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Register a new userConformal scalar and torsion do not go together
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We investigate the conformal transformation of vierbein-Einstein-Palatini (VEP) action in terms of tetrads $e^I_mu$ and spin connection $A^{IJ}_mu$. The transformation of the spin connection is indeterminate off-shell unless equations of motion are satisfied. We construct the conformally invariant scalar field in the torsion-free VEP formalism. In presence of fermionic matter, torsion does not vanish, and shows up in the dynamics of conformal scalar, affecting the invariance. It is not possible to maintain conformal invariance of the scalar field equation when fermions are present.
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A teleparallel geometry is an n-dimensional manifold equipped with a frame basis and an independent spin connection. For such a geometry, the curvature tensor vanishes and the torsion tensor is non-zero. A straightforward approach to characterizing teleparallel geometries is to compute scalar polynomial invariants constructed from the torsion tensor and its covariant derivatives. An open question has been whether the set of all scalar polynomial torsion invariants, $mathcal{I}_T$ uniquely characterize a given teleparallel geometry. In this paper we show that the answer is no and construct the most general class of teleparallel geometries in four dimensions which cannot be characterized by $mathcal{I}_T$. As a corollary we determine all teleparallel geometries which have vanishing scalar polynomial torsion invariants.
We investigate the cosmological dynamics in teleparallel gravity with nonminimal coupling. We analytically extract several asymptotic solutions and we numerically study the exact phase-space behavior. Comparing the obtained results with the corresponding behavior of nonminimal scalar-curvature theory, we find significant differences, such is the rare stability and the frequent presence of oscillatory behavior.
A viable model for inflation driven by a torsion function in a Friedmann background is presented. The scalar spectral index in the interval $0.92lesssim n_{s}lesssim 0.97$ is obtained in order to satisfy the initial conditions for inflation. The post inflationary phase is also studied, and the analytical solutions obtained for scale factor and energy density generalizes that ones for a matter dominated universe, indicating just a small deviation from the standard model evolution. The same kind of torsion function used also describes satisfactorily the recent acceleration of the universe, which could indicate a possible unification of different phases, apart form specific constants.
We study spherically symmetric soliton solutions in a model with a conformally coupled scalar field as well as in full conformal gravity. We observe that a new type of limiting behaviour appears for particular choices of the self-coupling of the scalar field, i.e. the solitons interpolate smoothly between the Anti-de Sitter vacuum and an uncharged configuration. Furthermore, within conformal gravity the qualitative approach of a limiting solution does not change when varying the charge of the scalar field - contrary to the Einstein-Hilbert case. However, it changes with the scalar self-coupling.
We investigate the cosmological applications of a bi-scalar modified gravity that exhibits partial conformal invariance, which could become full conformal invariance in the absence of the usual Einstein-Hilbert term and introducing additionally either the Weyl derivative or properly rescaled fields. Such a theory is constructed by considering the action of a non-minimally conformally-coupled scalar field, and adding a second scalar allowing for a nonminimal derivative coupling with the Einstein tensor and the energy-momentum tensor of the first field. At a cosmological framework we obtain an effective dark-energy sector constituted from both scalars. In the absence of an explicit matter sector we extract analytical solutions, which for some parameter regions correspond to an effective matter era and/or to an effective radiation era, thus the two scalars give rise to mimetic dark matter or to dark radiation respectively. In the case where an explicit matter sector is included we obtain a cosmological evolution in agreement with observations, that is a transition from matter to dark energy era, with the onset of cosmic acceleration. Furthermore, for particular parameter regions, the effective dark-energy equation of state can transit to the phantom regime at late times. These behaviours reveal the capabilities of the theory, since they arise purely from the novel, bi-scalar construction and the involved couplings between the two fields.
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