Test the fluke hypothesis using E-mode data
Check if CMB temperature anomalies are simply a rare realization of the ΛCDM model, using future CMB polarization observations.
References:
I thank Tony Banday for detailed explanations.
The cosmic microwave background (CMB) temperature (T) anisotropy pattern shows deviations from the ΛCDM model at a 2-3 sigma level. This raises a key question: are these deviations simply a rare, though not impossible, realization of the ΛCDM model, i.e. the “fluke hypothesis”, or do they signal a failure of the model itself?
Our goal is to use CMB polarization anisotropies to test whether the T pattern is not compatible with a rare ΛCDM realization. In particular, since the fluctuations in the CMB temperature and in its polarization arise largely from the same source – the gravitational potential – one might have hoped that an anomaly in T modes would predict a similar anomaly in E modes, or in the cross-correlation between CMB temperature and polarization (TE).
In this approach, we trust the ΛCDM model and simply test if our observed CMB T map, while rare, is consistent with it. We follow the methodology outlined in Copi et al. (2013). First, we choose a suitable estimator (SE) based on CMB polarization and build its distribution using unconstrained ΛCDM simulations. We then build the same SE for a distribution of ΛCDM polarization simulations that are constrained by the Planck T observations. This second distribution, which can be seen as a deformation of the one obtained with unconstrained simulations, represents what we would expect to see in polarization if the observed T map is a rare but compatible ΛCDM realization.
The core idea is straightforward: if future CMB polarization observations are found to be incompatible with the constrained SE distribution, the fluke hypothesis is ruled out. Conversely, if future polarization observations are compatible, the observed T pattern is consistent with the fluke hypothesis and no definitive conclusion can be drawn.
Since we assume ΛCDM holds, the probability of ruling out the fluke hypothesis is calculated by finding the area of the unconstrained distribution that is not compatible with the constrained one. Actually, we mean how likely the independent polarization observations from a future experiement (that follows the unconstrained SE distribution assuming ΛCDM holds) are incompatible with previous Planck T observations.
This computation is useful only for assessing the estimator’s efficiency. For example, we could choose the hyperparameters (e.g., the multipole range) of the SE so that the largest fraction of unconstrained realizations fall above the value at some (99% or 99.9%) confidence level in constrained realizations. With real data of future experiments, the analysis will simply compare the observations directly with the constrained simulations.