Stability issues in the modified starobinsky model

Nuclear Physics B, 2003

We analyze various phases of inflation based on the anomaly-induced effective action of gravity (modified Starobinsky model), taking the cosmological constant Λ and k = 0, ±1 topologies into account. The total number of the inflationary e-folds may be enormous, but at the last 65 of them the inflation greatly slows down due to the contributions of the massive particles. For the supersymmetric particle content, the stability of inflation holds from the initial point at the sub-Planck scale until the supersymmetry breaks down. After that the universe enters into the unstable regime with the eventual transition into the stable FRW-like evolution with small positive cosmological constant. It is remarkable, that all this follows automatically, without fine-tuning of any sort, independent on the values of Λ and k. Finally, we consider the stability under the metric perturbations during the last 65 e-folds of inflation and find that the amplitude of the ones with the wavenumber below a certain cutoff have an acceptable range.

arXiv (Cornell University), 2018

Starobinsky has suggested an inflation model which is obtained from the vacuum Einstein's equations modified by the one-loop corrections due to quantized matter fields. Although the one-loop gravitational action is not known for a general FRW background, it can be obtained in a de Sitter space to give M 2 p R+αR 2 +βR 2 ln(R/M 2). Thus, one needs to investigate the inflationary behavior of this model compared to the Starobinsky model (i.e. β = 0). The coefficient α can be changed by varying the renormalization scale M 2 and β is obtained from the quantum anomaly which is related to the numbers of quantum fields. It has been assumed that α β. We investigate the viable values of α and β based on the CMB observation. We also scrutinize the reheating process in this model.

Journal of Cosmology and Astroparticle Physics, 2022

We study several extensions of the Starobinsky model of inflation, which obey all observational constraints on the inflationary parameters, by demanding that both the inflaton scalar potential in the Einstein frame and the F(R) gravity function in the Jordan frame have the explicit dependence upon fields and parameters in terms of elementary functions. Our models are continuously connected to the original Starobinsky model via changing the parameters. We modify the Starobinsky (R + R 2) model by adding an R 3-term, an R 4-term, and an R 3/2-term, respectively, and calculate the scalar potentials, the inflationary observables and the allowed limits on the deformation parameters by using the latest observational bounds. We find that the tensor-to-scalar ratio in the Starobinsky model modified by the R 3/2-term significantly increases with raising the parameter in front of that term. On the other side, we deform the scalar potential of the Starobinsky model in the Einstein frame in pow...

Journal of Cosmology and Astroparticle Physics

The European Physical Journal C

Quantum effects derived through conformal anomaly lead to an inflationary model that can be either stable or unstable. The unstable version requires a large dimensionless coefficient of about 5 × 10 8 in front of the R 2 term that results in the inflationary regime in the R + R 2 ("Starobinsky") model being a generic intermediate attractor. In this case the non-local terms in the effective action are practically irrelevant, and there is a 'graceful exit' to a low curvature matter-like dominated stage driven by high-frequency oscillations of R-scalarons, which later decay to pairs of all particles and antiparticles, with the amount of primordial scalar (density) perturbations required by observations. The stable version is a genuine generic attractor, so there is no exit from it. We discuss a possible transition from stable to unstable phases of inflation. It is shown that this transition is automatic if the sharp cutoff approximation is assumed for quantum corrections in the period of transition. Furthermore, we describe two different quantum mechanisms that may provide a required large R 2-term in the transition period.

Physical Review D, 2006

It is believed that soon after the Planck era, space time should have a semi-classical nature. According to this, the escape from General Relativity theory is unavoidable. Two geometric counter-terms are needed to regularize the divergences which come from the expected value. These counter-terms are responsible for a higher derivative metric gravitation. Starobinsky idea was that these higher derivatives could mimic a cosmological constant. In this work it is considered numerical solutions for general Bianchi I anisotropic space-times in this higher derivative theory. The approach is "experimental" in the sense that there is no attempt to an analytical investigation of the results. It is shown that for zero cosmological constant Λ = 0, there are sets of initial conditions which form basins of attraction that asymptote Minkowski space. The complement of this set of initial conditions form basins which are attracted to some singular solutions. It is also shown, for a cosmological constant Λ > 0 that there are basins of attraction to a specific de Sitter solution. This result is consistent with Starobinsky's initial idea. The complement of this set also forms basins that are attracted to some type of singular solution. Because the singularity is characterized by curvature scalars, it must be stressed that the basin structure obtained is a topological invariant, i.e., coordinate independent.

International Journal of Modern Physics D, 2009

The Starobinsky model is a natural inflationary scenario in which inflation arises due to quantum effects of the massless matter fields. A modified version of the Starobinsky (MSt) model takes the masses of matter fields and the cosmological constant, Λ, into account. The equations of motion become much more complicated; however, approximate analytic and numeric solutions are possible. In the MSt model, inflation starts due to the supersymmetric (SUSY) particle content of the underlying theory, and the transition to the radiation-dominated epoch occurs due to the relatively heavy s-particles decoupling. For Λ = 0 the inflationary solution is stable until the last stage, just before decoupling. In the present paper we generalize this result for Λ ≠ 0, since Λ should be nonvanishing at the SUSY scale. We also take into account the radiative corrections to Λ. The main result is that the inflationary solution of the MSt model remains robust and stable.

ECU 2023

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Physical Review D, 2015

We consider the simplest extension to the Starobinsky model, by allowing an extra scalar field to help drive inflation. We perform our analysis in the Einstein frame and calculate the power spectra at the end of inflation to second order in the slow-roll parameters. We find that the model gives predictions in great agreement with the current Planck data without the need for fine-tuning. Our results encourage current efforts to embed the model in a supergravity setting.

International Journal of Modern Physics D, 2021

In this work, we study numerically one kind of generalization of the Starobinsky inflationary model (power-law type), which is characterized by the parameter [Formula: see text]. In order to find the parameter [Formula: see text] that fixes with observations, we compute the cosmological parameters [Formula: see text], [Formula: see text] and [Formula: see text] for several values of [Formula: see text]. We have found that the value of [Formula: see text] reproduces the value of [Formula: see text], [Formula: see text] and [Formula: see text] is in agreement with the current observational data.