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Register a new userInflationary solutions and inhomogeneous Kaluza-Klein cosmology in 4+n dimensions
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PEREZ BERGLIAFFA San
Publication date
1997
fields
Physics
and research's language is
English
Authors
Santiago E. Perez Bergliaffa
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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.
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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.
We investigate the Kaluza-Klein braneworld cosmology from the point of view of observers on the brane. We first generalize the Shiromizu-Maeda-Sasaki (SMS) equations to higher dimensions. As an application, we study a (4+n)-dimensional brane with n dimensions compactified on the brane, in a (5+n)-dimensional bulk. By assuming that the size of the internal space is static, that the bulk energy-momentum tensor can be neglected, we determine the effect of the bulk geometry on the Kaluza-Klein braneworld. Then we derive the effective Friedmann equation on the brane. It turns out that the Friedmann equation explicitly depends on the equation of state, in contrast to the braneworld in a 5-dimensional bulk spacetime. In particular, in a radiation-dominated era, the effective Newton constant depends on the scale factor logarithmically. If we include a pressureless matter on the brane, this dependence disappears after the radiation-matter equality. This may be interpreted as stabilization of the Newton constant by the matter on the brane. Our findings imply that the Kaluza-Klein braneworld cosmology is quite different from the conventional Kaluza-Klein cosmology even at low energy.
We reconsider theories with low gravitational (or string) scale M_* where Newtons constant is generated via new large-volume spatial dimensions, while Standard Model states are localized to a 3-brane. Utilizing compact hyperbolic manifolds (CHMs) we show that the spectrum of Kaluza-Klein (KK) modes is radically altered. This allows an early universe cosmology with normal evolution up to substantial temperatures, and completely negates the constraints on M_* arising from astrophysics. Furthermore, an exponential hierarchy between the usual Planck scale and the true fundamental scale of physics can emerge with only order unity coefficients. The linear size of the internal space remains small. The proposal has striking testable signatures.
The Kaluza-Klein formalism of the Einsteins theory, based on the (2,2)-fibration of a generic 4-dimensional spacetime, describes general relativity as a Yang-Mills gauge theory on the 2-dimensional base manifold, where the local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. As a way of illustrating how to use this formalism in finding exact solutions, we apply this formalism to the spherically symmetric case, and obtain the Schwarzschild solution by solving the field equations.
We perform the 4-dimensional Kaluza-Klein (KK) reduction of the 5-dimensional locally scale invariant Weyl-Dirac gravity. While compactification unavoidably introduces an explicit length scale into the theory, it does it in such a way that the KK radius can be integrated out from the low energy regime, leaving the KK vacuum to still enjoy local scale invariance at the classical level. Imitating a $U(1)timestilde{U}(1)$ gauge theory, the emerging 4D theory is characterized by a kinetic Maxwell-Weyl mixing whose diagonalization procedure is carried out in detail. In particular, we identify the unique linear combination which defines the 4D Weyl vector, and fully classify the 4D scalar sector. The later consists of (using Weyl language) a co-scalar and two in-scalars. The analysis is performed for a general KK $m$-ansatz, parametrized by the power $m$ of the scalar field which factorizes the 4D metric. The no-ghost requirement, for example, is met provided $-frac{1}{2}leq m leq 0$. An $m$-dependent dictionary is then established between the original 5D Brans-Dicke parameter $omega_5$ and the resulting 4D $omega_4$. The critical $omega_5=-frac{4}{3}$ is consistently mapped into critical $omega_4 = -frac{3}{2}$. The KK reduced Maxwell-Weyl kinetic mixing cannot be scaled away as it is mediated by a 4D in-scalar (residing within the 5D Weyl vector). The mixing is explicitly demonstrated within the Einstein frame for the special physically motivated choice of $m=-frac{1}{3}$. For instance, a super critical Brans-Dicke parameter induces a tiny positive contribution to the original (if introduced via the 5-dimensional scalar potential) cosmological constant. Finally, some no-scale quantum cosmological aspects are studied at the universal mini-superspace level.
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