A Low CMB Quadrupole from Dark Energy Isocurvature Perturbations

TL;DR

This paper investigates the unusually low CMB quadrupole by proposing a dark-energy isocurvature mechanism with anticorrelated perturbations (A&I) that can coherently cancel the Sachs-Wolfe contribution via a dark-energy ISW effect. Through transfer-function analysis, it shows that the SW quadrupole can be sharply suppressed while largely preserving polarization, making TE and EE spectra key discriminants. A likelihood analysis with WMAP data favors negative isocurvature amplitudes (S_i \approx -12 to -15) at about the $95\%$ CL for a flat, scale-invariant model, though polarization data temper the inferred amplitude. The inflationary realization of such perturbations faces a severe gravitational-wave constraint, suggesting that simple inflation-based generation of A&I is disfavored, while alternative explanations like a cut-off in the primordial spectrum have distinct polarization signatures. Overall, the study provides a concrete, testable framework linking dark-energy perturbations to large-angle CMB anomalies and highlights polarization as the decisive probe for distinguishing among competing scenarios.

Abstract

We explicate the origin of the temperature quadrupole in the adiabatic dark energy model and explore the mechanism by which scale invariant isocurvature dark energy perturbations can lead to its sharp suppression. The model requires anticorrelated curvature and isocurvature fluctuations and is favored by the WMAP data at about the 95% confidence level in a flat scale invariant model. In an inflationary context, the anticorrelation may be established if the curvature fluctuations originate from a variable decay rate of the inflaton; such models however tend to overpredict gravitational waves. This isocurvature model can in the future be distinguished from alternatives involving a reduction in large scale power or modifications to the sound speed of the dark energy through the polarization and its cross correlation with the temperature. The isocurvature model retains the same polarization fluctuations as its adiabatic counterpart but reduces the correlated temperature fluctuations. We present a pedagogical discussion of dark energy fluctuations in a quintessence and k-essence context in the Appendix.

Figures (12)

• Figure 1: The quadrupole transfer function in the fiducial adiabatic model (see text). The temperature quadrupole receives Sachs-Wolfe (SW) contributions peaking around $k=0.0002$ Mpc$^{-1}$ and Integrated Sachs-Wolfe (ISW) contributions peaking around $k=0.001$ Mpc$^{-1}$ but extending to $k\sim 0.01$ Mpc$^{-1}$. The ISW effect arises from the dark energy dominated regime $z \lesssim 1$. The polarization arises through rescattering of quadrupole anisotropies at $z > 1$ and hence reflects the SW contributions. The cross correlation is proportional to the product of the transfer functions.
• Figure 2: Temperature power spectrum in the fiducial model compared with the data from the first year WMAP release Ver03. Bands are 68% and 95% cosmic variance confidence regions (see text).
• Figure 3: Time evolution of gravitational potential $\Phi$ and quadrupole $T_2^\Theta$ in the fiducial adiabatic model compared an adiabatic plus isocurvature model with $S_{i} \equiv \delta_{Qi}/\zeta_{i}=-15$ (A&I; see § \ref{['sec:isocurvaturemodel']}). (a) $k=0.0002$ Mpc$^{-1}$ SW dominated mode. In the adiabatic model, the decay of the potential at $z\lesssim 1$ has little effect on the quadrupole due to the inefficiency in the transfer represented by $j_2$. A much larger change of $\Delta \Phi \sim -\zeta_i$ from the isocurvature perturbation can cancel the SW quadrupole. (b) $k=0.001$ Mpc$^{-1}$ ISW dominated mode. The adiabatic potential decay transfers efficiently onto the quadrupole moment. The additional isocurvature perturbations decay by dark energy domination and have little effect (see Fig. \ref{['fig:qevol']}).
• Figure 4: Isocurvature dark energy density perturbation evolution for a nearly frozen background quintessence field (see text). On superhorizon scales the comoving gauge density perturbation remains frozen at nearly its initial value. On subhorizon scales, the pressure gradients associated with field fluctuations cause the density perturbation to oscillate and decay. Also shown are the dark energy equation of state $w_Q = p_Q/\rho_Q$ and the adiabatic sound speed squared $c_a^2 = \dot p_Q /\dot \rho_Q$ (not to be confused with the effective sound speed $c_e=1$) which indicate the field is Hubble drag dominated until recently (see Appendix).
• Figure 5: Quadrupole transfer functions in the fiducial adiabatic model ("A") and a model with additional isocurvature perturbations of $S_{i}=-15$ ("A&I"). The isocurvature ISW effect (iISW) cancel the SW effect for the temperature quadrupole from large scales while leaving the polarization nearly unchanged.