Inflation (Chapters 5 and 8) 415
scale structure of the universe.Soviet Physics JETP, 56 (1982), 258.) It is shown that
the stage of cosmic acceleration considered in Starobinsky (1980) (see above) does not
solve the singularity problem because quantum fluctuations make its duration finite.
The graceful exit to a Friedmann stage due to the quantum fluctuations is calculated.
The red-tilted logarithmic spectrum of initial inhomogeneities produced from initial
quantum fluctuations during cosmic acceleration is discovered:“... models in which
the de Sitter stage exists only as an intermediate stage in the evolution are attractive
because fluctuations of the metric sufficient for the galaxy formation can occur.”
Guth, A. The inflationary universe: a possible solution to the horizon and flatness problems.
Physical Review D, 23 (1981), 347. It is noted that the stage of cosmic acceleration,
which the author calls inflation, can solve the horizon and flatness problems. It is
pointed out that inflation can also solve the monopole problem. No working model
with a graceful exit to the Freedman stage is presented:“... random formation of
bubbles of the new phase seems to lead to a much too inhomogeneous universe.”
Linde, A., A new inflationary scenario: a possible solution of the horizon, flatness, homo-
geneity, isotropy, and primordial monopole problems.Physics Letters,108B(1982),- The new inflationary scenario with a graceful exit based on“improved Coleman–
Weinberg theory”for the scalar field is proposed.
Albrecht, A., Steinhardt, P. Cosmology for grand unified theories with radiatively induced
symmetry breaking.PhysicalReviewLetters, 48 (1982), 1220. Confirms the conclusion
of Linde (1982) (see above).
Linde, A. Chaotic inflation.Physics Letters,129B(1983), 177. The generic character of
inflationary expansion is discovered for a broad class of scalar field potentials, which
must simply satisfy the slow-roll conditions.“... inflation occurs for all reasonable
potentials V(φ).This suggests that inflation is not a peculiar phenomenon... , but that
it is a natural and maybe even inevitable consequence of the chaotic initial conditions
in the very early universe.”
Whitt, B. Fourth order gravity as general relativity plus matter.Physics Letters,B145
(1984), 176. The conformal equivalence between Einstein theory with a scalar field
and a higher-derivative gravity is established.
Mukhanov, V. Gravitational instability of the universe filled with a scalar field.JETP Letters,
41 (1985), 493; Quantum theory of gauge invariant cosmological perturbations.Soviet
Physics JETP, 67 (1988), 1297. The self-consistent theory of quantum cosmological
perturbations in generic inflationary models is developed†.
Mukhanov, B., Feldman, H., Brandenberger, R. Theory of cosmological perturbations.
Physics Report, 215 (1992), 203. This paper contains the derivation of the action for
cosmological perturbations in different models from first principles. Explicit formulae
in higher-derivative gravity and for cases of nonzero spatial curvature can be found
here. (See also Garriga, J., Mukhanov, V. Perturbations ink-inflation.Physics Letters,
458B(1999), 219.)
Damour, T., Mukhanov, V. Inflation without slow-roll.Physical Review Letters, 80 (1998), - Fast oscillation inflation in the case of a convex potential is discussed (see
Section 4.5.2).
Armendariz-Picon, C., Damour, T., Mukhanov, V. k-Inflation.Physics Letters,458B(1999), - Inflation based on a nontrivial kinetic term for the scalar field is discussed (Section
5.6).
†The papers by Hawking, S.Phys. Lett.,115B(1982), 295; Starobinsky, A.Phys. Lett.,117B(1982), 175; Guth,
A., Pi, S.Phys. Rev. Lett., 49 (1982), 1110; Bardeen, J., Steinhardt, P., Turner, M.Phys. Rev. D, 28 (1983), 679
are devoted to perturbations in the new inflationary scenario. However, bearing in mind the considerations of
Chapter 8 and solving Problems 8.4, 8.5, 8.7 and 8.8, the reader can easily find out that none of the above papers
contains a consistent derivation of the result.