Open and closed CDM isocurvature models contrasted with the CMB data

TL;DR

The paper evaluates whether pure isocurvature CDM perturbations in open or closed universes can fit the CMB data as well as the flat adiabatic model. It performs a comprehensive six-parameter search over $n_{\rm iso}$, $\Omega_m$, $\Omega_\Lambda$, $\omega_b$, $\omega_c$, and normalization using CAMB to generate spectra and a $\chi^2$-based comparison against COBE, Boomerang, and Maxima-1, including a large-scale-structure constraint via $\sigma_8\Omega_m^{0.56}$. The main finding is that all pure isocurvature scenarios yield significantly larger $\chi^2$ values (best around $80$–$121$) than the flat adiabatic benchmark ($\chi^2=44$), with the Boomerang data in particular incompatible with the isocurvature peak structure; hence pure isocurvature CDM models are strongly disfavored by current data. This strengthens the case for adiabatic initial conditions and demonstrates that non-flat, purely isocurvature models cannot reproduce the observed CMB peak pattern and large-scale structure.

Abstract

We consider pure isocurvature cold dark matter models in the case of open and closed universe. We allow for a large spectral tilt and scan the 6-dimensional parameter space for the best fit to the COBE, Boomerang, and Maxima-1 data. Taking into account constraints from large-scale structure and big bang nucleosynthesis, we find a best fit with $χ^2 = 121$, which is to be compared to $χ^2 = 44$ of a flat adiabatic reference model. Hence the current data strongly disfavour pure isocurvature perturbations.

Figures (3)

• Figure 1: The best-$\chi^2$ contours on the $(\Omega_m,\Omega_\Lambda)$ plane. The best fit, which has $\chi^2=80$, is indicated by an asterisk ($\ast$) near to the lower right corner. The contours for deviation from the best fit are as follows: white $\Delta\chi^2 < 10$; light gray $10 < \Delta\chi^2 < 40$; medium gray $40 < \Delta\chi^2 < 100$; and dark gray $\Delta\chi^2 > 100$. (a) Dashed lines show the position ($\ell$) of the first acoustic peak and solid lines the second peak. (b) Solid lines give the values of $\sigma_8\Omega_m^{0.56}$, and the dotted area is that allowed by the LSS constraint $0.43 < \sigma_8\Omega_m^{0.56} < 0.70$.
• Figure 2: (a) As Fig. \ref{['fig:2']}(a) but now with the LSS constraint $0.43 < \sigma_8\Omega_m^{0.56} < 0.70$. The best fit marked by an asterisk has $\chi^2=103$. The contours for deviation from the best fit are as follows: white $\Delta\chi^2 < 35$; light gray $35 < \Delta\chi^2 < 140$; medium gray $140 < \Delta\chi^2 < 350$; and dark gray $\Delta\chi^2 > 350$. The upper left corner corresponds to the closed models where the second acoustic peak fits the prominent peak in the $C_\ell$ data. (b) The best-fit physical region using the fine grid. The solid contours show the baryon density $\omega_b$. The best-fit model has $\chi^2 = 121$ and the gray levels are as follows: white $\Delta\chi^2 < 6$; light gray $6 < \Delta\chi^2 < 30$, medium gray $30 < \Delta\chi^2 < 60$, and dark gray $\Delta\chi^2 > 60$.
• Figure 3: Angular power spectra for different models along with COBE ($\diamond$), Boomerang ($\bullet$) , and Maxima-1 ($\circ$) data. (a) Best-fit isocurvature model of Fig. \ref{['fig:1']} (solid line) and best-fit open model with LSS constraint (dashed line). (b) Best physical isocurvature fit from the fine grid (solid line) and the adiabatic reference model (dashed line). Note that up to $\ell=25$ the $\ell$ axis is logarithmic.