Cosmological Inflation and the Quantum Measurement Problem

According to cosmological inflation, the inhomogeneities in our universe are of quantum mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains why the spectrum of cosmological perturbations is almost scale invariant. It is also an ideal playground to discuss deep questions among which is the quantum measurement problem in a cosmological context. Although the large squeezing of the quantum state of the perturbations and the phenomenon of decoherence explain many aspects of the quantum to classical transition, it remains to understand how a specific outcome can be produced in the early universe, in the absence of any observer. The Continuous Spontaneous Localization (CSL) approach to quantum mechanics attempts to solve the quantum measurement question in a general context. In this framework, the wavefunction collapse is caused by adding new non linear and stochastic terms to the Schroedinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wavefunction collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schroedinger equation. Then, we compute the power spectrum of the perturbations and show that it acquires a universal shape with two branches, one which remains scale invariant and one with nS=4, a spectral index in obvious contradiction with the Cosmic Microwave Background (CMB) anisotropy observations. The requirement that the non-scale invariant part be outside the observational window puts stringent constraints on the parameter controlling the deviations from ordinary quantum mechanics... (Abridged).Comment: References added, minor corrections, conclusions unchange

Non-Gaussianity of scalar perturbations generated by conformal mechanisms

We consider theories which explain the flatness of the power spectrum of scalar perturbations in the Universe by conformal invariance, such as conformal rolling model and Galilean Genesis. We show that to the leading {\it non-linear} order, perturbations in all models from this class behave in one and the same way, at least if the energy density of the relevant fields is small compared to the total energy density (spectator approximation). We then turn to the intrinsic non-Gaussianities in these models (as opposed to non-Gaussianities that may be generated during subsequent evolution). The intrinsic bispectrum vanishes, so we perform the complete calculation of the trispectrum and compare it with the trispecta of local forms in various limits. The most peculiar feature of our trispectrum is a (fairly mild) singularity in the limit where two momenta are equal in absolute value and opposite in direction (folded limit). Generically, the intrinsic non-Gaussianity can be of detectable size.Comment: 28 pages, 5 figures. Journal version. A comment on the size of the non-Gaussianities inserted. Misprints corrected. A reference adde

The Maximal Amount of Gravitational Waves in the Curvaton Scenario

The curvaton scenario for the generation of the cosmological curvature perturbation on large scales represents an alternative to the standard slow-roll scenario of inflation in which the observed density perturbations are due to fluctuations of the inflaton field itself. Its basic assumption is that the initial curvature perturbation due to the inflaton field is negligible. This is attained by lowering the energy scale of inflation, thereby highly suppressing the amount of gravitational waves produced during inflation. We compute the power-spectrum of the gravitational waves generated at second order in perturbation theory by the curvaton (isocurvature) perturbations between the end of inflation and the curvaton decay. An interesting property of this contribution to the tensor perturbations is that it is directly proportional to the amount of non-Gaussianity predicted within the curvaton scenario. We show that the spectrum of gravitational waves may be in the range of future gravitational wave detectors.Comment: 4 pages, laTeX; added a clarifying comment in the conclusions, version matches publication in PRD, Rapid Communication

Enhancing the tensor-to-scalar ratio in simple inflation

We show that in theories with a nontrivial kinetic term the contribution of the gravitational waves to the CMB fluctuations can be substantially larger than that is naively expected in simple inflationary models. This increase of the tensor-to-scalar perturbation ratio leads to a larger B-component of the CMB polarization, thus making the prospects for future detection much more promising. The other important consequence of the considered model is a higher energy scale of inflation and hence higher reheating temperature compared to a simple inflation.Comment: 9 pages, 1 figure and references are added, discussion is slightly extended, published versio

Path Integral Quantization of Cosmological Perturbations

We derive the first order canonical formulation of cosmological perturbation theory in a Universe filled by a few scalar fields. This theory is quantized via well-defined Hamiltonian path integral. The propagator which describes the evolution of the initial (for instance, vacuum) state, is calculated.Comment: 16 pages, ETH-TH/94-0

Back-reaction of Cosmological Fluctuations during Power-Law Inflation

We study the renormalized energy-momentum tensor of cosmological scalar fluctuations during the slow-rollover regime for power-law inflation and find that it is characterized by a negative energy density at the leading order, with the same time behaviour as the background energy. The average expansion rate appears decreased by the back-reaction of the effective energy of cosmological fluctuations, but this value is comparable with the energy of background only if inflation starts at a Planckian energy. We also find that, for this particular model, the first and second order inflaton fluctuations are decoupled and satisfy the same equation of motion. To conclude, the fourth order adiabatic expansion for the inflaton scalar field is evaluated for a general potential V(\phi).Comment: 9 pages, no figures, revtex. Some changes made, comments and references added, conclusions unchanged, version accepted for pubblication in Phys. Rev.

A Radiation Bounce from the Lee-Wick Construction?

It was recently realized that matter modeled by the scalar field sector of the Lee-Wick Standard Model yields, in the context of a homogeneous and isotropic cosmological background, a bouncing cosmology. However, bouncing cosmologies induced by pressure-less matter are in general unstable to the addition of relativistic matter (i.e. radiation). Here we study the possibility of obtaining a bouncing cosmology if we add not only radiation, but also its Lee-Wick partner, to the matter sector. We find that, in general, no bounce occurs. The only way to obtain a bounce is to choose initial conditions with very special phases of the radiation field and its Lee-Wick partner.Comment: 11 page

Non-Gaussian features of primordial magnetic fields in power-law inflation

We show that a conformal-invariance violating coupling of the inflaton to electromagnetism produces a cross correlation between curvature fluctuations and a spectrum of primordial magnetic fields. According to this model, in the case of power-law inflation, a primordial magnetic field is generated with a nearly flat power spectrum and rms amplitude ranging from nG to pG. We study the cross correlation, a three-point function of the curvature perturbation and two powers of the magnetic field, in real and momentum space. The cross-correlation coefficient, a dimensionless ratio of the three-point function with the curvature perturbation and magnetic field power spectra, can be several orders of magnitude larger than expected as based on the amplitude of scalar metric perturbations from inflation. In momentum space, the cross-correlation peaks for flattened triangle configurations, and is three orders of magnitude larger than the squeezed triangle configuration. These results suggest likely methods for distinguishing the observational signatures of the model.Comment: 15 pages, 2 figure

Free Quantum Fields on the Poincare' Group

A class of free quantum fields defined on the Poincare' group, is described by means of their two-point vacuum expectation values. They are not equivalent to fields defined on the Minkowski spacetime and they are "elementary" in the sense that they describe particles that transform according to irreducible unitary representations of the symmetry group, given by the product of the Poincare' group and of the group SL(2, C) considered as an internal symmetry group. Some of these fields describe particles with positive mass and arbitrary spin and particles with zero mass and arbitrary helicity or with an infinite helicity spectrum. In each case the allowed SL(2, C) internal quantum numbers are specified. The properties of local commutativity and the limit in which one recovers the usual field theories in Minkowski spacetime are discussed. By means of a superposition of elementary fields, one obtains an example of a field that present a broken symmetry with respect to the group Sp(4, R), that survives in the short-distance limit. Finally, the interaction with an accelerated external source is studied and and it is shown that, in some theories, the average number of particles emitted per unit of proper time diverges when the acceleration exceeds a finite critical value.Comment: 49 pages, plain tex with vanilla.st

New Ekpyrotic Cosmology

In this paper, we present a new scenario of the early Universe that contains a pre big bang Ekpyrotic phase. By combining this with a ghost condensate, the theory explicitly violates the null energy condition without developing any ghost-like instabilities. Thus the contracting universe goes through a non-singular bounce and evolves smoothly into the expanding post big bang phase. The curvature perturbation acquires a scale-invariant spectrum well before the bounce in this scenario. It is sourced by the scale-invariant entropy perturbation engendered by two ekpyrotic scalar fields, a mechanism recently proposed by Lehners et al. Since the background geometry is non-singular at all times, the curvature perturbation remains nearly constant on super horizon scales. It emerges from the bounce unscathed and imprints a scale-invariant spectrum of density fluctuations in the matter-radiation fluid at the onset of the hot big bang phase. The ekpyrotic potential can be chosen so that the spectrum has a ``red'' tilt, in accordance with the recent data from WMAP. As in the original Ekpyrotic scenario, the model predicts a negligible gravity wave signal on all observable scales. As such ``New Ekpyrotic Cosmology" provides a consistent and distinguishable alternative to inflation to account for the origin of the seeds of large scale structure.Comment: 41 pages, 4 figures. v2: minor corrections, references added. v3: small modifications in bounce section, references added. v4: version published in PR