Ekpyrotic Collapse Research Articles

Tilted ekpyrosis

We consider a simple model of cosmological collapse driven by canonical fields with exponential potentials. We generalize the two-field ekpyrotic collapse to consider nonorthogonal or tilted potentials and give the general condition for isocurvature field fluctuations to have a scale-invariant spectrum in this model. In particular we show that tilted potentials allow for a slightly red spectrum of perturbations as required by current observations. However a red spectrum of fluctuations implies that the two-field ekpyrotic phase must have a finite duration and requires a preceding phase which sets the initial conditions for what otherwise appears to be a fine-tuned trajectory in the phase space.

Cosmological Perturbations Through the Big Bang

Several scenarios have been proposed in which primordial perturbations could originate from quantum vacuum fluctuations in a phase corresponding to a collapse phase (in an Einstein frame) preceding the Big Bang. I briefly review three models which could produce scale-invariant spectra during collapse: (1) curvature perturbations during pressureless collapse, (2) axion field perturbations in a pre big bang scenario, and (3) tachyonic fields during multiple-field ekpyrotic collapse. In the separate universes picture one can derive generalised perturbation equations to describe the evolution of large scale perturbations through a semi-classical bounce, assuming a large-scale limit in which inhomogeneous perturbations can be described by locally homogeneous patches. For adiabatic perturbations there exists a conserved curvature perturbation on large scales, but isocurvature perturbations can change the curvature perturbation through the non-adiabatic pressure perturbation on large scales. Different models for the origin of large scale structure lead to different observational predictions, including gravitational waves and non-Gaussianity.

Generalized perturbation equations in bouncing cosmologies

We consider linear perturbation equations for long-wavelength scalar metric perturbations in generalized gravity, applicable to nonsingular cosmological models including a bounce from collapse to expansion in the very early universe. We present the general form for the perturbation equations, which follows from requiring that the inhomogeneous universe on large scales obeys the same local equations as the homogeneous Friedmann-Robertson-Walker background cosmology (the separate universes approach). In a pseudolongitudinal gauge this becomes a homogeneous second-order differential equation for adiabatic perturbations, which reduces to the usual equation for the longitudinal gauge metric perturbation in general relativity with vanishing anisotropic stress. As an application we show that the scale-invariant spectrum of perturbations in the longitudinal gauge generated during an ekpyrotic collapse are not transferred to the growing mode of adiabatic density perturbations in the expanding phase in a simple bounce model.

Non-Gaussianities from ekpyrotic collapse with multiple fields

We compute the non-Gaussianity of the curvature perturbation generated by ekpyroticcollapse with multiple fields. The transition from the multi-field scaling solution to asingle-field dominated regime converts initial isocurvature field perturbations to an almostscale invariant comoving curvature perturbation. In the specific model of two fields,ϕ1 andϕ2, with exponentialpotentials, −Viexp(−ciϕi), we calculate the bispectrum of the resulting curvature perturbation. We find that thenon-Gaussianity is dominated by non-linear evolution on super-Hubble scales and hence isof the local form. The non-linear parameter of the curvature perturbation is given byfNL = 5cj2/12,where cj is the exponent of the potential for the field which becomes subdominant at late times. Sincecj2 must be large, in order to generate an almost scale invariant spectrum, the non-Gaussianityis inevitably large. Thus, the model is strongly constrained by observational bounds on thespectral index and non-Gaussianity.

Curvature perturbations from ekpyrotic collapse with multiple fields

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in the ekpyrotic scaling solution in models where multiple fields have steep negative exponential potentials. The scale invariance of the spectrum is realized by a tachyonic instability in the isocurvature field. This instability drives the scaling solution to the late-time attractor that is the old ekpyrotic collapse dominated by a single field. We show that the transition from the scaling solution to the single-field-dominated ekpyrotic collapse automatically converts the initial isocurvature perturbations about the scaling solution to comoving curvature perturbations about the late-time attractor. The final amplitude of the comoving curvature perturbation is determined by the Hubble scale at the transition.

Ekpyrotic collapse with multiple fields

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in thescaling solution in models where two or more fields have steep negative exponentialpotentials. The scale invariance of the spectrum is realized by a tachyonic instability in theisocurvature field. We show that this instability is due to the fact that the scaling solutionis a saddle point in the phase space. The late-time attractor is identified with asingle-field-dominated ekpyrotic collapse in which a steep blue spectrum for isocurvatureperturbations is found. Although quantum fluctuations do not necessarily to disrupt theclassical solution, an additional preceding stage is required to establish classicalhomogeneity.