Linear point and sound horizon as purely geometric standard rulers

Abstract

The Baryon Acoustic Oscillations feature (BAO) imprinted in the clustering correlation function is known to furnish us cosmic distance determinations that are independent of the cosmologicalbackground model and the primordial perturbation parameters. These measurements can be accomplished rigorously by means of the Purely Geometric BAO methods. To date two different Purely Geometric BAO approaches have been proposed. The first exploits the linear-point standard ruler. The second, called correlation-function model-fitting, exploits the sound-horizon standard ruler. A key difference between them is that, when estimated from clustering data, the linear point makes use of a cosmological-model-independent procedure to extract the ratio of the ruler to the cosmic distance, while the correlation-function model-fitting relies on a phenomenological cosmological model for the correlation function. Nevertheless the two rulers need to be precisely defined independently of any specific observable (e.g. the BAO). We define the linear point and sound horizon and we fully characterize and compare the two rulers' cosmological-parameter dependence. We find that they are both geometrical (i.e. independent of the primordial cosmological parameters) within the required accuracy, and that they have the same parameter dependence for a wide range of parameter values. We estimate the rulers' best-fit values and errors, given the cosmological constraints obtained by the Planck Satellite team from their measurements of the Cosmic Microwave Background temperature and polarization anisotropies. We do this for three different cosmological models encompassed by the Purely Geometric BAO methods. In each case we find that the relative errors of the two rulers coincide and they are insensitive to the assumed cosmological model. Interestingly both the linear point and the sound horizon shift by 0.5σ when we do not fix the spatial geometry to be flat in ΛCDM. This points toward a sensitivity of the rulers to different cosmological models when they are estimated from the Cosmic Microwave Background.

The clustering of critical points in the evolving cosmic web

“…It is surprisingly consistent with a multiplicative linear bias model at that scale, see Appendix A and would be interesting to study further as a possible robust cosmological probe (less sensitive to non-linearities). This situation seems similar to the so-called Linear Point (Anselmi et al 2015;O'Dwyer et al 2020) which is the mid-point between the first dip and peak of the BAO pattern at ∼ 100 h −1 Mpc . This point in the halo correlation function was shown to be robust against nonlinear evolution, biasing effects and redshift space distortions and eventually can serve as a purely geometric cosmological test without the need for assuming any prior on the cosmological model or any model for the late-time galaxy correlation function evolution.…”

BAO signatures in the 2-point angular correlations and the Hubble tension

“…For recent discussions on the cosmological constraints investigations under the perspective of BAO measurements by other groups see, e.g., [40][41][42][43].…”

Laguerre reconstruction of the correlation function on Baryon Acoustic Oscillation scales

“…Fig. 2 of [16] shows that = 0.005 works well -in the sense that it corrects r LP to within 0.5% of the linear theory value -for a wide range of cosmological parameters. Indeed, multiplying the r LP−pre values in Table I by 1.005 does bring them to within 0.5% of linear theory (although the systematic trend with halo mass remains).…”

“…In what follows, we outline a rather different approach which is much cheaper and less tied to a cosmological model. We use the Linear Point (LP) -the scale that lies midway between the peak and dip, which previous work has shown can be used as a standard cosmological ruler [12][13][14][15][16] -to quantify the accuracy of our approach.…”