Bounds on CDM and neutrino isocurvature perturbations from CMB and LSS data

TL;DR

The paper investigates bounds on cold dark matter/baryon and neutrino isocurvature perturbations using CMB, LSS, and SN data within a mixed adiabatic–isocurvature framework. It employs a Bayesian likelihood approach over a 13-parameter space (amplitudes, tilts, and cross-correlation) with a pivot scale $k_0=0.05~{\rm Mpc}^{-1}$, neglecting spatial curvature and tensor modes. The results show no significant improvement from including isocurvature components; at 2$\sigma$, the isocurvature fraction bounds are $\alpha_{\rm CDI}<0.60$, $\alpha_{\rm NID}<0.40$, and $\alpha_{\rm NIV}<0.30$, with a tendency toward blue isocurvature tilts when Lyman-$\alpha$ data are omitted. They also translate these bounds to two-field inflation models, finding only loose constraints on the mass ratio (e.g., $R>5$ excluded at $2\sigma$), and discuss how future Planck-like data could tighten or reveal isocurvature components.

Abstract

Generic models for the origin of structure predict a spectrum of initial fluctuations with a mixture of adiabatic and isocurvature perturbations. Using the observed anisotropies of the cosmic microwave backgound, the matter power spectra from large scale structure surveys and the luminosity distance vs redshift relation from supernovae of type Ia, we obtain strong bounds on the possible cold dark matter/baryon as well as neutrino isocurvature contributions to the primordial fluctations in the Universe. Neglecting the possible effects of spatial curvature and tensor perturbations, we perform a Bayesian likelihood analysis with thirteen free parameters, including independent spectral indexes for each of the modes and for their cross-correlation angle. We find that around a pivot wavenumber of k=0.05 h/Mpc the amplitude of the correlated isocurvature component cannot be larger than about 60% for the cold dark matter mode, 40% for the neutrino density mode, and 30% for the neutrino velocity mode, at 2 sigma. In the first case, our bound is larger than the WMAP first-year result, presumably because we prefer not to include any data from Lyman-alpha forests, but then obtain large blue spectral indexes for the non-adiabatic contributions. We also translate our bounds in terms of constraints on double inflation models with two uncoupled massive fields.

Figures (5)

• Figure 1: The one-dimensional likelihood functions for our basis of eleven independent cosmological parameters (not including the tilts of the two redshift surveys), for the adiabatic mode alone (AD) or mixed with the three different types of isocurvature modes (AD+CDI, AD+NID, AD+NIV). The first seven parameters are those of the standard $\Lambda$CDM model, extended to dark energy with a constant equation of state. The last four parameters $(\alpha, \beta, n_{\rm iso}, \delta_{\rm cor})$ describe the isocurvature initial conditions. ($\delta_{\rm cor}$ is define in Eq. (\ref{['eqdeltancor']}.))
• Figure 2: Continuation of figure \ref{['1Dplots']}, showing the 1D likelihood of some derived cosmological parameters, for the same cases. These likelihoods should be considered with care, because the parameters shown here do not belong to the basis used by the Markov chain algorithm. Therefore, the shape of the above likelihoods depends not only on the likelihood of the underlying parameters, but also on the properties of the functions relating them to the parameters of the basis. This explains for instance why $n_{\rm cor}=\delta_{\rm cor} \, \ln(|\beta|^{-1})$ seems to be well-constrained, while $\delta_{\rm cor}$ and $\beta$ are not.
• Figure 3: The 2-$\sigma$ contours of $\alpha$ and the cross-correlated mode coefficient $2 \beta\sqrt{\alpha(1-\alpha)}$, for a) the CDI isocurvature mode; b) the NID mode; c) the NIV mode; d) the CDI mode, with the constraint $n_{\rm cor}=0$ and the contours of equal $2(R^2-1)/s_k=0, \pm 0.5, \pm 1, \pm 2$ from double inflation.
• Figure 4: Temperature, E-polarization and matter power spectra for two particular CDI and NID models. In order to get a better understanding of our bounds, we chose here two models with large values of $\alpha$, still allowed at the 2-$\sigma$ level: respectively, $\alpha=0.53$ and $\alpha=0.41$. Other parameter values are for the CDI (resp. NID) model: $\omega_{\rm B}=0.0217$ (0.0196), $\omega_{\rm cdm}=0.112$ (0.131), $\theta=1.06$ (1.01), $\tau=0.068$ (0.131), $w=-0.88$ (-1.44), $n_{\rm ad}=0.96$ (1.02), $n_{\rm iso}=2.93$ (2.95), $n_{\rm cor}=0.05$ (0.03), $\ln[10^{10}{\cal R}_{\rm rad}]=3.73$ (3.98), $\beta=-0.62$ (0.88). The $\chi^2$ of the two models is respectively 1675 and 1674. From top to bottom, we show the $C_l^{\rm TT}$, $C_l^{\rm TE}$ and $P(k)$ power spectra, as well as the contribution of each component: adiabatic, isocurvature, cross-correlated, total. The CDI isocurvature and cross-correlated components have been rescaled by a factor indicated in each figure. We also show the data points that we use throughout the analysis, from WMAP (black), ACBAR (grey), CBI (blue), VSA (yellow), 2dF (black) and SDSS (blue). In the case of the matter power spectrum, one should not trust a "$\chi^2$-by-eye" comparison with the data: first, because the spectrum has to be convolved with the experimental window function before the comparison (this changes its slope significantly); second, because we show here the data points before rescaling by the two bias factors, which are left arbitrary for each experiment.
• Figure 5: The values of parameters $\alpha$ and $\beta$ as a function of the angle $\theta$, for different values of the ratio $R=m_1/m_2$ in double inflation.