Production of scalar and tensor perturbations in inflationary models

Journal Article · Fri Oct 15 00:00:00 EDT 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.48.3502· OSTI ID:6042722

Turner, M S ^[1]

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1. Departments of Physics and of Astronomy Astrophysics, Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637-1433 (United States) NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510-0500 (United States)

Scalar (density) and tensor (gravity-wave) perturbations provide the basis for the fundamental observable consequences of inflation, including CBR anisotropy and the formation of structure in the Universe. These perturbations are nearly scale invariant (Harrison-Zel'dovich spectrum), though a slight deviation from scale invariance ( tilt'') can have significant consequences for both CBR anisotropy and structure formation. In particular, a slightly tilted spectrum of scalar perturbations may improve the agreement of the cold dark matter scenario with the observational data. The amplitude and spectrum of the scalar and tensor perturbations depend upon the shape of the inflationary potential in the small interval where the scalar field responsible for inflation was between about 46 and 54 [ital e]-folds before the end of inflation. By expanding the inflationary potential in a Taylor series over this interval we show that the amplitudes of the perturbations and the power-law slopes of their spectra can be expressed in terms of the value of the potential 50 [ital e]-folds before the end of inflation, [ital V][sub 50], its steepness [ital x][sub 50][equivalent to][ital m][sub Pl][ital V50][sup [prime]]/[ital V][sub 50], and the rate of change of its steepness, [ital x][sub 50][sup [prime]] (a prime denotes a derivative with respect to the scalar field). In addition, the power-law index of the cosmic-scale factor at this time is [ital q][sub 50][equivalent to][[ital d]ln[ital R]/[ital d]ln[ital t]][sub 50][congruent]16[pi]/[ital x][sub 50][sup 2].

• OSTI ID: 6042722
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 48:8; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
INFLATIONARY UNIVERSE
PERTURBATION THEORY
SCALAR FIELDS
TENSOR FIELDS
AMPLITUDES
ANISOTROPY
DENSITY
FLUCTUATIONS
GRAVITATIONAL WAVES
SPECTRA
COSMOLOGICAL MODELS
MATHEMATICAL MODELS
PHYSICAL PROPERTIES
VARIATIONS
661310* - Relativity & Gravitation- (1992-)