We investigate the stability of general-relativistic boson stars by classifying singularities of differential mappings and compare it with the results of perturbation theory. Depending on the particle number, the star has the following regimes of beh
avior: stable, metastable, pulsation, and collapse.
We reconsider the nonlinear second order Abel equation of Stewart and Lyth, which follows from a nonlinear second order slow-roll approximation. We find a new eigenvalue spectrum in the blue regime. Some of the discrete values of the spectral index n
_s have consistent fits to the cumulative COBE data as well as to recent ground-base CMB experiments.
There is accumulating evidence that (fundamental) scalar fields may exist in Nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. Similarly as for white dwarfs and neutron stars,
there exists a limiting mass, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and the spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation, however, modifications of general relativity, as in the case of Jordan-Brans-Dicke theory as a low energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing halo, a critical mass inversely proportional to constituent mass, an effective radius, and a large particle number. Due to the Heisenberg principle, there exists a completely stable branch, and as a coherent state, it allows for rotating solutions with quantised angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: Possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.
The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double d
uality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a `vacuum degeneracy. By modifying the duality via a scale breaking term, we demonstrate that only Einsteins equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of `dark energy as well as `dark matter modeled by a torsion induced quintaxion.
A possible equivalence of scalar dark matter, the inflaton, and modified gravity is analyzed. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einstein
ian spaces, distinguished only by a different effective gravitational strength and cosmological constant. A swallow tail catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This `triple unification may shed new light on the nature and large scale distribution not only of dark matter but also on `dark energy, regarded as an effective cosmological constant, and inflation.
