Dark energy and curvature from a future baryonic acoustic oscillation survey using the Lyman-alpha forest

TL;DR

This work forecasts the cosmological utility of a three-dimensional Ly$\alpha$ forest BAO survey to measure $D_A(z)$ and $H(z)$ in the range $2<z<4$ using a Fisher-matrix formalism, incorporating a physically motivated model for the Ly$\alpha$ flux power spectrum and realistic sampling/aliasing noise. It shows that a $\sim2000$ deg$^2$ survey with $g\lesssim23$ and $R>250$ can reach ~1.4\% precision on both radial and transverse BAO scales at $z\sim2.8$, with potential improvements to ~0.5\% if fainter sources are included; broader, shallower surveys can be more efficient at fixed time. The paper also analyzes both parametric dark energy models and non-parametric scale-based tests, finding that high-redshift BAO measurements are particularly valuable for constraining curvature and for breaking degeneracies when Planck priors are included. It concludes that Ly$\alpha$ BAO is a robust high-redshift probe with manageable systematics, and that a modest pilot survey (e.g., ~30 deg$^2$) could demonstrate the BAO signal in the Ly$\alpha$ forest, paving the way for substantial cosmological gains.

Abstract

We explore the requirements for a Lyman-alpha forest (LyaF) survey designed to measure the angular diameter distance and Hubble parameter at 2~<z~<4 using the standard ruler provided by baryonic acoustic oscillations (BAO). The goal would be to obtain a high enough density of sources to probe the three-dimensional density field on the scale of the BAO feature. A percent-level measurement in this redshift range can almost double the Dark Energy Task Force Figure of Merit, relative to the case with only a similar precision measurement at z~1, if the Universe is not assumed to be flat. This improvement is greater than the one obtained by doubling the size of the z~1 survey, with Planck and a weak SDSS-like z=0.3 BAO measurement assumed in each case. Galaxy BAO surveys at z~1 may be able to make an effective LyaF measurement simultaneously at minimal added cost, because the required number density of quasars is relatively small. We discuss the constraining power as a function of area, magnitude limit (density of quasars), resolution, and signal-to-noise of the spectra. For example, a survey covering 2000 sq. deg. and achieving S/N=1.8 per Ang. at g=23 (~40 quasars per sq. deg.) with an R~>250 spectrograph is sufficient to measure both the radial and transverse oscillation scales to 1.4% from the LyaF (or better, if fainter magnitudes and possibly Lyman-break galaxies can be used). At fixed integration time and in the sky-noise-dominated limit, a wider, noisier survey is generally more efficient; the only fundamental upper limit on noise being the need to identify a quasar and find a redshift. Because the LyaF is much closer to linear and generally better understood than galaxies, systematic errors are even less likely to be a problem.

Figures (6)

• Figure 1: Upper thick lines show constraints as a function of g magnitude limit on the radial and transverse BAO scales for a survey similar to the proposed WFMOS low-z galaxy survey 2005astro.ph..7457G, assuming 2000 sq. deg. and R=2000. Magnitude limits (21, 22, 23, 24, 25) correspond to (8, 20, 41, 77, 136) quasars per sq. deg. for the 2006astro.ph..2569J luminosity function, and we assume S/N=(11, 4.5, 1.8, 0.7, 0.3) per Å. Lower thick curves add spectra from LBGs. Thin lines show the completely unrealistic case where we ignore the aliasing-like noise power caused by discrete sampling.
• Figure 2: Error bars show the fractional error on the power in bands of $\Delta k=0.02 \, h\, {\rm Mpc}^{-1}$, for the $g<25$ case from Fig. \ref{['wfmoswide']} (without LRGs). Lines show the ratio of Ly$\alpha$ forest flux power for $\Omega_b=0.0462$ to $\Omega_b=0.001$. Black (solid line, error bars shifted slightly right) shows $\mu=k_\parallel/k>2/3$, red (dashed) shows $1/3<\mu<2/3$, and green (dotted, error bars shifted left) shows $\mu<1/3$. For comparison, the thin line shows the ratio of power without aliasing noise (renormalized for clarity).
• Figure 3: Similar to Fig. \ref{['wfmoswide']}, except covering 300 sq. deg. with longer exposures, following the high-z galaxy survey proposed in 2005astro.ph..7457G. g magnitude limits (21, 22, 23, 24, 25) correspond to S/N=(32, 13, 5.1, 2.0, 0.8) per Å.
• Figure 4: Similar to Fig. \ref{['wfmoswide']}, but investigating the effect of the trade-off between noise and area. From top to bottom (black, blue, cyan, green, magenta, red) we show, at g=22.5, S/N=(5.7, 4.1, 2.9, 2.0, 1.4, 1.0) per Å. The results improve with decreasing S/N because in each case the area of the survey is $A=2000~(2.9~N/S)^2$ sq. deg., assuming sky-dominated noise. Errors scale as $A^{-1/2}$.
• Figure 5: Similar to Fig. \ref{['wfmoswide']}, but investigating the effect of the changing the noise level at fixed 2000 sq. deg. survey area. From bottom to top (black, blue, cyan, green, magenta, red, black) we show, at g=22.5, S/N=(5.7, 4.1, 2.9, 2.0, 1.4, 1.0, 0.72) per Å.