Trans-Planckian Issues for Inflationary Cosmology

The accelerated expansion of space during the period of cosmological inflation leads to trans-Planckian issues which need to be addressed. Most importantly, the physical wavelength of fluctuations which are studied at the present time by means of cosmological observations may well originate with a wavelength smaller than the Planck length at the beginning of the inflationary phase. Thus, questions arise as to whether the usual predictions of inflationary cosmology are robust considering our ignorance of physics on trans-Planckian scales, and whether the imprints of Planck-scale physics are at the present time observable. These and other related questions are reviewed in this article.Comment: 32 pages, 11 figures; invited review for "Classical and Quantum Gravity

Bounds on Generic High-Energy Physics Modifications to the Primordial Power Spectrum from Back-Reaction on the Metric

Modifications to the primordial power spectrum of inflationary density perturbations have been studied recently using a boundary effective field theory approach. In the approximation of a fluctuating quantum field on a fixed background, the generic effect of new physics is encoded in parameters of order H/M. Here, we point out that the back-reaction on the metric can be neglected only when these parameters obey certain bounds that may put them beyond the reach of observation.Comment: 6 pages, Latex. References added, misprints corrected. To appear in Phys. Lett.

Non-commutative inflation and the CMB

Non-commutative inflation is a modification of standard general relativity inflation which takes into account some effects of the space-time uncertainty principle motivated by ideas from string theory. The corrections to the primordial power spectrum which arise in a model of power-law inflation lead to a suppression of power on large scales, and produce a spectral index that is blue on large scales and red on small scales. This suppression and running of the spectral index are not imposed ad hoc, but arise from an early-Universe stringy phenomenology. We show that it can account for some loss of power on the largest scales that may be indicated by recent WMAP data. Cosmic microwave background anisotropies carry a signature of these very early Universe corrections, and can be used to place constraints on the parameters appearing in the non-commutative model. Applying a likelihood analysis to the WMAP data, we find the best-fit value for the critical wavenumber k_* (which involves the string scale) and for the exponent p (which determines the power-law inflationary expansion). The best-fit value corresponds to a string length of L_s \sim 10^{-28} cm.Comment: Revised to clarify discussion of primordial power spectrum; to appear Phys Lett

Running of the Spectral Index and Violation of the Consistency Relation Between Tensor and Scalar Spectra from trans-Planckian Physics

One of the firm predictions of inflationary cosmology is the consistency relation between scalar and tensor spectra. It has been argued that such a relation -if experimentally confirmed- would offer strong support for the idea of inflation. We examine the possibility that trans-Planckian physics violates the consistency relation in the framework of inflation with a cut-off proposed in astro-ph/0009209. We find that despite the ambiguity that exists in choosing the action, Planck scale physics modifies the consistency relation considerably. It also leads to the running of the spectral index. For modes that are larger than our current horizon, the tensor spectral index is positive. For a window of k values with amplitudes of the same order of the modes which are the precursor to structure formation, the behavior of tensor spectral index is oscillatory about the standard Quantum Field theory result, taking both positive and negative values. There is a hope that in the light of future experiments, one can verify this scenario of short distance physics.Comment: v1: 18 pages, 8 figures; v4: matched with the NPB versio

Trans-Planckian Physics and the Spectrum of Fluctuations in a Bouncing Universe

In this paper, we calculate the spectrum of scalar field fluctuations in a bouncing, asymptotically flat Universe, and investigate the dependence of the result on changes in the physics on length scales shorter than the Planck length which are introduced via modifications of the dispersion relation. In this model, there are no ambiguities concerning the choice of the initial vacuum state. We study an example in which the final spectrum of fluctuations depends sensitively on the modifications of the dispersion relation without needing to invoke complex frequencies. Changes in the amplitude and in the spectral index are possible, in addition to modulations of the spectrum. This strengthens the conclusions of previous work in which the spectrum of cosmological perturbations in expanding inflationary cosmologies was studied, and it was found that, for dispersion relations for which the evolution is not adiabatic, the spectrum changes from the standard prediction of scale-invariance.Comment: 10 pages, 6 figures, RevTeX4. Analytical determination of the spectrum, corrected some typos, conclusions unchange

Trans-Planckian footprints in inflationary cosmology

We consider a minimum uncertainty vacuum choice at a fixed energy scale Lambda as an effective description of trans-Planckian physics, and discuss its implications for the linear perturbations of a massless scalar field in power-law inflationary models. We find possible effects with a magnitude of order H/\Lambda in the power spectrum, in analogy with previous results for de-Sitter space-time.Comment: 4 pages, 1 figure, final version to appear in Physics Letters

Variational approximations for correlation functions in quantum field theories

Applying the time-dependent variational principle of Balian and V\'en\'eroni, we derive variational approximations for multi-time correlation functions in $\Phi^4$ field theory. We assume first that the initial state is given and characterized by a density operator equal to a Gaussian density matrix. Then, we study the more realistic situation where only a few expectation values are given at the initial time and we perform an optimization with respect to the initial state. We calculate explicitly the two-time correlation functions with two and four field operators at equilibrium in the symmetric phase.Comment: 60 pages, Latex, to be published in Annals of Physic

Cosmological Particle Creation in the Presence of Lorentz Violation

In recent years, the effects of Lorentz symmetry breaking in cosmology has attracted considerable amount of attention. In cosmological context several topics can be affected by Lorentz violation,e.g., inflationary scenario, CMB, dark energy problem and barryogenesis. In this paper we consider the cosmological particle creation due to Lorentz violation (LV). We consider an exactly solvable model for finding the spectral properties of particle creation in an expanding space-time exhibiting Lorentz violation. In this model we calculate the spectrum and its variations with respect to the rate and the amount of space-time expansion.Comment: 6 pages, 6 figures, To appear in Physics Letters

Evolution of Fields in a Second Order Phase Transition

We analyse the evolution of scalar and gauge fields during a second order phase transition using a Langevin equation approach. We show that topological defects formed during the phase transition are stable to thermal fluctuations. Our method allows the field evolution to be followed throughout the phase transition, for both expanding and non-expanding Universes. The results verify the Kibble mechanism for defect formation during phase transitions.Comment: 12 pages of text plus 17 diagrams available on request, DAMTP 94-8