INFLATION IN KALUZA-KLEIN COSMOLOGY II: FRIEDMANN MODELS

1990 ◽  
Vol 05 (24) ◽  
pp. 4671-4676 ◽  
Author(s):  
ULRICH BLEYER ◽  
HANS-JÜRGEN SCHMIDT
Keyword(s):  
Power Law ◽  
Fourth Order ◽  
Conformal Transformation ◽  
Preceding Paper ◽  
Internal Space ◽  
De Sitter ◽  
Scale Invariant ◽  
Attractor Solution ◽  
Friedmann Cosmological Models ◽  
Kaluza Klein

The conformal relation between scale-invariant fourth-order gravity and Kaluza-Klein models as derived in the preceding paper (I) is applied to Friedmann cosmological models. Especially, the result that power-law inflation is an attractor solution can be carried over, but the conformal transformation brings power-law inflation to de Sitter-like exponential inflation, or power-law inflation a ≈ t. The results depend essentially on the dimension of the internal space.

INFLATION IN KALUZA-KLEIN COSMOLOGY I: TRANSFORMATION TO FOURTH-ORDER GRAVITY

1990 ◽  
Vol 05 (24) ◽  
pp. 4661-4669 ◽  
Author(s):  
HANS-JÜRGEN SCHMIDT
Keyword(s):  
Fourth Order ◽  
Arbitrary Dimension ◽  
Internal Space ◽  
Vacuum Equation ◽  
Scale Invariant ◽  
Einstein Vacuum Equation ◽  
Higher Dimensional ◽  
Einstein Vacuum ◽  
Klein Model ◽  
Kaluza Klein

The higher-dimensional Einstein vacuum equation with Λ-term is shown to be conformally equivalent to the four-dimensional field equation of scale-invariant fourth-order gravity. This holds for a general warped product between space-time and internal space of arbitrary dimension m which turns out to be an Einstein space. (The limit m → ∞ makes sense!) Thus, the results concerning the attractor property of the power-law inflationary solution derived for fourth-order gravity hold for the Kaluza-Klein model, too.

scholarly journals Scale-invariant scalar spectrum from the nonminimal derivative coupling with fourth-order term

2015 ◽  
Vol 24 (14) ◽  
pp. 1550095 ◽  
Author(s):  
Yun Soo Myung ◽  
Taeyoon Moon
Keyword(s):  
Fourth Order ◽  
Order Term ◽  
Order Derivative ◽  
Scalar Perturbation ◽  
De Sitter ◽  
Scale Invariant ◽  
Derivative Coupling ◽  
Sitter Spacetime ◽  
Fourth Order Term ◽  
Derivative Term

In this paper, an exactly scale-invariant spectrum of scalar perturbation generated during de Sitter spacetime is found from the gravity model of the nonminimal derivative coupling with fourth-order term. The nonminimal derivative coupling term generates a healthy (ghost-free) fourth-order derivative term, while the fourth-order term provides an unhealthy (ghost) fourth-order derivative term. The Harrison–Zel’dovich spectrum obtained from Fourier transforming the fourth-order propagator in de Sitter space is recovered by computing the power spectrum in its momentum space directly. It shows that this model provides a truly scale-invariant spectrum, in addition to the Lee–Wick scalar theory.

POWER-LAW TYPE SOLUTIONS OF FOURTH-ORDER GRAVITY FOR MULTIDIMENSIONAL BIANCHI I UNIVERSES

1991 ◽  
Vol 02 (02) ◽  
pp. 601-611 ◽  
Author(s):  
H. CAPRASSE ◽  
J. DEMARET ◽  
K. GATERMANN ◽  
H. MELENK
Keyword(s):  
Computer Algebra ◽  
Power Law ◽  
Fourth Order ◽  
Dimensional Space ◽  
Internal Space ◽  
Algebraic Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
3 Dimensional ◽  
Bianchi I

This paper is devoted to the application of computer algebra to the study of solutions of the field equations derived from a non-linear Lagrangian, as suggested by recently proposed unified theories. More precisely, we restrict ourselves to the most general quadratic Lagrangian, i.e. containing quadratic contributions in the different curvature tensors exclusively. The corresponding field equations are then fourth-order in the metric tensor components. The cosmological models studied are the simplest ones in the class of spatially homogeneous but anisotropic models, i.e. Bianchi I models. For these models, we consider only power-law type solutions of the field equations. All the solutions of the associated system of algebraic equations are found, using computer algebra, from a search of its Groebner bases. While, in space dimension d=3, the Einsteinian-Kasner metric is still the most general power-law type solution, for d>3, no solution, other than the Minkowski space-time, is common to the three systems of equations corresponding to the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution to the Lagrangian (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the d-dimensional space into a (d−3)-dimensional internal space and a physical 3-dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when d=9).

scholarly journals Einstein-singleton theory and its power spectra in de Sitter inflation

2016 ◽  
Vol 25 (14) ◽  
pp. 1650107
Author(s):  
Yun Soo Myung ◽  
Taeyoon Moon ◽  
Young-Jai Park
Keyword(s):  
Fourth Order ◽  
Power Spectra ◽  
Integral Function ◽  
De Sitter ◽  
Scale Invariant ◽  
Exponential Integral ◽  
Scalar Theory ◽  
Inflation Model ◽  
Slow Roll ◽  
Sitter Spacetime

We study the Einstein-singleton theory during de Sitter inflation since it provides a way to degenerate fourth-order scalar theory. We obtain an exact solution expressed in terms of the exponential-integral function by solving the degenerate fourth-order scalar equation in de Sitter spacetime. Furthermore, we find that its power spectrum blows negatively up in the superhorizon limit, while it is negatively scale-invariant in the subhorizon limit. This suggests that the Einstein-singleton theory contains the ghost-instability and thus, it is not suitable for developing a slow-roll inflation model.

Kaluza–Klein cosmology with an external scalar field

1986 ◽  
Vol 64 (5) ◽  
pp. 617-619
Author(s):  
J. D. Gegenberg
Keyword(s):  
Scalar Field ◽  
Power Law ◽  
Einstein Equations ◽  
Internal Space ◽  
Field Source ◽  
Exponential Expansion ◽  
The One ◽  
Limiting Case ◽  
The Universe ◽  
Kaluza Klein

Simple cosmologies are constructed from solutions of the five-dimensional Einstein equations with a real, massless, non-self-interacting scalar-field source. It is demonstrated that nontrivial cosmological models occur only if the metric of the homogeneous and isotropic 3-space of the universe has nonpositive constant curvature. For the case of flat 3-space, it is further demonstrated that two classes of solutions result, one of which has a power-law type of expansion for 3-space and contraction of the one-dimensional internal space, while the other class has an exponential expansion for 3-space and exponential contraction of the internal space. The exponentially expanding solutions are the limiting case of the power-law expanding solutions. Hence, our model is consistent with a simple inflationary scenario.

scholarly journals HELICAL MAGNETIC FIELDS FROM INFLATION

2009 ◽  
Vol 18 (09) ◽  
pp. 1395-1411 ◽  
Author(s):  
LEONARDO CAMPANELLI
Keyword(s):  
Magnetic Fields ◽  
Power Law ◽  
Background Field ◽  
Wave Number ◽  
Conformal Time ◽  
De Sitter ◽  
Simple Power ◽  
Dimensionless Constant ◽  
Real Positive Number

We analyze the generation of seed magnetic fields during de Sitter inflation considering a noninvariant conformal term in the electromagnetic Lagrangian of the form [Formula: see text], where I(ϕ) is a pseudoscalar function of a nontrivial background field ϕ. In particular, we consider a toy model that could be realized owing to the coupling between the photon and either a (tachyonic) massive pseudoscalar field or a massless pseudoscalar field nonminimally coupled to gravity, where I follows a simple power law behavior I(k,η) = g/(-kη)β during inflation, while it is negligibly small subsequently. Here, g is a positive dimensionless constant, k the wave number, η the conformal time, and β a real positive number. We find that only when β = 1 and 0.1 ≲ g ≲ 2 can astrophysically interesting fields be produced as excitation of the vacuum, and that they are maximally helical.

scholarly journals De Sitter and power-law solutions in non-local Gauss–Bonnet gravity

2018 ◽  
Vol 15 (11) ◽  
pp. 1850188 ◽  
Author(s):  
E. Elizalde ◽  
S. D. Odintsov ◽  
E. O. Pozdeeva ◽  
S. Yu. Vernov
Keyword(s):  
Power Law ◽  
Sufficient Conditions ◽  
Model Parameters ◽  
Local Form ◽  
De Sitter ◽  
Dynamical Equations ◽  
Non Local ◽  
Necessary And Sufficient ◽  
The Universe ◽  
Universe Evolution

The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d’Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as corresponding de Sitter and power-law solutions. Necessary and sufficient conditions on the model parameters for the existence of de Sitter solutions are obtained. The possible existence of power-law solutions is investigated, and it is proven that models with de Sitter solutions have no power-law solutions. A model is found, which allows to describe the matter-dominated phase of the Universe evolution.

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