A General Analytic Formula for the Spectral Index of the Density
  Perturbations produced during Inflation

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Abstract

The standard calculation of the spectrum of density perturbations produced during inflation assumes that there is only one real dynamical degree of freedom during inflation. However, there is no reason to believe that this is actually the case. In this paper we derive general analytic formulae for the spectrum and spectral index of the density perturbations produced during inflation.

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False Vacuum Inflation with Einstein Gravity

David Wands, Ewan Stewart, David H. Lyth … (1994)

We investigate chaotic inflation models with two scalar fields, such that one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the inflaton field falls below some critical value, and a first or second order transition to the true vacuum ensues. Particular attention is paid to Linde's second-order `Hybrid Inflation'; with the false vacuum dominating, inflation differs from the usual true vacuum case both in its cosmology and in its relation to particle physics. The spectral index of the adiabatic density perturbation can be very close to 1, or it can be around ten percent higher. The energy scale at the end of inflation can be anywhere between \(10^{16}\)\,GeV and \(10^{11}\)\,GeV, though reheating is prompt so the reheat temperature can't be far below \(10^{11}\,\)GeV. Topological defects are almost inevitably produced at the end of inflation, and if the inflationary energy scale is near its upper limit they can have significant effects. Because false vacuum inflation occurs with the inflaton field far below the Planck scale, it is easier to implement in the context of supergravity than standard chaotic inflation. That the inflaton mass is small compared with the inflationary Hubble parameter is still a problem for generic supergravity theories, but remarkably this can be avoided in a natural way for a class of supergravity models which follow from orbifold compactification of superstrings. This opens up the prospect of a truly realistic, superstring

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Supersymmetry Breaking in the Early Universe

Scott Thomas, Lisa Randall, Michael Dine (1995)

Supersymmetry breaking in the early universe induces scalar soft potentials with curvature of order the Hubble constant. This has a dramatic effect on the coherent production of scalar fields along flat directions. For the moduli problem it generically gives a concrete realization of the problem by determining the field value subsequent to inflation. However it might suggest a solution if the minimum of the induced potential coincides with the true minimum. The induced Hubble scale mass also has important implications for the Affleck-Dine mechanism of baryogenesis. This mechanism requires large squark or slepton expectation values to develop along flat directions in the early universe. This is generally not the case if the induced mass squared is positive, but does occur if it is negative. The resulting baryon to entropy ratio depends mainly on the dimension of the nonrenormalizable operator in the superpotential which stabilizes the flat direction, and the reheat temperature after inflation. Unlike the original scenario, it is possible to obtain an acceptable baryon asymmetry without subsequent entropy releases.

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Inflation, Supergravity and Superstrings

Ewan Stewart (1994)

The positive potential energy required for inflation spontaneously breaks supersymmetry and in general gives any would-be inflaton an effective mass of order the inflationary Hubble parameter thus ruling it out as an inflaton. In this paper I give simple conditions on the superpotential that eliminate some potential sources for this mass, and derive a form for the Kahler potential that eliminates the rest. This reduces the problem of constructing a model of inflation in supergravity to that of constructing one in global supersymmetry with the extra conditions \(W=W_\varphi=\psi=0\) during inflation (where \(W\) is the superpotential, the inflaton \(\in\varphi\), and \(W_\psi\neq0\)). I then point out that Kahler potentials of the required form often occur in superstrings and that the target space duality symmetries of superstrings often contain R-parities which would make \(W=W_\varphi=0\) automatic for \(\psi=0\).

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Publication date Created: 03 July 1995

Publication date Updated: 1995-11-28

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DOI: 10.1143/PTP.95.71

ArXiV ID: astro-ph/9507001

SO-VID: 09ce6636-6b2b-44a5-8c91-671503f04837

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Report No LANCASTER-TH/9504, OU-TAP-22

Journal reference Prog.Theor.Phys.95:71-78,1996

Comments 10 pages, more explanation and references added, version to be published in Progress of Theoretical Physics

A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation

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Most cited references 3

False Vacuum Inflation with Einstein Gravity

Supersymmetry Breaking in the Early Universe

Inflation, Supergravity and Superstrings

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