We present an analytic formula for the galaxy bispectrum in redshift space on the basis of the halo approach description with the halo occupation distribution of central galaxies and satellite galaxies. This work is an extension of a previous work on the galaxy power spectrum, which illuminated the significant contribution of satellite galaxies to the higher multipole spectrum through the non-linear redshift space distortions of their random motions. Behaviors of the multipoles of the bispectrum are compared with results of numerical simulations assuming a halo occupation distribution of the LOWZ sample of the SDSS-III BOSS survey. Also presented are analytic approximate formulas for the multipoles of the bispectrum, which is useful to understanding their characteristic properties. We demonstrate that the Fingers of God effect is quite important for the higher multipoles of the bispectrum in redshift space, depending on the halo occupation distribution parameters.

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As a generalization of our previous work [Phys. Rev. D 95 043528 (2017)], in which an analytic model for the galaxy bispectrum in redshift space was developed on the basis of the halo approach, we here investigate its higher multipoles that have not been known so far. The redshift-space bispectrum includes the two variables ω and φ for the line-of-sight direction, and the higher multipole bispectra are defined by the coefficients in the expansion of the redshift-space bispectrum using the spherical harmonics. We find 6 new nonvanishing components out of 25 total components up to ℓ = 4, in addition to 3 components discussed in the previous work (monopole, quadruple, and hexadecapole of m = 0). The characteristic behaviors of the new nonvanishing multipoles are compared with the results of galaxy mock catalogs that match the halo occupation distribution of the Sloan Digital Sky Survey Baryonic Oscillation Spectroscopic Survey low-redshift sample. We find that the multipoles with m = 0 are also sensitive to redshift-space distortion (RSD) as well as those with m = 0 and thus are key ingredients in the RSD analysis using the galaxy bispectrum. Analytic approximation formulas for these nonzero components are also presented; these are useful for understanding the characteristic behaviors.

We study the relations of the positive frequency mode functions of Dirac field in 4-dimensional Minkowski spacetime covered with Rindler and Kasner coordinates, and describe the explicit form of the Minkowski vacuum state with the quantum states in Kasner and Rindler regions, and analytically continue the solutions. As a result, we obtain the correspondence of the positive frequency mode functions in Kasner region and Rindler region in a unified manner which derives vacuum entanglement.

We construct an analytic model for the void-galaxy cross-correlation function that enables theoretical predictions of the dipole signal produced dominantly by the gravitational redshift within voids for the first time. By extending a theoretical formulation for the redshift-space distortion of galaxies to include the second order terms of the galaxy peculiar velocity v and the gravitational potential, we formulate the void-galaxy cross-correlation function multipoles in the redshift space, the monopole ξ (s) 0 , dipole ξ (s) 1 and quadrupole ξ (s)2 . We find that the dipole ξ (s) 1 is dominated by the gravitational redshift, which provide a unique opportunity to detect the gravitational potential of voids. Thus, for the dipole ξ (s) 1 (s), the gravitational redshift is crucial. Although the higher order effect is almost negligible on the monopole ξ (s) 0 , it has an influence on the quadrupole ξ (s) 2 .The effects from the random velocity of galaxies and the definition of the void center on the dipole signal are also discussed. Our model offers a new theoretical probe for the detection of gravitational redshift with voids and further tests on cosmology and gravity.