PRIMORDIAL NON-GAUSSIANITY, SCALE-DEPENDENT BIAS, AND THE BISPECTRUM OF GALAXIES
- Texas Cosmology Center, University of Texas at Austin, 1 University Station, C1400, Austin, TX 78712 (United States)
The three-point correlation function of cosmological fluctuations is a sensitive probe of the physics of inflation. We calculate the bispectrum, B{sub g} (k{sub 1}, k{sub 2}, k{sub 3}), Fourier transform of the three-point function of density peaks (e.g., galaxies), using two different methods: the Matarrese-Lucchin-Bonometto formula and the locality of galaxy bias. The bispectrum of peaks is not only sensitive to that of the underlying matter density fluctuations, but also to the four-point function. For a physically motivated, local form of primordial non-Gaussianity in the curvature perturbation, PHI = phi + f{sub NL}phi{sup 2} + g{sub NL}phi{sup 3}, where phi is a Gaussian field, we show that the galaxy bispectrum contains five physically distinct pieces: (1) non-linear gravitational evolution, (2) non-linear galaxy bias, (3) f{sub NL}, (4) f{sup 2}{sub NL}, and (5) g{sub NL}. While (1), (2), and a part of (3) have been derived in the literature, (4) and (5) are derived in this paper for the first time. We also find that, in the high-density peak limit, (3) receives an enhancement of a factor of {approx}15 relative to the previous calculation for the squeezed triangles (k{sub 1} {approx} k{sub 2} >> k{sub 3}). Our finding suggests that the galaxy bispectrum is more sensitive to f {sub NL} than previously recognized, and is also sensitive to a new term, g{sub NL}. For a more general form of local-type non-Gaussianity, the coefficient f{sup 2}{sub NL} can be interpreted as tau{sub NL}, which allows us to test multi-field inflation models using the relation between the three- and four-point functions. The usual terms from Gaussian initial conditions, (1) and (2), have the smallest signals in the squeezed configurations, while the others have the largest signals; thus, we can distinguish them easily. We cannot interpret the effects of f{sub NL} on B{sub g} (k{sub 1}, k{sub 2}, k{sub 3}) as a scale-dependent bias, and thus replacing the linear bias in the galaxy bispectrum with the scale-dependent bias known for the power spectrum results in an incorrect prediction. As the importance of primordial non-Gaussianity relative to the non-linear gravity evolution and galaxy bias increases toward higher redshifts, galaxy surveys probing a high-redshift universe are particularly useful for probing the primordial non-Gaussianity.
- OSTI ID:
- 21371916
- Journal Information:
- Astrophysical Journal, Vol. 703, Issue 2; Other Information: DOI: 10.1088/0004-637X/703/2/1230; ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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COSMOLOGY AND ASTRONOMY
CORRELATION FUNCTIONS
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FOURIER TRANSFORMATION
GALACTIC EVOLUTION
GALAXIES
GRAVITATION
INFLATIONARY UNIVERSE
NONLINEAR PROBLEMS
PERTURBATION THEORY
RED SHIFT
UNIVERSE
COSMOLOGICAL MODELS
EVOLUTION
FUNCTIONS
INTEGRAL TRANSFORMATIONS
MATHEMATICAL MODELS
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