### [1006.3226] Tracing The Sound Horizon Scale With Photometri

Posted:

**June 29 2010**This paper looks at how to model the baryon acoustic peak in the angular correlation function, and in particular how to compensate for the substantial projection effects which push the peak down to smaller angular scales.

The approach here is to adopt a simple parametric fit, equation (7), involving a power law plus a Gaussian (plus a constant). The key is linking the angular position of the best-fit Gaussian to the expected scale of the acoustic peak, [tex]\theta_{BAO}[/tex]. After seeing equation (8), I was hoping to find a fitting function for alpha, but I suppose the idea is to interpolate the lines plotted in Figure 3.

The authors claim the fractional shift in the Gaussian's position is unchanged by the background cosmology, which seems like a fairly good approximation. But let’s not forget that this 1% change in [tex]\theta[/tex] would typically propagate to a ~4% change in the estimated equation of state [tex]w[/tex].

So I’m left with a few questions:

- If we converted the redshift bin width to a fractional change in angular diameter distance, would this help remove the 1% dispersion due to changes in the background cosmology?

- To what extent does the shape of the redshift bin influence Figure 3?

- It would also be nice to see how the uncertainty in [tex]\theta_{fit}[/tex] changes as a function of [tex]z[/tex] and [tex]\Delta z[/tex]. For example, for large bin widths the gaussian becomes very hard to identify. Similarly, how much does this error improve if we use fewer degrees of freedom in the parametric fit?

The approach here is to adopt a simple parametric fit, equation (7), involving a power law plus a Gaussian (plus a constant). The key is linking the angular position of the best-fit Gaussian to the expected scale of the acoustic peak, [tex]\theta_{BAO}[/tex]. After seeing equation (8), I was hoping to find a fitting function for alpha, but I suppose the idea is to interpolate the lines plotted in Figure 3.

The authors claim the fractional shift in the Gaussian's position is unchanged by the background cosmology, which seems like a fairly good approximation. But let’s not forget that this 1% change in [tex]\theta[/tex] would typically propagate to a ~4% change in the estimated equation of state [tex]w[/tex].

So I’m left with a few questions:

- If we converted the redshift bin width to a fractional change in angular diameter distance, would this help remove the 1% dispersion due to changes in the background cosmology?

- To what extent does the shape of the redshift bin influence Figure 3?

- It would also be nice to see how the uncertainty in [tex]\theta_{fit}[/tex] changes as a function of [tex]z[/tex] and [tex]\Delta z[/tex]. For example, for large bin widths the gaussian becomes very hard to identify. Similarly, how much does this error improve if we use fewer degrees of freedom in the parametric fit?