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Register a new userNumerical analysis of the generalized Starobinsky inflationary model
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In this work we study numerically one kind of generalization of the Starobinsky inflationary model (power-law type), which is characterized by the parameter $p$. In order to find the parameter $p$ that fixes with observations, we compute the cosmological parameters $A_S$, $n_S$, and $r$ for several values of $psimeq 1$. We have found that the value of $p=1.0004$ reproduces the value of $A_S$, $n_sca$, and $r$ in agreement with current observational data.
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In this work we study the scalar power spectrum and the spectral index for the Starobinsky inflationary model using the phase integral method up-to third-order of approximation. We show that the semiclassical methods reproduce the scalar power spectrum for the Starobinsky model with a good accuracy, and the value of the spectral index compares favorably with observations. Also, we compare the results with the uniform approximation method and the second-order slow-roll approximation.
We study the $R^p$ inflationary model of [Muller:1989rp] for $p>2$ using the result of Ref. [Motohashi:2014tra]. After reproducing the observable quantities: the power spectral index $n_s$, its corresponding running $alpha=frac{dn_s}{dln(k)}$ and the tensor to scalar ration $r$ in terms of e-folding number $N$ and $p$, we show that $R^p$ inflation model is still alive as $p$ is from $2$ to $2.02$. In this range, our calculation confirms that $n_s$ and $r$ agree with observations and $alpha$ is of order $10^{-4}$ which needs more precise observational constraints. We find that, as the value of $p$ increases, all $n_s$, $r$ and $|alpha|$ decrease. However, the precise interdependence between these observables is such that this class of models can in principle be tested by the next generation of dedicated satellite CMB probes.
The first inflationary model conceived was the one proposed by Starobinsky which includes an additional term quadratic in the Ricci-scalar R in the Einstein-Hilbert action. The model is now considered a target for several future cosmic microwave background experiments given its compatibility with current observational data. In this paper, we analyse the robustness of the Starobinsky inflation by inserting it into a generalized scenario based on a $beta$-Starobinsky inflation potential, which is motivated through brane inflation. In the Einstein frame, the generalized model recovers the original model for $beta=0$, whereas $forall beta eq 0$ represents an extended class of models that admit a wider range of solutions. We investigate limits on $beta$ from current cosmic microwave background and baryonic acoustic oscillation data and find that only a small deviation from the original scenario is allowed, $beta=-0.08 pm 0.12$ (68% C.L.), which is fully compatible with zero and confirms the robustness of the Starobinsky inflationary model in light of current observations.
We classify singularities in FRW cosmologies, which dynamics can be reduced to the dynamical system of the Newtonian type. This classification is performed in terms of geometry of a potential function if it has poles. At the sewn singularity, which is of a finite scale factor type, the singularity in the past meets the singularity in the future. We show, that such singularities appear in the Starobinsky model in $f(hat{R})=hat{R}+gamma hat{R}^2$ in the Palatini formalism, when dynamics is determined by the corresponding piece-wise smooth dynamical system. As an effect we obtain a degenerated singularity. Analytical calculations are given for the cosmological model with matter and the cosmological constant. The dynamics of model is also studied using dynamical system methods. From the phase portraits we find generic evolutionary scenarios of the evolution of the Universe. For this model, the best fit value of $Omega_gamma=3gamma H_0^2$ is equal $9.70times 10^{-11}$. We consider model in both Jordan and Einstein frames. We show that after transition to the Einstein frame we obtain both form of the potential of the scalar field and the decaying Lambda term.
We review some recent trends in the inflationary model building, the supersymmetry (SUSY) breaking, the gravitino Dark Matter (DM) and the Primordial Black Holes (PBHs) production in supergravity. The Starobinsky inflation can be embedded into supergravity when the inflaton belongs to the massive vector multiplet associated with a (spontaneously broken) $U(1)$ gauge symmetry. The SUSY and R-symmetry can be also spontaneously broken after inflation by the (standard) Polonyi mechanism. Polonyi particles and gravitinos are super heavy and can be copiously produced during inflation via the Schwinger mechanism sourced by the Universe expansion. The overproduction and instability problems can be avoided, and the positive cosmological constant (dark energy) can also be introduced. The observed abundance of the Cold Dark Matter (CDM) composed of gravitinos can be achieved in our supergravity model too, thus providing the unifying framework for inflation, supersymmetry breaking, dark energy and dark matter genesis. Our supergravity approach may also lead to a formation of primordial non-linear structures like stellar-mass-type black holes, and may include the SUSY GUTs inspired by heterotic string compactifications, unifying particle physics with quantum gravity.
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