Abstract
We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers of the subsequent orders of the scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution due to the suppression of the n-dependency in the energy momentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This contribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations of about 180 ∘ . The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure T z z for discrete values of the azimuthal-angle. There could be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and this could be evidence for the existence of cosmic strings. Careful comparison of this spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available. It turns out that, for late time, the vacuum 5D spacetime is conformally invariant if the warp factor fulfils the equation of a vibrating “drum”, describing standing normal modes of the brane.
Highlights
It is a great challenge for theoretical physicists and cosmologists to find an explanation for the dark energy needed for the observed acceleration of our universe without the need of a cosmological constant
Our Ω-field can play a crucial role in this context if one introduces an unavoidable dilaton field. It is found on a five dimensional warped brane world spacetime, using a multiple-scale approximation scheme, that, to second order, the metric and scalar gauge field show a spectrum of azimuthal-angle dependent wavelike modes with extremal values dependent of the winding numbers of the background, first and second order perturbations of the scalar field
The model can explain the late-time acceleration of our universe without the need of a controversial cosmological constant
Summary
It is a great challenge for theoretical physicists and cosmologists to find an explanation for the dark energy needed for the observed acceleration of our universe without the need of a cosmological constant. The dark energy term in the effective Einstein equations on the brane will be provided by the projected 5D Weyl tensor [3] There is, another possibility to test the existence of large extra dimensions. This U(1) scalar gauge field with a “Mexican hat” potential has lived up its reputation in the theory of superconductivity, where vortex lines occur as topological defects and in the standard model of particle physics In cosmology it could trigger the inflationary period of expansion and could solve the horizon and flatness problem. There are already tight constraints on the gravitational wave signatures due to string loops via observations of the millisecond pulsar-timing data, the cosmic microwave background radiation (CMB) and analysis of data of the LIGO-Virgo gravitational-wave detector [11,12] Evidence of these objects would give us information at very high energies in the early stages of the universe. In the appendices we collected all the relevant equations in order to keep the main text readable
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