Cosmological parameters after WMAP5: forecasts for Planck and future galaxy surveys

TL;DR

This paper provides a comprehensive forecast of Planck's cosmological parameter constraints relative to WMAP5, using simplified mock data and MCMC techniques to quantify performance under different channel combinations and model spaces. It shows that Planck can improve most parameter precisions by a factor of 3–4 (and the tensor-to-scalar ratio by ~9×), with strong gains when including BB polarization for r, and with high-l TT data crucial for n_s and Ω_b. The analysis emphasizes that data-analysis choices (foreground cleaning, beam calibration) and the inclusion of B-modes critically affect the results, and highlights that Planck will greatly enhance the returns of future galaxy surveys (LSST, CIP) by breaking degeneracies in curvature, dark energy, inflationary parameters, and neutrino properties. The work underscores the importance of Planck as a foundation for multi-probe cosmology, enabling tighter constraints on inflationary physics, the matter content of the Universe, and the nature of dark energy when combined with external datasets.

Abstract

The Planck satellite is expected to improve the measurement of most cosmological parameters by several factors with respect to current WMAP results. The actual performance may depend upon various aspects of the data analysis. In this paper we analyse the impact of specifics of the data analysis on the actual final results. We also explore the synergies in combining Planck results with future galaxy surveys. We find that Planck will improve constraints on most cosmological parameters by a factor 3-4 and on the tensor-to-scalar ratio r by a factor 9. Also inflationary parameters, like r, n_s and n_run, are no longer degenerate. The tensor spectral index, however, is little constrained. A combination of the 70 to 143 GHz channels will contain ~90% of all possible information, with 143 GHz polarisation information carrying about half of the constraining power on r. Also, the error on r degrades by a factor 2 if no B modes are included in the analysis. High-l temperature information is essential for determination of n_s and Ω_b, while improving noise properties increase the l-range where Planck would be cosmic variance limited in polarisation, with a significant improvement on the determination of r, τand A_s. However, a sub-percent difference in the FWHM used in the data analysis with respect to the one in the map will result in a bias for several parameters. Finally, Planck will greatly help future missions like LSST and CIP reach their potentials by providing tight constraints on parameters like n_s and n_run. Considering Planck together with these probes will help in breaking degeneracies between Ω_K and Ω_Λor Ω_dm and f_ν, resulting in improvements of several factors in the error associated to these parameters.

Figures (15)

• Figure 1: Marginalised distributions and joint 2D confidence regions for the base fiducial model analysed assuming a combination of $70, 100$ and $143$ GHz Planck channels (blue/cyan lines) or WMAP 5yr specifications (red/orange lines). The 2D plots show the $1$-- and $2$--$\sigma$ regions; crosses mark the input values for the parameters.
• Figure 2: Planck sensitivity to the fiducial $C_l$ spectra for different channels or channels combinations. Thick lines show the signal--to--noise ratio, thin lines show the Cosmic Variance--to--noise ratio. Left panel shows sensitivity to the TT spectrum, right panel is for the EE spectrum.
• Figure 3: Left:Sensitivity to the different parameters as a function of the maximum multipole considered in the analysis. Plot shows error estimates for the various parameters as a function of $\ell_{\rm max}$ considered in the analysis, normalised to the error for $\ell_{\rm max} = 800$. Heavy lines are for the combination of the $70, 100, 143$ and $217$GHz Planck channels, thin lines are for an ideal experiment with cosmic variance temperature measurements and polarization sensitivity equal to the Planck configuration considered here. It is clear that up to $\ell_{\rm max} \sim 1500$ a CVL experiment would not offer a significant advantage over Planck. Right : Impact of higher sensitivity polarization data on parameter constraints. Plot shows parameter estimates for an ideal experiment with CVL polarization data up to $\ell_{\rm CV}$ and sensitivity equal to Planck $70 - 217$ GHz channels for $\ell \ge \ell_{\rm CV}$. Error estimates are normalised to Planck estimates, corresponding to $\ell_{\rm CV} = 2$.
• Figure 4: Impact of $B$--modes detection on the determination of the tensor--to--scalar ratio, $r$, for different fiducial values of $r$. For $r > 0$ bars show the expected $1\sigma$ error on the tensor--to--scalar ratio including (blue) or excluding (gold) $B$--modes in the analysis. For a fiducial $r= 0$ bars show the upper $95 \%$ c.l. instead. If $B$--modes information is not available, error on $r$ increase by a factor $\sim 2$. Notice that for $r \la 0.10$, the corresponding marginalised distribution is markedly non--Gaussian and quoting the standard deviation does not properly characterise the $1\sigma$ confidence interval. Results shown are for the $70 - 143$ GHz channels combination.
• Figure 5: Impact of small angular scales on parameter determination. Histograms shows the uncertainties on $\omega_{\rm b}$, $n_{\rm s}$ and $\theta$ for nominal beams (left bar), beam enlarged by $10\%$ (middle) or by $30 \%$ (right). For each parameter, the left panel refers to the $70 - 143$GHz channels, the right panel is for $70 - 217$ GHz channels.