English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce a new method for calculating density perturbations in hybridinflation which avoids treating the fluctuations of the "waterfall" field as ifthey were small perturbations about a classical trajectory. We quantize onlythe waterfall field, treating it as a free quantum field with a time-dependent$m^2$, which evolves from positive values to tachyonic values. Although thispotential has no minimum, we think it captures the important dynamics thatoccurs as $m^2$ goes through zero, at which time a large spike in the densityperturbations is generated. We assume that the time-delay formalism provides anaccurate approximation to the density perturbations, and proceed to calculatethe power spectrum of the time delay fluctuations. While the evolution of thefield is linear, the time delay is a nonlinear function to which all modescontribute. Using the Gaussian probability distribution of the mode amplitudes,we express the time-delay power spectrum as an integral which can be carriedout numerically. We use this method to calculate numerically the spectrum ofdensity perturbations created in hybrid inflation models for a wide range ofparameters. A characteristic of the spectrum is the appearance of a spike atsmall length scales, which can be used to relate the model parameters toobservational data. It is conceivable that this spike could seed the formationof black holes that can evolve to become the supermassive black holes found atthe centers of galaxies.

Density Perturbations in Hybrid Inflation Using a Free Field Theory Time-Delay Approach