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Register a new userCosmological inflation driven by a scalar torsion function
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Added by
Thiago Guimar\\~aes
Publication date
2020
fields
Physics
and research's language is
English
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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.
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We consider cosmological dynamics of nonminimally coupled scalar field in the scalar-torsion gravity in the presence of a hydrodynamical matter. Potential of the scalar field have been chosen as power-law with negative index, this type of potentials is usually used in quintessence scenarios. We identify several asymptotic regimes, including de Sitter, kinetic dominance, kinetic tracker and tracker solution and study conditions for their existence and stability. We show that for each combination of coupling constant and potential power index one of regimes studied in the present paper is stable to the future.
Suppose that the early Universe starts with a quantum spacetime originated cosmological $Lambda$-term at the Planck scale $M_{rm pl}$. The cosmological energy density $rho_{_{_Lambda}}$ drives inflation and simultaneously reduces its value to create the matter-energy density $rho_{_{_M}}$ via the continuous pair productions of massive fermions and antifermions. The decreasing $rho_{_{_Lambda}}$ and increasing $rho_{_{_M}}$, in turn, slows down the inflation to its end when the pair production rate $Gamma_M$ is larger than the Hubble rate $H$. The density $rho_{_{_Lambda}}$ and Hubble rate $H$ are uniquely determined by two independent equations from the Einstein equation and energy conservation law, besides the $rho_{_{_M}}$ is determined by pair productions. As a result, inflation naturally appears and theoretical results agree with Planck 2018 observations. Suppose that the reheating efficiently converts $rho_{_{_Lambda}}$ to $rho_{_{_M}}gg rho_{_{_Lambda}}$ accounting for the most relevant Universe mass, and some massive pairs decay to relativistic particles of energy density $rho_{_{_R}}$ starting the hot Big Bang. The back reaction $rho_{_{_M}}leftrightarrow Hleftrightarrow rho_{_{_Lambda}}$ is weak but continues. As a consequence, $rho_{_Lambda}$ closely tracks down $rho_{_R}$ from the reheating end up to the radiation-matter equilibrium, then it varies very slowly, $rho_{_Lambda}propto$ constant, due to the transition from radiation dominant epoch to matter dominant epoch. Therefore the cosmic coincidence problem can be possibly avoided.
The very basics of cosmological inflation are discussed. We derive the equations of motion for the inflaton field, introduce the slow-roll parameters, and present the computation of the inflationary perturbations and their connection to the temperature fluctuations of the cosmic microwave background.
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.
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