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Register a new userGravitational Stability of inflaton and torsion in Einstein-Cartan-Klein-Gordon cosmology with kinky potentials
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Added by
L. C. Garcia de Andrade
Publication date
2002
fields
Physics
and research's language is
English
Authors
L.C. Garcia de Andrade
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Gravitational stability of torsion and inflaton field in a four-dimensional spacetime de Sitter solution in scalar-tensor cosmology where Cartan torsion propagates is investigated in detail. Inflaton and torsion evolution equations are derived by making use of a Lagrangean method. Stable and unstable modes for torsion and inflatons are found to be dependent of the background torsion and inflaton fields. Present astrophysical observations favour a stable mode for torsion since this would explain why no relic torsion imprint has been found on the Cosmic Background Radiation in the universe.
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Hawkings singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a nonnegative effective energy density (EED), thereby guaranteeing the timelike convergence property. However, there are models that do not satisfy the SEC and therefore lie outside the scope of Hawkings hypotheses, an important example being the massive Klein-Gordon field. Here we derive lower bounds on local averages of the EED for solutions to the Klein-Gordon equation, allowing nonzero mass and nonminimal coupling to the scalar curvature. The averages are taken along timelike geodesics or over spacetime volumes, and our bounds are valid for a range of coupling constants including both minimal and conformal coupling. Using methods developed by Fewster and Galloway, these lower bounds are applied to prove a Hawking-type singularity theorem for solutions to the Einstein-Klein-Gordon theory, asserting that solutions with sufficient initial contraction at a compact Cauchy surface will be future timelike geodesically incomplete.
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A Friedmann like cosmological model in Einstein-Cartan framework is studied when the torsion function is assumed to be proportional to a single $phi(t)$ function coming just from the spin vector contribution of ordinary matter. By analysing four different types of torsion function written in terms of one, two and three free parameters, we found that a model with $phi(t)=- alpha H(t) big({rho_{m}(t)}/{rho_{0c}}big)^n$ is totally compatible with recent cosmological data, where $alpha$ and $n$ are free parameters to be constrained from observations, $rho_m$ is the matter energy density and $rho_{0c}$ the critical density. The recent accelerated phase of expansion of the universe is correctly reproduced by the contribution coming from torsion function, with a deceleration parameter indicating a transition redshift of about $0.65$.
We extend the treatment of quantum cosmology to a manifold with torsion. We adopt a model of Einstein-Cartan-Sciama-Kibble compatible with the cosmological principle. The universe wavefunction will be subject to a $mathcal{PT}$-symmetric Hamiltonian. With a vanishing energy-momentum tensor, the universe evolution in the semiclassical and classical regimes is shown to reflect a two-stage inflationary process induced by torsion.
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