Sensitivity of Redshift Distortion Measurements to Cosmological Parameters

Laix, Andrew A. de; Starkman, Glenn D.

doi:10.1086/305828

Cited by 15 publications

(16 citation statements)

References 14 publications

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“…With this in mind, there are a number of improvements that could be done in this analysis. The redshift distortions could be measured directly, and the effects could be included directly into the Fisher matrix analysis (cf., de Laix &Starkman 1998 and for a discussion of how well redshift-space distortions can be measured from the SDSS data). Similarly, we could parameterize the effects of galaxy and clustering evolution, and include these as parameters in the analysis.…”

Section: Discussionmentioning

confidence: 99%

Cosmology in the Next Millennium: Combining Microwave Anisotropy Probe and Sloan Digital Sky Survey Data to Constrain Inflationary Models

Wang

Spergel

Strauss

1999

ApJ

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The existence of primordial adiabatic Gaussian random-phase density fluctuations is a generic prediction of inflation. The properties of these fluctuations are completely specified by their power spectrum A 2 S (k). The basic cosmological parameters and the primordial power spectrum together completely specify predictions for the cosmic microwave background radiation anisotropy and large scale structure. Here we show how we can strongly constrain both A 2 S (k) and the cosmological parameters by combining the data from the Microwave Anisotropy Probe (MAP) and the galaxy redshift survey from the Sloan Digital Sky Survey (SDSS). We allow A 2 S (k) to be a free function, and thus probe features in the primordial power spectrum on all scales. If we assume that the cosmological parameters are known a priori and that galaxy bias is linear and scale-independent, and neglect non-linear redshift distortions, the primordial power spectrum in 20 steps in log k to k ≤ 0.5hMpc −1 can be determined to ∼ 16% accuracy for k ∼ 0.01hMpc −1 , and to ∼ 1% accuracy for k ∼ 0.1hMpc −1 . The uncertainty in the primordial power spectrum increases by a factor up to 3 on small scales if we solve simultaneously for the dimensionless Hubble constant h, the cosmological constant Λ, the baryon fraction Ω b , the reionization optical depth τ ri , and the effective bias between the matter density field and the redshift space galaxy density field b eff . Alternately, if we restrict A 2 S (k) to be a power law, we find that inclusion of the SDSS data breaks the degeneracy between the amplitude of the power spectrum and the optical depth inherent in the MAP data, significantly reduces the uncertainties in the determination of the matter density and the cosmological constant, and allows a determination of the galaxy bias parameter. Thus, combining the MAP and 1 Alfred P. Sloan Foundation Fellow 2 Cottrell Scholar of Research Corporation SDSS data allows the independent measurement of important cosmological parameters, and a measurement of the primordial power spectrum independent of inflationary models, giving us valuable information on physics in the early Universe, and providing clues to the correct inflationary model. Recently, Adams, Ross, & Sarkar (1997) proposed a new multiple inflation model. Since 3 Certain two-field inflationary models predict isocurvature as well as adiabatic fluctuations (Kofman & Linde 1987). Since the CMB and LSS predictions of isocurvature models differ significantly from adiabatic models and since these differences are not degenerate with parameter variation, we could, in principle, also fit for an isocurvature power spectrum. However, in this paper, we limit ourselves to considering adiabatic fluctuations.

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Section: Discussionmentioning

confidence: 99%

Cosmology in the Next Millennium: Combining Microwave Anisotropy Probe and Sloan Digital Sky Survey Data to Constrain Inflationary Models

Wang

Spergel

Strauss

1999

ApJ

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“…These coefficients are equivalent to the result that Hamilton (1992) derived in z → 0 limit with distant observer approximation, which is a direct Fourier transform of Kaiser's original form in Fourier space (Kaiser 1987). For finite z, the equivalent result is obtained by Matsubara & Suto (1996) for correlation function and Ballinger, Peacock & Heavens (1996) for power spectrum [see also Nakamura, Matsubara & Suto (1998) de Laix & Starkman (1998, Nair (1999)]. All these previous studies are based on the distant observer approximation, and our general formula correctly has the limit of these cases.…”

Section: Recovery Of the Known Formulas Of The Redshift Distortions Omentioning

confidence: 94%

The Correlation Function in Redshift Space: General Formula with Wide‐Angle Effects and Cosmological Distortions

Matsubara

2000

ApJ

140

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A general formula for the correlation function in redshift space is derived in linear theory. The formula simultaneously includes wide-angle effects and cosmological distortions. The formula is applicable to any pair with arbitrary angle θ between lines of sight, and arbitrary redshifts, z 1 , z 2 , which are not necessarily small. The effects of the spatial curvature both on geometry and on fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lemaître universe with arbitrary cosmological parameters Ω 0 and λ 0 . We illustrate the pattern of the resulting correlation function with several models, and also show that validity region of the conventional distant observer approximation is θ ≤ 10 • .

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“…This degeneracy could in principle be resolved because the cosmological and peculiar velocity signals evolve differently with redshift, but in practice the uncertain evolution of bias muddies the issue (Ballinger, Peacock & Heavens 1996). Nakamura, Matsubara & Suto (1997) emphasize that cosmological redshift distortions will affect the linear distortion parameter β at the 10-20% level in the Sloan Digital Sky Survey (SDSS), which aims to go to a median depth of z ≈ 0.1. de Laix & Starkman (1997) conclude that the SDSS will not provide a clean signal of cosmological parameters from redshift distortions in the linear regime.…”

Section: Cosmological Redshift Distortionsmentioning

confidence: 95%

Linear Redshift Distortions: A Review

Hamilton

1998

Astrophysics and Space Science Library

383

370

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Abstract. Redshift maps of galaxies in the Universe are distorted by the peculiar velocities of galaxies along the line of sight. The amplitude of the distortions on large, linear scales yields a measurement of the linear redshift distortion parameter, which is β ≈ Ω 0.6 0 /b in standard cosmology with cosmological density Ω 0 and light-to-mass bias b. All measurements of β from linear redshift distortions published up to mid 1997 are reviewed. The average and standard deviation of the reported values is β optical = 0.52 ± 0.26 for optically selected galaxies, and β IRAS = 0.77 ± 0.22 for IRAS selected galaxies. The implied relative bias is b optical /b IRAS ≈ 1.5. If optical galaxies are unbiased, then Ω 0 = 0.33

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Sensitivity of Redshift Distortion Measurements to Cosmological Parameters

Cited by 15 publications

References 14 publications

Cosmology in the Next Millennium: Combining Microwave Anisotropy Probe and Sloan Digital Sky Survey Data to Constrain Inflationary Models

Cosmology in the Next Millennium: Combining Microwave Anisotropy Probe and Sloan Digital Sky Survey Data to Constrain Inflationary Models

The Correlation Function in Redshift Space: General Formula with Wide‐Angle Effects and Cosmological Distortions

Linear Redshift Distortions: A Review

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