Correlation Function in Deep Redshift Space as a Cosmological Probe

By Takahiko Matsubara. 2004

137 citations recorded by the source corpus.

Recent developments in galaxy surveys enable us to investigate the deep, high-redshift, universe. We quantitatively present the physical information extractable from the observable correlation function in deep redshift space in a framework of linear theory. The correlation function depends on the underlying power spectrum, velocity distortions, and the Alcock-Paczyński (AP) effect. The underlying power spectrum is sensitive to the constituents of matter in the universe, the velocity distortions are sensitive to the galaxy bias as well as the amount of total matter, and the Alcock-Paczyński effect is sensitive to the dark energy components. Measuring the dark energy by means of the baryonic feature in the correlation function is one of the most interesting applications. We show that the "baryon ridge" in the correlation function serves as a statistically circular object in the AP effect. In order to sufficiently constrain the dark energy components, the redshift range of the galaxy survey should be as broad as possible. The survey area on the sky should be smaller at deep redshifts than at shallow redshifts to keep the number density as dense as possible. We illustrate an optimal survey design that is useful in cosmology. Assuming future redshift surveys of z ≲ 3, which are within the reach of present-day technology, achievable error bounds on cosmological parameters are estimated by calculating the Fisher matrix. According to an illustrated design, the equation of state of dark energy can be constrained within ±5% error assuming that the bias is unknown and marginalized over. Even when all the other cosmological parameters should be simultaneously determined, the error bound for the equation of state is up to ±10%.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/18f42b0de5c9cec6753766c228f4857ee81ca4f4

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Citations in the corpus

Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample (2013, methodology): “Thus, using the BAO signature imprinted on the galaxy clustering as a standard ruler, these distortions can be measured, leading to a precise determination of DA(z) and H(z) (e.g. Matsubara 2004e; Seo & Eisenstein 2003).”
Cosmological parameter constraints from SDSS luminous red galaxies: a new treatment of large-scale clustering (2009, unknown): “In the correlation function, the Fourier transform of the power spectrum, the BAO appear as a broad peak at large pair separations (Matsubara 2004).”
The clustering of galaxies in the SDSS‐III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large‐scale two‐point correlation function (2012, background): “In the correlation function these are transformed into a single peak whose position is related to the sound horizon at the drag redshift (Matsubara 2004).”
The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant (2011, background): “The wide angle description of redshift space distortions has been laid out in several papers (Szalay et al. 1997; Szapudi 2004; Matsubara 2004; Papai & Szapudi 2008; Raccanelli et al. 2010), which we summarise in Appendix C.”
The 6dF Galaxy Survey: z \approx 0 measurement of the growth rate and sigma_8 (2012, background): “The wide-angle description of redshift-space distortions has been laid out in several papers (Szalay et al. 1997; Szapudi 2004; Matsubara 2004; Papai & Szapudi 2008; Raccanelli et al. 2010).”
Measuring DA and H at z = 0.35 from the SDSS DR7 LRGs using baryon acoustic oscillations (2012, background): “…(Eisenstein & Hu 1998; Eisenstein, Hu & Tegmark 1998; Blake & Glazebrook 2003; Eisenstein 2003; Hu & Haiman 2003; Linder 2003; Seo & Eisenstein 2003; Matsubara 2004; Abdalla & Rawlings 2005; Amendola, Quercellini & Giallongo 2005; Angulo et al. 2005; Glazebrook & Blake 2005; Dolney, Jain & Takada…”
Baryonic Acoustic Oscillations in Simulated Galaxy Redshift Surveys (2005, background): “See Blake & Glazebrook (2003), Linder (2003), Hu & Haiman (2003), Amendola et al. (2005), Cooray (2004), Dolney et al. (2004), and Matsubara (2004) for similar studies.”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the full shape of the clustering wedges in the data release 10 and 11 galaxy samples (2013, background): “This signal, referred to as baryon acoustic oscillations (BAO), appears as a modulation in the amplitude of the galaxy power spectrum, P(k), and a broad peak in the largescale two-point correlation function, ξ (s) (Eisenstein & Hu 1998; Meiksin, White & Peacock 1999; Matsubara 2004).”
Observational probes of cosmic acceleration (2012, background): “In practice the two effects must be modeled together (see, e.g., Matsubara 2004), and the principal systematic uncertainty for AP measurements is the uncertainty in modeling non-linear redshift-space distortions.”
Improved Forecasts for the Baryon Acoustic Oscillations and Cosmological Distance Scale (2007, methodology): “…using the BAO from future galaxy redshift surveys (Eisenstein 2003; Blake&Glazebrook 2003; Linder 2003; Hu &Haiman 2003; Seo & Eisenstein 2003; Cooray 2004; Matsubara 2004; Amendola et al. 2005; Blake & Bridle 2005; Glazebrook & Blake 2005; Dolney et al. 2006; Zhan & Knox 2006; Blake et al. 2006).”
Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies (2005, background): “…can provide precise and robust constraints (Blake & Glazebrook 2003; Hu & Haiman 2003; Linder 2003; Seo & Eisenstein 2003; Amendola et al. 2004; Dolney, Jain, & Takada 2004; Matsubara 2004) on the acceleration of the expansion rate of the universe (Riess et al. 1998; Perlmutter et al. 1999).”
Interpreting large-scale redshift-space distortion measurements (2011, methodology): “The wide-angle linear redshift-space correla- tion function and power-spectrum as a function of all three variables have been computed (Zaroubi & Hoffman 1993; Szalay, Matsubara & Landy 1998; Szapudi 2004; Matsubara 2004; Papai & Szapudi 2008).”
Large-Scale Anisotropic Correlation Function of SDSS Luminous Red Galaxies (2007, methodology): “For the details of the dependence of the anisotropic 2PCF on cosmological parameters, see Matsubara (2004).”
Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample (2009, methodology): “The apparent size of the BAO measured from observations then leads to measurements of the Hubble parameter and the angular diameter distance (Bond & Glazebrook 2003; Seo & Eisenstein 2003; Matsubara 2004; Hu & Haiman 2006).”
The clustering of luminous red galaxies in the Sloan Digital Sky Survey imaging data (2006, background): “…diameter distance as a function of redshift (Eisenstein, Hu & Tegmark 1998; Blake & Glazebrook 2003; Hu & Haiman 2003; Linder 2003; Matsubara & Szalay 2003; Seo & Eisenstein 2003; Matsubara 2004; Blake & Bridle 2005; Seo & Eisenstein 2005; White 2005; Blake et al. 2006; Dolney, Jain & Takada 2006).”