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Register a new userSingle field inflationary models with non-compact Kaluza-Klein theory
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Authors
Diego S. Ledesma
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We discuss a semiclassical treatment to inflationary models from Kaluza-Klein theory without the cylinder condition. We conclude that the evolution of the early universe could be described by a geodesic trayectory of a cosmological 5D metric here proposed, so that the effective 4D FRW background metric should be a hypersurface on a constant fifth dimension.
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We study teleparallel gravity in the emph{original} Kaluza-Klein (KK) scenario. Our calculation of the KK reduction of teleparallel gravity indicates that the 5-dimensional torsion scalar $^{(5)}T$ generates the non-Brans-Dicke type effective Lagrangian in 4-dimension due to an additional coupling between the derivative of the scalar field and torsion, but the result is equivalent to that in general relativity. We also discuss the cosmological behavior in the FLRW universe based on the effective teleparallel gravity.
We analyze the existence of inflationary solutions in an inhomogeneous Kaluza-Klein cosmological model in 4+n dimensions. It is shown that the 5-dimensional case is the exception rather than the rule, in the sense that the system is integrable (under the assumption of the equation of state $rho= kp$) for any value of k. It is also shown that the cases k=0 and k=1/3 are integrable if and only if n=1.
A new spherically-symmetric solution is determined in a noncompactified Kaluza-Klein theory in which a time character is ascribed to the fifth coordinate. This solution contains two independent parameters which are related with mass and electric charge. The solution exhibits a Schwarzschild radius and represents a generalization of the Schwarzschild solution in four dimensions. The parameter of the solution connected with the electric charge depends on the derivative of the fifth (second time) coordinate with respect to the ordinary time coordinate. It is shown that the perihelic motion in four-dimensional relativity has a counterpart in five dimensions in the perinucleic motion of a negatively-charged particle. If the quantization conditions of the older quantum theory are applied to that motion, an analogue of the fine-structure formula of atomic spectra is obtained.
We study the extensions of teleparallism in the Kaluza-Klein (KK) scenario by writing the analogous form to the torsion scalar $T_{text{NGR}}$ in terms of the corresponding antisymmetric tensors, given by $T_{text{NGR}} = a,T_{ijk} , T^{ijk} + b,T_{ijk} ,T^{kji} + c,T^{j}{}_{ji} , T^{k}{}_{k}{}^{i}$, in the four-dimensional New General Relativity (NGR) with arbitrary coefficients $a$, $b$ and $c$. After the KK dimensional reduction, the Lagrangian in the Einstein-frame can be realized by taking $2a+b+c=0$ with the ghost-free condition $cleq0$ for the one-parameter family of teleparallelism. We demonstrate that the pure conformal invariant gravity models can be constructed by the requirements of $2a+b=0$ and $c=0$. In particular, the torsion vector can be identified as the conformal gauge field, while the conformal gauge theory can be obtained by $2a+b+4c=0$ or $2a+b=0$, which is described on the Weyl-Cartan geometry $Y_4$ with the ghost-free conditions $2a+b+c>0$ and $c eq0$. We also consider the weak field approximation and discuss the non-minimal coupled term of the scalar current and torsion vector. For the conformal invariant models with $2a+b=0$, we find that only the anti-symmetric tensor field is allowed rather than the symmetric one.
We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high friction limit. In particular, with the help of the non-minimally derivative coupling, the quartic power law potential is consistent with the observational constraint at 95% CL.
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