close to the squeezed limit. Both $\bar{B}^0_{2}$ and $\bar{B}^0_4$ are similar to $\bar{B}^0_0$, however, the quadrupole $\bar{B}^0_2$ exceeds $\bar{B}^0_0$ over a significant range of shapes. The other multipoles, many of which become negative, have magnitudes smaller than $\bar{B}^0_0$. In most cases, the maxima or minima, or both, occur very close to the squeezed limit. $\mid \bar{B}^m_{\ell } \mid$ is found to decrease rapidly if or m are increased. The shape dependence shown here is characteristic of non-linear gravitational clustering. Non-linear bias, if present, will lead to a different shape dependence.

KW - large-scale structures of Universe

KW - methods: statistical

UR - http://www.scopus.com/inward/record.url?scp=85096861289&partnerID=8YFLogxK

U2 - 10.1093/mnras/staa2548

DO - 10.1093/mnras/staa2548

M3 - Article

AN - SCOPUS:85096861289

SN - 0035-8711

VL - 498

SP - 3975

EP - 3984

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

IS - 3

ER -