Space-time correlations within pairs produced during inflation, a wave-packet analysis

In homogeneous universes the propagation of quantum fields gives rise to pair creation of quanta with opposite momenta. When computing expectation values of operators, the correlations between these quanta are averaged out and no space-time structure is obtained. In this article, by an appropriate use of wave packets, we reveal the space-time structure of these correlations. We show that every pair emerges from vacuum configurations which are torn apart so as to give rise to two semi-classical currents: that carried by the particle and that of its `partner'. The partner's current lives behind the Hubble horizon centered around the particle. Hence any measurement performed within a Hubble patch would correspond to an uncorrelated density matrix, as for Hawking radiation. However, when inflation stops, the Hubble radius grows and eventually encompasses the partner. When this is realized the coherence is recovered within a patch. Our analysis applies to rare pair creation events as well as to cases leading to arbitrary high occupation numbers. Hence it might be applied to primordial gravitational waves which evolve into highly squeezed states.Comment: discussion clarified, acknowledgements and references added, version accepted in PR

Quantum correlations in inflationary spectra and violation of Bell inequalities

In spite of the macroscopic character of the fluctuation amplitudes, we show that the standard inflationary distribution of primordial density fluctuations still exhibits inherently quantum mechanical correlations (which cannot be mimicked by any classical stochastic ensemble). To this end, we propose a Gedanken experiment for which certain Bell inequalities are violated. We also compute the effect of decoherence and show that the violation persists provided that the decoherence lies below a certain non-vanishing threshold. Moreover, there exists a higher threshold above which no violation of any Bell inequalities can occur, so that the corresponding distributions can be interpreted as stochastic ensembles of classical fluctuations.Comment: Proceedings of the conference "100 years in relativity", Sao Paulo, August 22-24. To appear in a special issue of the Brazilian Journal of Physics (BJP

Decoherence and entropy of primordial fluctuations. I: Formalism and interpretation

We propose an operational definition of the entropy of cosmological perturbations based on a truncation of the hierarchy of Green functions. The value of the entropy is unambiguous despite gauge invariance and the renormalization procedure. At the first level of truncation, the reduced density matrices are Gaussian and the entropy is the only intrinsic quantity. In this case, the quantum-to-classical transition concerns the entanglement of modes of opposite wave-vectors, and the threshold of classicality is that of separability. The relations to other criteria of classicality are established. We explain why, during inflation, most of these criteria are not intrinsic. We complete our analysis by showing that all reduced density matrices can be written as statistical mixtures of minimal states, the squeezed properties of which are less constrained as the entropy increases. Pointer states therefore appear not to be relevant to the discussion. The entropy is calculated for various models in paper II.Comment: 23 page

Reactive Atom Plasma (RAP) figuring machine for meter class optical surfaces

A new surface figuring machine called Helios 1200 is presented in this paper. It is designed for the figuring of meter sized optical surfaces with form accuracy correction capability better than 20 nm rms within a reduced number of iterations. Unlike other large figuring facilities using energy beams, Helios 1200 operates a plasma torch at atmospheric pressure, offers a high material removal rate, and a relatively low running cost. This facility is ideal to process large optical components, lightweight optics, silicon based and difficult to machine materials, aspheric, and free form surfaces. Also, the surfaces processed by the reactive atom plasma (RAP) are easy to fine polish through hand conventional sub-aperture polishing techniques. These unique combined features lead to a new capability for the fabrication of optical components opening up novel design possibilities for optical engineers. The key technical features of this large RAP machine are fast figuring capabilities, non-contact material removal tool, the use of a near Gaussian footprint energy beam, and a proven tool path strategy for the management of the heat transfer. Helios 1200 complies with the European machine safety standard and can be used with different types of reactive gases using either fluorine or chlorine compounds. In this paper, first the need for large optical component is discussed. Then, the RAP facility is described: radio frequency R.F generator, plasma torch, and 3 axis computer numerically controlled motion system. Both the machine design and the performance of the RAP tool is assessed under specific production conditions and in the context of meter class mirror and lens fabrication

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 {\it 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 non-vanishing 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, {\it in practice}, an observational verification seems excluded.Comment: 5 pages, 1 figure; new presentation and extended discussio

Decoherence and entropy of primordial fluctuations II. The entropy budget

We calculate the entropy of adiabatic perturbations associated with a truncation of the hierarchy of Green functions at the first non trivial level, i.e. in a self-consistent Gaussian approximation. We give the equation governing the entropy growth and discuss its phenomenology. It is parameterized by two model-dependent kernels. We then examine two particular inflationary models, one with isocurvature perturbations, the other with corrections due to loops of matter fields. In the first model the entropy grows rapidely, while in the second the state remains pure (at one loop).Comment: 28 page