Possible constraints on the duration of inflationary expansion from quantum stress tensor fluctuations

We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function, in four-dimensional Minkowski vacuum. These distributions share some properties with previous results in two-dimensional spacetime. Specifically, there is a lower bound at a finite negative value, but no upper bound. Thus arbitrarily large positive energy density fluctuations are possible. We are not able to give closed form expressions for the probability distribution, but rather use calculations of a finite number of moments to estimate the lower bounds, the asymptotic forms for large positive argument, and possible fits to the intermediate region. The first 65 moments are used for these purposes. All of our results are subject to the caveat that these distributions are not uniquely determined by the moments. We apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.

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“…[10][11][12]. Another implication of our form for the tail is that vacuum fluctuations will dominate thermal fluctuations at high energies.…”

Section: B Summarymentioning

confidence: 86%

Probability distributions for quantum stress tensors in four dimensions

2012

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“…(1), and h µν is the perturbation. We will employ the transverse trace-free gauge defined by h µν ;ν = 0, h = 0 and h µν u ν = 0 .…”

Section: Weakly Perturbed De Sitter Spacetimementioning

confidence: 99%

Quantum modifications to gravity waves in de Sitter spacetime

et al. 2011

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We treat a model in which tensor perturbations of de Sitter spacetime, represented as a spatially flat model, are modified by the effects of the vacuum fluctuations of a massless conformally invariant field, such as the electromagnetic field. We use the semiclassical theory of gravity with the expectation value of the conformal field stress tensor as a source. We first study the stability of de Sitter spacetime by searching for growing, spatially homogeneous modes, and conclude that it is stable within the limits of validity of the semiclassical theory. We next examine the modification of linearized plane gravity waves by the effects of the quantum stress tensor. We find a correction term which is of the same form as the original wave, but displaced in phase by π/2, and with an amplitude which depends upon an initial time. The magnitude of this effect is proportional to the change in scale factor after this time. We discuss alternative interpretations of this time, but pay particular attention to the view that this is the beginning of inflation. So long as the energy scale of inflation and the proper frequency of the mode at the beginning of inflation are well below the Planck scale, the fractional correction is small. However, modes which are transplanckian at the onset of inflation can undergo a significant correction. The increase in amplitude can potentially have observable consequences through a modification of the power spectrum of tensor perturbations in inflationary cosmology. This enhancement of the power spectrum depends upon the initial time, and is greater for shorter wavelengths.

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“…[33], where the effect of electromagnetic stress tensor fluctuations in inflation were studied. Take the spacetime to be a spatially flat Robertson-Walker universe…”

Section: Stress Tensor Fluctuations In Inflationmentioning

confidence: 99%

Quantum Stress Tensor Fluctuations and their Physical Effects

Ford

2008

AIP Conference Proceedings

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We summarize several aspects of recent work on quantum stress tensor fluctuations and their role in driving fluctuations of the gravitational field. The role of correlations and anticorrelations is emphasized. We begin with a review of the properties of the stress tensor correlation function. We next consider some illuminating examples of non-gravitational effects of stress tensors fluctuations, specifically fluctuations of the Casimir force and radiation pressure fluctuations. We next discuss passive fluctuations of spacetime geometry and some of their operational signatures. These include luminosity fluctuations, line broadening, and angular blurring of a source viewed through a fluctuating gravitational field. Finally, we discuss the possible role of quantum stress tensor fluctuations in the early universe, especially in inflation. The fluctuations of the expansion of a congruence of comoving geodesics grows during the inflationary era, due to non-cancellation of anticorrelations that would have occurred in flat spacetime. This results in subsequent non-Gaussian density perturbations and allows one to infer an upper bound on the duration of inflation. This bound is consistent with adequate inflation to solve the horizon and flatness problems.

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Possible constraints on the duration of inflationary expansion from quantum stress tensor fluctuations

Cited by 36 publications

References 50 publications

Probability distributions for quantum stress tensors in four dimensions

Probability distributions for quantum stress tensors in four dimensions

Quantum modifications to gravity waves in de Sitter spacetime

Quantum Stress Tensor Fluctuations and their Physical Effects

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