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Register a new userExtrasolar scale change in Newtons Law from 5D `plain R^2-gravity
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I.L. Zhogin
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Galactic rotation curves and lack of direct observations of Dark Matter may indicate that General Relativity is not valid (on galactic scale) and should be replaced with another theory. There is the only variant of Absolute Parallelism which solutions are free of arising singularities, if D=5 (there is no room for changes). This variant does not have a Lagrangian, nor match GR: an equation of `plain R^2-gravity (ie without R-term) is in sight instead. Arranging an expanding O_4-symmetrical solution as the basis of 5D cosmological model, and probing a universal_function of mass distribution (along very-very long the extra dimension) to place into bi-Laplace equation (R^2 gravity), one can derive the Law of Gravitation: 1/r^2 transforms to 1/r with distance (not with acceleration).
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This paper has been withdrawn by the author, due to obsolete reference [4], insufficient discussion in sec. 4, and major conceptual error in sec. 5.
We study the propagation of gravitons within 5-D supersymmetric braneworld models with a bulk scalar field. The setup considered here consists of a 5-D bulk spacetime bounded by two 4-D branes localized at the fixed points of an $S^1/Z_2$ orbifold. There is a scalar field $phi$ in the bulk which, provided a superpotential $W(phi)$, determines the warped geometry of the 5-D spacetime. This type of scenario is common in string theory, where the bulk scalar field $phi$ is related to the volume of small compact extra dimensions. We show that, after the moduli are stabilized by supersymmetry breaking terms localized on the branes, the only relevant degrees of freedom in the bulk consist of a 5-D massive spectrum of gravitons. Then we analyze the gravitational interaction between massive bodies localized at the positive tension brane mediated by these bulk gravitons. It is shown that the Newtonian potential describing this interaction picks up a non-trivial contribution at short distances that depends on the shape of the superpotential $W(phi)$. We compute this contribution for dilatonic braneworld scenarios $W(phi) = e^{alpha phi}$ (where $alpha$ is a constant) and discuss the particular case of 5-D Heterotic M-theory: It is argued that a specific footprint at micron scales could be observable in the near future.
Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we examine the consequences of the simple hypothesis that the three-dimensional space has a global R^2 X S^1 topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newtons gravitational potential and we find that for distances smaller than the S^1-radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newtons force from 1/r^2 to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level.
In braneworld models coming from string theory one generally encounters massless scalar degrees of freedom -moduli- parameterizing the volume of small compact extra-dimensions. Here we discuss the effects of such moduli on Newtons law for a fairly general 5-D supersymmetric braneworld scenario with a bulk scalar field $phi$. We show that the Newtonian potential describing the gravitational interaction between two bodies localized on the visible brane picks up a non-trivial contribution at short distances that depends on the shape of the superpotential $W(phi)$ of the theory. In particular, we compute this contribution for dilatonic braneworld scenarios $W(phi) = e^{alpha phi}$ (where $alpha$ is a constant) and discuss the particular case of 5-D Heterotic M-theory.
It has recently been suggested that the Standard Model Higgs boson could act as the inflaton while minimally coupled to gravity - given that the gravity sector is extended with an $alpha R^2$ term and the underlying theory of gravity is of Palatini, rather than metric, type. In this paper, we revisit the idea and correct some shortcomings in earlier studies. We find that in this setup the Higgs can indeed act as the inflaton and that the tree-level predictions of the model for the spectral index and the tensor-to-scalar ratio are $n_ssimeq 0.941$, $rsimeq 0.3/(1+10^{-8}alpha)$, respectively, for a typical number of e-folds, $N=50$, between horizon exit of the pivot scale $k=0.05, {rm Mpc}^{-1}$ and the end of inflation. Even though the tensor-to-scalar ratio is suppressed compared to the usual minimally coupled case and can be made compatible with data for large enough $alpha$, the result for $n_s$ is in severe tension with the Planck results. We briefly discuss extensions of the model.
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