Inflationary spectra and violations of Bell inequalities

In spite of the macroscopic character of the primordial fluctuations, the standard inflationary distribution (that obtained using linear mode equations) exhibits inherently quantum properties, that is, properties which cannot be mimicked by any stochastic distribution. This is demonstrated by a Gedanken experiment for which certain Bell inequalities are violated. These violations are in principle measurable because, unlike for Hawking radiation from black holes, in inflationary cosmology we can have access to both members of correlated pairs of modes delivered in the same state. We then compute the effect of decoherence and show that the violations persist provided the decoherence level (and thus the entropy) lies below a certain nonvanishing threshold. Moreover, there exists a higher threshold above which no violation of any Bell inequality can occur. In this regime, the distributions are “separable” and can be interpreted as stochastic ensembles of fluctuations. Unfortunately, the precision which is required to have access to the quantum properties is so high that, in practice, an observational verification seems excluded.

Figure 1

The loss of violation as decoherence increases. We have represented $\mathcal{C}(v,-v,\delta )$ as a function of $x=|v{|}^2$ for $n=100$ and for three values of $\delta$: 0 (upper), 0.05 (middle), and 0.1 (lower). The horizontal line ($\mathcal{C}=1$) is the maximal value allowed by classically correlated states.