Limits on the validity of the semiclassical theory

For want of a more natural proposal, it is generally assumed that the back-reaction of a quantised matter field on a classical metric is given by the expectation value of its energy-momentum tensor, evaluated in a specified state. This proposal can be expected to be quite sound only when the fluctuations in the energy-momentum tensor of the quantum field are negligible. Based on this condition, a dimensionless criterion has been suggested earlier by Kuo and Ford for drawing the limits on the validity of this semiclassical theory. In this paper, we examine this criterion for the case of a toy model, constructed with two degrees of freedom and a coupling between them that exactly mimics the behaviour of a scalar field in a Friedmann universe. To reproduce the semiclassical regime of the field theory, in the toy model, one of degrees of freedom is assumed to be classical and the other quantum mechanical. Also the backreaction is assumed to be given by the expectation values of the quantum operators involved in the equations of motion for the classical system. Motivated by the same physical reasoning as Kuo and Ford, we, here, suggest another criterion, one which will be shown to perform more reliably as we evaluate these criterions for different states of the quantum system in the toy model. Finally, from the results obtained we conclude that the semiclassical theory being considered for the toy model is reliable, during all stages of its evolution, only if the quantum system is specified to be in coherent like states. The implications of these investigations on field theory are discussed.Comment: 20 pages in Te

Trans-Planckian corrections to the primordial spectrum in the infra-red and the ultra-violet

Due to the tremendous red-shift that occurs during the inflationary epoch in the early universe, it has been realized that trans-Planckian physics may manifest itself at energies much lower than the Planck energy. The presence of a fundamental scale suggests that local Lorentz invariance may be violated at sufficiently high energies. Motivated by this possibility, recently, different models that violate Lorentz invariance locally have been used to evaluate the trans-Planckian corrections to the inflationary density perturbation spectrum. However, certain astrophysical observations seem to indicate that local Lorentz invariance may be preserved to extremely high energies. In such a situation, to study the trans-Planckian effects, it becomes imperative to consider models that preserve local Lorentz invariance even as they contain a fundamental scale. In this work, we construct one such model and evaluate the resulting spectrum of density perturbations in the power-law inflationary scenario. While our model reproduces the standard spectrum on small scales, it naturally predicts a suppression of power on large scales. In fact, the spectrum we obtain has some features which are similar to the one that has recently been obtained from non-commutative inflation. However, we find that the amount of suppression predicted by our model is far less than that is required to fit the observations. We comment on the fact that, with a suitable choice of initial conditions, our approach can lead to corrections at the infra-red as well as at the ultra-violet ends of the spectrum.Comment: 11 pages, 3 figures, Revtex 4; References adde

On the response of detectors in classical electromagnetic backgrounds

I study the response of a detector that is coupled non-linearly to a quantized complex scalar field in different types of classical electromagnetic backgrounds. Assuming that the quantum field is in the vacuum state, I show that, when in {\it inertial} motion, the detector responds {\it only} when the electromagnetic background produces particles. However, I find that the response of the detector is {\it not} proportional to the number of particles produced by the background.Comment: 10 pages, LaTeX, Final versio