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# The Linear Point Standard Ruler for galaxy survey data: validation with mock catalogues

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### Abstract

Due to late time non-linearities, the location of the acoustic peak in the two-point galaxy correlation function is a redshift-dependent quantity, thus it cannot be simply employed as a cosmological standard ruler. This has motivated the recent proposal of a novel ruler, also located in the Baryon Acoustic Oscillation range of scales of the correlation function, dubbed the "linear point". Unlike the peak, it is insensitive at the $$0.5\%$$ level to many of the non-linear effects that distort the clustering correlation function and shift the peak. However, this is not enough to make the linear point a useful standard ruler. In addition, we require a model-independent method to estimate its value from real data, avoiding the need to deploy a poorly known non-linear model of the correlation function. In this manuscript, we precisely validate a procedure for model-independent estimation of the linear point. We also identify the optimal set-up to estimate the linear point from the correlation function using galaxy catalogs. The methodology developed here is of general validity, and can be applied to any galaxy correlation-function data. As a working example, we apply this procedure to the LOWZ and CMASS galaxy samples of the Twelfth Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS), for which the estimates of cosmic distances using the linear point have been presented in Anselmi et al. (2017) [1].

### Most cited references2

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### Eppur Si Muove': On The Motion of the Acoustic Peak in the Correlation Function

(2007)
The baryonic acoustic signature in the large-scale clustering pattern of galaxies has been detected in the two-point correlation function. Its precise spatial scale has been forwarded as a rigid-rod ruler test for the space-time geometry, and hence as a probe for tracking the evolution of Dark Energy. Percent-level shifts in the measured position can bias such a test and erode its power to constrain cosmology. This paper addresses some of the systematic effects that might induce shifts: namely non-linear corrections from matter evolution, redshift space distortions and biasing. We tackle these questions through analytic methods and through a large battery of numerical simulations, with total volume of the order ~100[Gpc\h]^3. A toy-model calculation shows that if the non-linear corrections simply smooth the acoustic peak, then this gives rise to an apparent' shifting to smaller scales. However if tilts in the broad band power spectrum are induced then this gives rise to more pernicious `physical' shifts. Our numerical simulations show evidence of both: in real space and at z=0, for the dark matter we find percent level shifts; for haloes the shifts depend on halo mass, with larger shifts being found for the most biased samples, up to 3%. From our analysis we find that physical shifts are greater than ~0.4% at z=0. In redshift space these effects are exacerbated, but at higher redshifts are alleviated. We develop an analytical model to understand this, based on solutions to the pair conservation equation using characteristic curves. When combined with modeling of pairwise velocities the model reproduces the main trends found in the data. The model may also help to unbias the acoustic peak.
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### Failures of homogeneous and isotropic cosmologies in Extended Quasi-Dilaton Massive Gravity

(2017)
We analyze the Extended Quasi-Dilaton Massive Gravity model around a Friedmann-Lema\^itre-Robertson-Walker cosmological background. We present a careful stability analysis of asymptotic fixed points. We find that the traditional fixed point cannot be approached dynamically, except from a perfectly fine-tuned initial condition involving both the quasi-dilaton and the Hubble parameter. A less-well examined fixed-point solution, where the time derivative of the 0-th St\"uckelberg field vanishes $$\dot\phi^0=0$$, encounters no such difficulty, and the fixed point is an attractor in some finite region of initial conditions. We examine the question of the presence of a Boulware-Deser ghost in the theory. We show that the additional constraint which generically allows for the elimination of the Boulware-Deser mode is only present under special initial conditions. We find that the only possibility corresponds to the traditional fixed point and the initial conditions are the same fine-tuned conditions that allow the fixed point to be approached dynamically.
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### Author and article information

###### Journal
24 November 2017
###### Article
1711.09063