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Register a new userCosmological inflation
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Scientific Information Service CERN
Publication date
2012
fields
Physics
and research's language is
English
Authors
K. Enqvist
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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.
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By making a suitable generalization of the Starobinsky stochastic inflation, we propose a classical phase space formulation of stochastic inflation which may be used for a quantitative study of decoherence of cosmological perturbations during inflation. The precise knowledge of how much cosmological perturbations have decohered is essential to the understanding of acoustic oscillations of cosmological microwave background (CMB) photons. In order to show how the method works, we provide the relevant equations for a self-interacting inflaton field. For pedagogical reasons and to provide a link to the field theoretical case, we consider the quantum stochastic harmonic oscillator.
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.
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.
A new idea of deriving a cosmological term from an underlying theory has been proposed in order to explain the expansion history of the universe. We obtain the scale factor with this derived cosmological term and demonstrate that it reflects all the characteristics of the expanding universe in different era so as to result in a transition from inflation to late acceleration through intermediate decelerating phases by this single entity. We further discuss certain observational aspects of this paradigm.
In the framework of polynomial Palatini cosmology, we investigate a simple cosmological homogeneous and isotropic model with matter in the Einstein frame. We show that in this model during cosmic evolution, it appears the early inflation and the accelerating phase of the expansion for the late times. In this frame we obtain the Friedmann equation with matter and dark energy in the form of a scalar field with the potential whose form is determined in a covariant way by the Ricci scalar of the FRW metric. The energy density of matter and dark energy are also parametrized through the Ricci scalar. The early inflation is obtained only for an infinitesimally small fraction of energy density of matter. Between the matter and dark energy, there exists interaction because the dark energy is decaying. For characterization of inflation we calculate the slow roll parameters and the constant roll parameter in terms of the Ricci scalar. We have found a characteristic behaviour of the time dependence of density of dark energy on the cosmic time following the logistic-like curve which interpolates two almost constant value phases. From the required numbers of $N$-folds we have found a bound on model parameter.
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