*by Massimo Giovannini.*

**Which is the origin of the temperature and polarization anisotropies of the Cosmic Microwave Background? Classical or quantum? The temperature and the polarization anisotropies of the Cosmic Microwave Background (CMB) are customarily explained in terms of large-scale curvature inhomogeneities. Are curvature perturbations originally classical or are they inherently quantum mechanical, as speculated many years ago by Sakharov?
**

In the conventional view these questions are quickly dismissed since the quantum origin of large-scale curvature fluctuations is, according to some, an indisputable fact of nature. This is true if and when the Universe inflates and the space-time curvature is almost constant (or slightly decreasing). Since the classical fluctuations are suppressed during inflation, the only candidates for the initial conditions of large-scale curvature inhomogeneities are the quantum fluctuations of the inflation, i.e. the scalar field that drives the expansion rate.

Inflation is however only a paradigm which has been successful so far, but whose tests have only been indirect. After thinking about these issues I realized in 2011 that a very similar problem arose in the field of quantum optics, namely the study of the effects and properties of the electromagnetic radiation in the visible range of frequencies. The classical and the quantum features of visible light are distinguished by looking at the coherence properties of the radiation field. Until the mid-1950s of the past century the only tool to investigate the coherence of visible radiation was the analysis of amplitude correlations: a field was said to be coherent when the interference fringes are maximized in a Young-type (two-slit) correlation experiment. Starting in 1955 Hanbury Brown and Twiss developed a new type of interferometry: the idea was to study the correlations of the intensities rather than the correlations of the amplitudes of the electric fields (like in the Young-type experiment). The study of the correlations of the intensities (which are quadratic in the amplitudes) is now dubbed Hanbury-Brown Twiss (HBT) effect. The applications of HBT interferometry are today essential for different areas: stellar astronomy, quantum optics, nuclear and subatomic physics all deal with intensity correlations for different purposes, which are however conceptually related.

In the early sixties the quantum theory of optical coherence has been developed by Roy Glauber with essential contributions coming from Sudarshan, Mandel and Wolf. One of the purposes of the quantum theory of optical coherence is the correct interpretation of the HBT effect. The Glauber theory of optical coherence is today employed to distinguish the statistical properties of classical and quantum radiation fields. Similar ideas can be translated from the optical frequencies to the other branches of the electromagnetic spectrum.

In a paper recently published in Classical and Quantum Gravity (“Glauber theory and the quantum coherence of curvature inhomogeneities”) the idea has been to use the Glauber approach for the analysis of the statistical properties of curvature inhomogeneities with the ultimate purpose of understanding if their origin can be proved (and not simply assumed) to be quantum mechanical. This paper follows another paper published in 2011 (“Hanbury Brown–Twiss interferometry and second-order correlations of inflaton quanta” Phys. Rev. D 83, 023515 (2011)) where the tenets of HBT interferometry have been applied for the first time to the curvature inhomogeneities.

One of the main results of the applications of Glauber theory to curvature inhomogeneities is surprising: the degree of second-order coherence does not seem to describe unambiguously the correlation properties of large-scale curvature perturbations. Since Glauber theory allows for a systematic scrutiny of the higher-order correlations, I argued that the analysis of the degrees of third- and fourth-order coherence is necessary to assess the statistical properties of curvature inhomogeneities and their plausible quantum origin. Similar conclusions have been recently drawn in a quantum optical context, where higher-order autocorrelations are mandatory for characterizing the multiphoton nature of nonclassical light.

All in all, the statistical properties of the quantum states can be disambiguated by examining the higher degrees of coherence. The applications of the Glauber theory to large-scale curvature inhomogeneities mirror a rich experimental endeavour aimed at developing photon counting experiments for microwave frequencies. To begin with, a potential target for the new generations of CMB detectors can be the Hanbury Brown-Twiss interferometry in the THz region with the hope of resolving the features of the last scattering surface. While this possibility seems rather interesting, there are some who might object that an improved statistical accuracy in the determination of the parameters of the concordance paradigm should be the primary target of future experimental endeavours. This debate is potentially interesting for the CMB experiments which are now at the stage of discussion and will be planned for the incoming decade. In spite of the future observational priorities, in the years to come the CMB will be scrutinised with ever increasing precision and, in this quest,

it will inevitably meet quantum mechanics.

*Read the full article in Classical and Quantum Gravity:
Glauber theory and the quantum coherence of curvature inhomogeneities*

*M Giovannini 2017 Class. Quantum Grav.*

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