Quantum Squeezing and Cosmological Entropy Production†

The entropy growth in a cosmological process of pair production is completely determined by the associated squeezing parameter, and is insensitive to the number of particles in the initial state. The total produced entropy may represent a significant fraction of the entropy stored today in the cosmic black-body radiation, provided pair production originates from a change in the background metric at a curvature scale of the Planck order. To appear in Class. Quantum Grav. CERN-TH.6954/93 July 1993 † Essay written for the 1993 Awards for Essays on Gravitation of the Gravity Research Foundation, and awarded with Honorable Mention. ∗ Permanent address: Dipartimento di Fisica Teorica, Via P.Giuria 1, 10125 Turin, Italy. One of the greatest challenges of modern cosmic physics is that of explaining the large level of entropy observed on a cosmological scale. While it seems clear that inflationary kinematics has to play a fundamental role in providing such an explanation, the nature of the (micro)physical mechanism that may have acted as a source of the cosmic entropy is, on the contrary, still unclear. A natural candidate for such a mechanism, well known even before the advent of the inflationary models, is the production of particles by the changing background metric. The pair production from the vacuum (otherwise stated, in a wave-mechanics language, the parametric amplification of the background fluctuations) provides indeed a natural cosmological arrow [1], which is not inverted even if the expansion turns into a contraction, and which may thus be used to define also an appropriate arrow of time [2]. The problem is, however, that of quantifying in an unambiguous way, and in agreement with the usual notion of entropy, the information loss associated with pair production. A possible solution to this problem comes from the observation that the production of particles by an external gravitational field can be conveniently represented in the squeezed state formalism [3]. Within this context, one can define indeed two canonically conjugate quantum variables (the so-called “quadrature operators”[4]): one operator has a variance that is “squeezed” with respect to the vacuum, while the variance of the other (the “superfluctuant” one) is correspondingly expanded. Using this approach, we have recently proposed [5] a way to measure the loss of information associated to the cosmological particle production, in terms of the increased dispersion of the superfluctuant operator. According to the standard (information-theoretic) definition of non-equilibrium entropy, such a coarse graining approach then provides an expression in which the entropy growth ∆Sk is