Frequency Spectra and Probability Distributions for Quantum Fluctuations

The difficult issues related to the interpretation of quantum mechanics and, in particular, the "measurement problem" are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry ...

Inflation predicts that quantum fluctuations determine the large scale structure of the Universe. This raises the striking possibility that quantum mechanics, developed to describe nature at short distances, can be tested by studying nature at its most immense -- cosmology. We illustrate the potential of such a test by adapting the simplest form of the inflationary paradigm. A nonlinear generalization of quantum mechanics modifies predictions for the cosmological power spectr...

The theory of cosmological fluctuations assumes that the pre-inflationary state of the universe was the quantum vacuum of a scalar field(s) coupled to gravity. The observed cosmic microwave background fluctuations are then interpreted as quantum fluctuations. Here we consider alternate interpretations of the classic calculations of scalar and tensor power spectra by replacing the Bunch-Davies quantum vacuum with a classical statistical distribution, which may have been the co...

Large vacuum fluctuations of a quantum stress tensor operator can be described by the asymptotic behavior of the probability distribution of the time or spacetime averaged operator. Here we focus on the case of stress tensor operators averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability d...

We consider the effects of the quantum stress tensor fluctuations of a conformal field in generating gravity waves in inflationary models. We find a non-scale invariant, non-Gaussian contribution which depends upon the total expansion factor between an initial time and the end of inflation. This spectrum of gravity wave perturbations is an illustration of a negative power spectrum, which is possible in quantum field theory. We discuss possible choices for the initial conditio...

Recently, we presented a unified way of analysing classical cosmological perturbation in generalized gravity theories. In this paper, we derive the perturbation spectrums generated from quantum fluctuations again in unified forms. We consider a situation where an accelerated expansion phase of the early universe is realized in a particular generic phase of the generalized gravity. We take the perturbative semiclassical approximation which treats the perturbed parts of the met...

It is widely believed that quantum field fluctuation in an inflating background creates the primeval seed perturbation which through subsequent evolution leads to the observed large scale structure of the universe. The standard inflationary scenario produces scale invariant power spectrum quite generically but it produces, unless fine tuned, too large amplitude for the primordial density perturbation than observed. Using similar techniques it is shown that loop quantum cosmol...

Does the observable spectrum of cosmic fluctuations depend on detailed initial conditions? This addresses the question if the general inflationary paradigm is sufficient to predict within a given model the spectrum and amplitude of cosmic fluctuations, or if additional particular assumptions about the initial conditions are needed. The answer depends on the number of e-foldings $N_{in}$ between the beginning of inflation and horizon crossing of the observable fluctuations. We...

The recent three-year WMAP data selects large-field models with certain power-law potentials and small-field models for all power-law potentials as consistent inflation models. We study the large-field and small-field inflation model with a quadratic and a quartic potential within the framework of quantum field theory in an expanding Friedmann-Robertson-Walker universe. We find that quantum fluctuations in the small-field model lead to a significant contribution to the effect...

Astronomers seem to be observing the fossilized remnants of quantum gravitational processes which took place during the epoch of {\it primordial inflation} that is conjectured to have occurred during the first $10^{-32}$ seconds of cosmic history. We give a non-technical description of what causes these processes and how they become preserved to survive to the current epoch. We also discuss some of the secondary effects which should result.