Starobinsky Model Of Inflation Research Articles

Solution for cosmological observables in the Starobinsky model of inflation

This paper focuses on the Starobinsky model of inflation in the Einstein frame. We derive solutions for various cosmological observables, such as the scalar spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r and their runnings, as well as the number of e-folds of inflation, reheating, and radiation, with minimal assumptions. The impact of reheating on inflation is explored by constraining the equation of state parameter ωre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{re}$$\\end{document} at the end of reheating. An equation linking inflation with reheating is established, which is solved for the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}. Using consistency relations of the model, we determine the other observables while the number of e-folds during inflation Nk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_k$$\\end{document}, and the number of e-folds during reheating Nre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{re}$$\\end{document} are determined by their respective formulas involving ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}. We find remarkable agreement between the Starobinsky model and current measurements of the power spectrum of primordial curvature perturbations and the present bounds on the spectrum of primordial gravitational waves.

New one-parametric extension of the Starobinsky inflationary model

We propose a one-parametric extension of the Starobinsky R + R 2 model by adding the term. The parameter m is the inflaton mass, which is determined in the same way as in the Starobinsky model, and β is a dimensionless constant. Using the Einstein frame and the scalar field potential, we get the inflationary parameters of the model proposed. The value of the tensor-to-scalar ratio r can be significantly larger than in the Starobinsky model. The considered inflationary model is in a good agreement with the current observational data. The corresponding scalar field potential is a polynomial of the exponential function.

(No) Eternal Inflation in the Starobinsky Inflation Corrected by Higher Curvature Invariants

The swampland criteria in string theory assert the no eternal inflation scenario. This work studied the impact of generic gravitational quantum corrections on eternal inflation. In particular, we find that the Starobinsky model of inflation should receive higher-order corrections stemming from quantum gravity. In this work, we studied the effect of the R3/2 and R4 corrections on the eternal inflation conditions for the Starobinsky model.

A grounded perspective on new early dark energy using ACT, SPT, and BICEP/Keck

We examine further the ability of the New Early Dark Energy model (NEDE) to resolve the current tension between the Cosmic Microwave Background (CMB) and local measurements of H 0 and the consequences for inflation. We perform new Bayesian analyses, including the current datasets from the ground-based CMB telescopes Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT), and the BICEP/Keck telescopes, employing an updated likelihood for the local measurements coming from the SH 0ES collaboration. Using the SH 0ES prior on H 0, the combined analysis with Baryonic Acoustic Oscillations (BAO), Pantheon, Planck and ACT improves the best-fit by Δχ 2 = -15.9 with respect to ΛCDM, favors a non-zero fractional contribution of NEDE, fNEDE > 0, by 4.8σ, and gives a best-fit value for the Hubble constant of H 0 = 72.09 km/s/Mpc (mean 71.49 ± 0.82 with 68% C.L.). A similar analysis using SPT instead of ACT yields consistent results with a Δχ 2 = -23.1 over ΛCDM, a preference for non-zero f NEDE of 4.7σ and a best-fit value of H0 = 71.77 km/s/Mpc (mean 71.43 ± 0.85 with 68% C.L.). We also provide the constraints on the inflation parameters r and ns coming from NEDE, including the BICEP/Keck 2018 data, and show that the allowed upper value on the tensor-scalar ratio is consistent with the ΛCDM bound, but, as also originally found, with a more blue scalar spectrum implying that the simplest curvaton model is now favored over the Starobinsky inflation model.

On the superstring-inspired quantum correction to the Starobinsky model of inflation

Superstring/M-theory is the theory of quantum gravity that can provide the UV-completion to viable inflation models. We modify the Starobinsky inflation model by adding the Bel-Robinson tensor Tμνλρ squared term proposed as the leading quantum correction inspired by superstring theory. The (R + 1/6m 2 R 2 - β/8m 6 T 2) model under consideration has two parameters: the inflaton mass m and the string-inspired positive parameter β. We derive the equations of motion in the Friedmann-Lemaitre-Robertson-Walker universe and investigate its solutions. We find the physical bounds on the value of the parameter β by demanding the absence of ghosts and consistency of the derived inflationary observables with the measurements of the cosmic microwave background radiation.

Asymptotically free and safe quantum gravity scenarios consistent with Hubble, laboratory, and inflation scale physics

To find out the possible scenarios for quantum gravity consistent with the observed universe, we numerically investigate the non-perturbative renormalization group equations of a general quadratic gravity theory recently derived by Sen, Wetterich and Yamada (\textit{JHEP} 03 (2022) 130). As boundary conditions, we impose consistency with the Hubble scale and the laboratory scale experiments, and the Starobinsky model of inflation. We find two kinds of trajectories which go to different regime at the trans-Planckian scales: i) a trajectory which flows to the asymptotically free regime, and ii) a trajectory which flows to the asymptotically safe regime. To determine the early-time cosmological scenario, an additional observational data from beyond the homogeneous and isotropic space-time is necessary.

Instability of the electroweak vacuum in Starobinsky inflation

We study the stability of the electroweak vacuum during and after the Starobinky inflation, assuming the existence of the non-minimal Higgs coupling to the Ricci scalar. In the Starobinsky inflation, there exists R2 term (with R being the Ricci scalar), which modifies the evolution equation of the Higgs field. We consider the case that the non-minimal coupling is sizable so that the quantum fluctuation of the Higgs field is suppressed and that the Higgs amplitude is settled near the origin during the inflation. In such a case, the Higgs amplitude may be amplified in the preheating epoch after inflation because of the parametric resonance due to the non-minimal coupling. We perform a detailed analysis of the evolution of the Higgs field in the preheating epoch by a numerical lattice simulation and derive an upper bound on the non-minimal coupling constant ξ in order to realize the electroweak vacuum in the present universe. We find that the upper bound on ξ in the Starobinsky inflation model is more stringent than that in conventional inflation models without the R2 term.

Study of scalar and tensor power spectra in the generalized Starobinsky inflationary model using semiclassical methods

In this work we solved the equation of scalar and tensor perturbations for the generalized Starobinsky inflationary model using the improved uniform approximation method and the phase-integral method up to third-order in deviation. We compare our results with the numerical integration. We have obtained that both semiclassical methods reproduce the scalar power spectra PS,T, the scalar spectral index nS, and the tensor-to-scalar ratio r. Also we present our results in the (nS,r) plane.

Calculation of the Precision Parameters of Relic Radiation in the Starobinsky Inflationary Model

Calculation of the Precision Parameters of Relic Radiation in the Starobinsky Inflationary Model

On brane cosmological behaviors of Starobinsky inflationary model

In this paper, we first study the brane cosmological behaviors of Starobinsky inflationary model. In particular, we compute the associated parameters including the perturbation ones. Among others, we find that the spectral index and the tensor-to-scalar ratio are in a good agreement with Planck observational and BICEP/Keck data. Varying the five-dimensional Planck mass [Formula: see text] values, we investigate the thermal behaviors. Concretely, we calculate and examine the reheating cosmological parameters. For a specific value of the stringy parameter, we provide good predictions of the involved quantities. Taking [Formula: see text] TeV, we obtain acceptable reheating temperatures.

Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation

This paper presents a noncommutative (NC) version of an extended Sáez–Ballester (SB) theory. Concretely, considering the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and, applying the Hamiltonian formalism, obtain deformed equations of motion. In our model, the NC parameter appears linearly in the deformed Poisson bracket and the equations of the NC SB cosmology. When it goes to zero, we get the corresponding commutative counterparts. Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; (ii) for the late times, there is a zero acceleration epoch. By establishing an appropriate dynamical framework, we show that the results (i) and (ii) can be obtained for many sets of the initial conditions and the parameters of the model. Finally, we indicate that, at the level of the field equations, one may find a close resemblance between our NC model and the Starobinsky inflationary model.

When does the Schwinger preheating occur?

When the inflaton couples to photons and amplifies electric fields, charged particles produced via the Schwinger effect can dominate the universe after inflation, which is dubbed as the Schwinger preheating. Using the hydrodynamic approach for the Boltzmann equation, we numerically study two cases, the Starobinsky inflation model with the kinetic coupling and the Watanabe-Kanno-Soda inflation model. The Schwinger preheating is not observed in the latter model but occurs for a sufficiently large inflaton-photon coupling in the first model. We analytically address its condition and derive a general attractor solution of the electric fields. The occurrence of the Schwinger preheating in the first model is determined by whether the electric fields enter the attractor solution during inflation or not.

Hidden dark matter from Starobinsky inflation

The Starobinsky inflation model is one of the simplest inflation models that is consistent with the cosmic microwave background observations. In order to explain dark matter of the universe, we consider a minimal extension of the Starobinsky inflation model with introducing the dark sector which communicates with the visible sector only via the gravitational interaction. In Starobinsky inflation model, a sizable amount of dark-sector particle may be produced by the inflaton decay. Thus, a scalar, a fermion or a vector boson in the dark sector may become dark matter. We pay particular attention to the case with dark non-Abelian gauge interaction to make a dark glueball a dark matter candidate. In the minimal setup, we show that it is difficult to explain the observed dark matter abundance without conflicting observational constraints on the coldness and the self-interaction of dark matter. We propose scenarios in which the dark glueball, as well as other dark-sector particles, from the inflaton decay become viable dark matter candidates. We also discuss possibilities to test such scenarios.

Numerical analysis of the generalized Starobinsky inflationary model

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.

Semiclassical analysis of the tensor power spectrum in the Starobinsky inflationary model

In this work, we calculate the tensor power spectrum and the tensor-to-scalar ratio [Formula: see text] within the frame of the Starobinsky inflationary model using the improved uniform approximation method and the third-order phase-integral method. We compare our results with those obtained with numerical integration and the slow-roll approximation to second-order. We have obtained consistent values of [Formula: see text] using the different approximations, and [Formula: see text] is inside the interval reported by observations.

Superheavy dark matter in R2-cosmology

The conventional Friedmann cosmology is known to be in tension with the existence of stable particles having interaction strength typical for supersymmetry and heavier than several TeV. A possible way to save life of such particles may be a modification of the standard cosmological expansion law in such a way that the density of these heavy relics would be significantly reduced. We study particle creation in the Starobinsky inflationary model for different decay channels of the scalaron. It is shown that the process of thermalization superheavy stable particles with the coupling strength typical for the GUT SUSY could be created with the density equal to the observed density of dark matter.

Quantum gravitational onset of Starobinsky inflation in a closed universe

Recent cosmic microwave background observations favor low-energy-scale inflationary models in a closed universe. However, the onset of inflation in such models for a closed universe is known to be severely problematic. In particular, such a universe recollapses within a few Planck seconds and encounters a big crunch singularity when initial conditions are given in the Planck regime. We show that this problem of the onset of inflation in low-energy-scale inflationary models can be successfully overcome in a quantum-gravitational framework where the big bang/big crunch singularities are resolved and a nonsingular cyclic evolution exists prior to inflation. As an example, we consider a model in loop quantum cosmology and demonstrate that the successful onset of low-energy-scale inflation in a closed universe is possible for the Starobinsky inflationary model starting from a variety of initial conditions where it is impossible in the classical theory. For comparison, we also investigate the onset of inflation in the ${\ensuremath{\phi}}^{2}$ inflationary model under highly unfavorable conditions and find similar results. Our numerical investigation including the phase-space analysis shows that the preinflationary phase with quantum gravity effects is composed of nonidentical cycles of bounces and recollapses resulting in a hysteresis-like phenomenon, which plays an important role in creating suitable conditions for inflation to occur after some number of nonsingular cycles. Our analysis shows that the tension in the classical theory amounting to the unsuitability of closed Friedmann-Lema\^{\i}tre-Robertson-Walker universes with respect to the onset of low-energy-scale inflation can be successfully resolved in loop quantum cosmology.

Brane inflation and the robustness of the Starobinsky inflationary model

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 $\forall \beta \neq 0$ 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.

UV freeze-in in Starobinsky inflation

In the Starobinsky model of inflation, the observed dark matter abundance can be produced from the direct decay of the inflaton field only in a very narrow spectrum of close-to-conformal scalar fields and spinors of mass ∼ 107 GeV. This spectrum can be, however, significantly broadened in the presence of effective non-renormalizable interactions between the dark and the visible sectors. In particular, we show that UV freeze-in can efficiently generate the right dark matter abundance for a large range of masses spanning from the keV to the PeV scale and arbitrary spin, without significantly altering the heating dynamics. We also consider the contribution of effective interactions to the inflaton decay into dark matter.

Semiclassical analysis of the Starobinsky inflationary model

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.