We are considering the cosmological consequences of an induced gravity theory coupled to the minimal standard model of particle physics. The non-minimal coupling parameter between gravity and the Higgs field must then be very large, yielding some new cosmological consequences for the early Universe and new constraints on the Higgs mass. As an outcome, new inflation is only possible for very special initial conditions producing first a short contraction era after which an inflationary expansion automatically follows; a chaotic inflationary scenario is successfully achieved. The contrast of density perturbations required to explain the seed of astronomic structures are obtained for very large values of the Higgs mass (M H >> G −1/2 F ), otherwise the perturbations have a small amplitude; in any case, the spectral index of scalar perturbations agrees with the observed one.

We use the general solution to the trace of the 4-dimensional Einstein equations for static, spherically symmetric configurations as a basis for finding a general class of black hole (BH) metrics, containing one arbitrary function gtt = A(r) which vanishes at some r = r h > 0, the horizon radius. Under certain reasonable restrictions, BH metrics are found with or without matter and, depending on the boundary conditions, can be asymptotically flat or have any other prescribed asymptotic. It is shown that our procedure generically leads to families of globally regular BHs with a Kerr-like global structure as well as symmetric wormholes. Horizons in space-times with zero scalar curvature are shown to be either simple or double. The same is generically true for horizons inside a matter distribution, but in special cases there can be horizons of any order. A few simple examples are discussed. A natural application of the above results is the brane world concept, in which the trace of the 4D gravity equations is the only unambiguous equation for the 4D metric, and its solutions can be continued into the 5D bulk according to the embedding theorems.Maeda and Sasaki [11] from 5-dimensional gravity with the aid of the Gauss and Codazzi equations [28]:

We give a comparative description of different types of regular static, spherically symmetric black holes (BHs) and discuss in more detail their particular type, which we suggest to call black universes. The latter have a Schwarzschild-like causal structure, but inside the horizon there is an expanding Kantowski-Sachs universe and a de Sitter infinity instead of a singularity. Thus a hypothetic BH explorer gets a chance to survive. Solutions of this kind are naturally obtained if one considers static, spherically symmetric distributions of various (but not all) kinds of phantom matter whose existence is favoured by cosmological observations. It also looks possible that our Universe has originated from phantom-dominated collapse in another universe and underwent isotropization after crossing the horizon. An explicit example of a black-universe solution with positive Schwarzschild mass is discussed.

We i n v estigate the cosmological consequences of a theory of induced gravity in which the scalar eld is identied with the Higgs eld of the rst symmetry breaking of a minimal SU(5) GUT. The mass of the X-boson determines a great value for the coupling constant of gravityparticle physics. Because of this fact, a "slow" rollover dynamics for the Higgs eld is not possible in a "new" ination scenario and, moreover, a contraction era for the scale factor in the early universe exists, after which ination follows automatically; "chaotic" ination is performed without problems. Ination is successfully achieved due to the relationship among the masses of particle physics at that scale: The Higgs-, X-boson-and Planck-masses. As a result the particle physics parameter is not ne-tuned as usual in order to predict acceptable values of re-heating temperature and density and gravitational wave perturbations. Moreover, if the coherent Higgs oscillations didn't decay they could explain the missing mass problem of cosmology.

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We discuss a non-minimal Einstein-Yang-Mills-Higgs model with uniaxial anisotropy in the group space associated with the Higgs field. We apply this theory to the problem of propagation of color and color-acoustic waves in the gravitational background related to the non-minimal regular Wu-Yang monopole.

We apply the method of moving anholonomic frames, with associated nonlinear connections, in (pseudo) Riemannian spaces and examine the conditions when various types of locally anisotropic (la) structures (Lagrange, Finsler like and more general ones) could be modeled in general relativity. New classes of solutions of the Einstein equations with generic local anisotropy are constructed. We formulate the theory of nearly autoparallel (na) maps and introduce the tensorial na-integration as the inverse operation to both covariant derivation and deformation of connections by na-maps. The problem of redefinition of the Einstein gravity theory on na-backgrounds, provided with a set of na-map invariant conditions and local conservation laws, is analyzed. There are illustrated some examples of generation of vacuum Einstein fields by Finsler like metrics and chains of na-maps.Comment: 41 page