Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak

TL;DR

The paper addresses the non-linear degradation of baryon acoustic oscillations as a barrier to precision distance measurements and proposes density-field reconstruction to reverse large-scale displacements. Using a linear-theory based reconstruction with Gaussian smoothing, tested on N-body simulations, the authors show substantial restoration of the acoustic peak and a roughly factor-of-two improvement in the precision of the acoustic scale at redshift about 0.3. This technique has direct implications for optimizing galaxy surveys aimed at constraining the distance scale and dark energy, particularly at lower redshifts. The work also discusses practical considerations and potential limitations, indicating that further improvements are possible with more sophisticated reconstruction and careful treatment of redshift-space distortions and biases.

Abstract

The baryon acoustic oscillations are a promising route to the precision measure of the cosmological distance scale and hence the measurement of the time evolution of dark energy. We show that the non-linear degradation of the acoustic signature in the correlations of low-redshift galaxies is a correctable process. By suitable reconstruction of the linear density field, one can sharpen the acoustic peak in the correlation function or, equivalently, restore the higher harmonics of the oscillations in the power spectrum. With this, one can achieve better measurements of the acoustic scale for a given survey volume. Reconstruction is particularly effective at low redshift, where the non-linearities are worse but where the dark energy density is highest. At z=0.3, we find that one can reduce the sample variance error bar on the acoustic scale by at least a factor of 2 and in principle by nearly a factor of 4. We discuss the significant implications our results have for the design of galaxy surveys aimed at measuring the distance scale through the acoustic peak.

Figures (4)

• Figure 1: The cumulative variance in the differential motion of pairs initially separated by 150 Mpc as a function of cutoff wavenumber, normalized to the total variance. These curves are calculated in the Zel'dovich approximation according to the formulae in Eis06. The displacement along the separation vector is shown as the solid line; the displacement along a single direction perpendicular to the separation vector is shown as the dashed line. Most of the integral is supported by wavenumbers between 0.02 and 0.2$h{\rm\,Mpc}^{-1}$. The horizontal dashed line is drawn at 75%, where half of the rms displacement has been fixed.
• Figure 2: The matter power spectrum after reconstruction by the linear-theory density-velocity relation, with the density field Gaussian filtered. The bottom panel shows the real-space power spectrum; the top panel shows the spherically averaged redshift-space power spectrum. The black solid line shows the input power spectrum at $z=49$; it has been displaced in the top panel for clarity. The blue short-dashed line shows the matter power spectrum at $z=0.3$; one can see that acoustic peaks have been lost. In the bottom panel, the red dot-dashed line and magenta long-dashed line show the effects of reconstruction for $20h^{-1}{\rm\,Mpc}$ and $10h^{-1}{\rm\,Mpc}$ Gaussian filtering, respectively. In the top panel, both lines show $10h^{-1}{\rm\,Mpc}$ filtering; the red dot-dashed line is without finger of God compression, while the magenta long-dashed line includes compression. The increase of power at large wavenumbers is essentially irrelevant to the quality of the acoustic signature; one would in practice marginalize over these broadband changes.
• Figure 3: The real-space matter correlation function after reconstruction by the linear-theory density-velocity relation, with the density field Gaussian filtered. The black solid line shows the correlation function at $z=49$. The blue short-dashed line shows it at $z=0.3$; the acoustic peak has been smeared out. The red dot-dashed and magenta long-dashed lines show the effects of reconstruction for $20h^{-1}{\rm\,Mpc}$ and $10h^{-1}{\rm\,Mpc}$ Gaussian filtering, respectively. Even this very simple reconstruction recovers nearly all of the linear acoustic peak.
• Figure 4: The redshift-space matter correlation function after reconstruction by the linear-theory density-velocity relation, with the density field Gaussian filtered. The black solid line shows the correlation function at $z=49$. The blue short-dashed line shows the redshift-space correlation function at $z=0.3$; the acoustic peak has been smeared out. The black dotted line shows the real-space correlation function for comparison. The red dot-dashed line line shows the effects of reconstruction for a $10h^{-1}{\rm\,Mpc}$ Gaussian filtering; the magenta long-dashed line is the result when one compresses the fingers of God prior to the reconstruction. These reconstructions significantly improve the acoustic peak.