The cosmological constant and general isocurvature initial conditions

TL;DR

This work investigates whether a nonzero cosmological constant is required by present CMB and LSS data when general isocurvature initial conditions are allowed, and contrasts Bayesian and frequentist analyses. The authors show that the COBE-normalized matter power spectrum is dominated by the adiabatic mode, breaking degeneracies among initial conditions and keeping the matter spectrum largely insensitive to isocurvature contributions. In flat universes, Bayesian inference favors $\Omega_{\Lambda} \neq 0$ at >$3\sigma$, whereas the frequentist approach allows $\Omega_{\Lambda}=0$ within ~3$\sigma$ for low $h$; these conclusions persist even when isocurvature modes are included. When isocurvature modes are allowed, CMB+LSS data still constrain $\Omega_{\Lambda}$ strongly in the Bayesian framework, though the limits broaden, while the COBE-normalized matter spectrum remains AD-dominated, limiting the impact of isocurvature components on large-scale structure. Overall, the study emphasizes the importance of statistical framework in cosmological parameter inference and demonstrates that, under the models considered, a cosmological constant remains a robust feature in Bayesian analysis, with nuances arising in non-Bayesian interpretations and non-flat geometries.

Abstract

We investigate in detail the question whether a non-vanishing cosmological constant is required by present-day cosmic microwave background and large scale structure data when general isocurvature initial conditions are allowed for. We also discuss differences between the usual Bayesian and the frequentist approaches in data analysis. We show that the COBE-normalized matter power spectrum is dominated by the adiabatic mode and therefore breaks the degeneracy between initial conditions which is present in the cosmic microwave background anisotropies. We find that in a flat universe the Bayesian analysis requires Ω_Λ\neq 0 to more than 3 σ, while in the frequentist approach Ω_Λ= 0 is still within 3 σfor a value of h < 0.48. Both conclusions hold regardless of initial conditions.

Figures (9)

• Figure 1: Joint likelihood contours (Bayesian), with CMB only (solid lines, showing $1 \sigma$, $2 \sigma$, $3 \sigma$ contours) and CMB+LSS (filled) for purely adiabatic initial conditions.
• Figure 2: Confidence contours (frequentist) with CMB only (solid lines, $1 \sigma$, $2 \sigma$, $3 \sigma$ contours and $F_{\rm eff} = 31$) and CMB+LSS (filled, $F_{\rm eff} = 50$) for purely adiabatic initial conditions.
• Figure 3: Best fit with $\Omega_{\Lambda} = 0$ and purely AD initial conditions, compatible with CMB and LSS data within $2 \sigma$ confidence level. In the lower panel, only the 2dF data points left of the vertical, dotted line --- i.e., in the linear region --- have been included in the analysis. Note the low first acoustic peak due to the joint effect of the red spectral index and of the absence of early ISW effect. In this fit, the calibration of BOOMERanG (red errorbars) and Archeops (blue errorbars) has been reduced by $34\%$ and $26\%$, respectively. This is more than 3 times the quoted $1 \sigma$ calibration errors for both experiments. To appreciate the difference, we plot the non recalibrated value of the BOOMERanG and Archeops data points as light blue and magenta crosses, respectively. In the upper panel, green errorbars are the COBE measurements. Even though the fit is "by eye" very good, it seems highly unlikely that the calibration error is so large.
• Figure 4: Joint likelihood contours (Bayesian) with general isocurvature initial conditions, with CMB only (solid lines, $1 \sigma$, $2 \sigma$, $3 \sigma$) and CMB+LSS (filled). The disconnected $1\sigma$ region is an artificial feature due to the grid resolution.
• Figure 5: Dark matter power spectra of the different auto- (upper panel) and cross-correlators (lower panel) for a concordance model with $\Omega_{\Lambda} = 0.70$, $h = 0.65$, $n_{\rm S} = 1.0$, $\omega_{\rm b} = 0.020$, with the corresponding CMB power spectrum COBE-normalized (see the text for details). The color codes are as follows: in the upper panel, AD: solid/black line, CI: dotted/green line, NID: short-dashed/red line, NIV: long-dashed/blue line; in the lower panel, AD: solid/black line (for comparison), $<{\rm AD},{\rm CI}>$: long-dashed/magenta line, $<{\rm AD},{\rm NID}>$: dotted/green line, $<{\rm AD},{\rm NIV}>$: short-dashed/red line, $<{\rm CI},{\rm NID}>$: dot-short dashed/blue line, $<{\rm CI},{\rm NIV}>$: dot-long dashed/light-blue line, and $<{\rm NID},{\rm NIV}>$: solid/yellow line. The adiabatic mode is by far dominant over all others.