The production of GWs during preheating in the Starobinsky model with a nonminimally coupled auxiliary scalar field is studied through the lattice simulation in this paper. We find that the GW spectrum $Ω_{\rm gw}$ grows fast with the increase of the absolute value of coupling parameter $ξ$. This is because the resonant bands become broad with the increase of $|ξ|$. When $ξ<0$, $Ω_{\rm gw}$ begins to grow once the inflation ends and grows faster than the case of $ξ>0$. $Ω_{\rm gw}$ reaches the maximum at $ξ=-20$ ($ξ=42$ for the case $ξ>0$) and then decreases with slight oscillation. Furthermore we find that the GWs produced in the era of preheating satisfy the limits from the Planck and next-generation CMB experiments.
We study the preheating after inflation in the Starobinsky model with a nonminimally coupled scalar field $χ$. Using the lattice simulation, we analyze the rescattering between the $χ$ particles and the inflaton condensate, and the backreaction effect of the scalar metric perturbations. We find that the rescattering is an efficient mechanism promoting the growth of the $χ$ field variance. Meanwhile, copious inflaton particles can be knocked out of the inflaton condensate by rescattering. As a result, the inflaton field can become a nonnegligible gravitational wave source, even comparable with …
The Preheating Stage on The Starobinsky Inflation after ACT
Research Center for Quantum Physics, National Research and Innovation Agency (BRIN)（量子物理研究中心，国家研究与创新署（BRIN））；Dept. of Physics Education, Universitas Islam Negeri Sunan Kalijaga（苏南卡利贾加伊斯兰大学物理教育系）；Physics Department, Universitas Gadjah Mada（加查马达大学物理系）
We propose a one-parametric extension of the Starobinsky $R+R^2$ model by adding the $(R+m^2β^2)^{3/2}$ 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 poten…
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 $P_{S,T}$, the scalar spectral index $n_S$, and the tensor-to-scalar ratio $r$. Also we present our results in the $(n_S,r)$ plane.
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 $β$-Starobinsky inflation potential, which is motivated through brane inflation. In the Einstein frame, the generalized model recovers the original m…
The inflationary dynamics and preheating in a model with a non-minimally coupled inflaton field in the metric and Palatini formalisms are studied in this paper. We find that in both formalisms, irrespective of the initial conditions, our Universe will evolve into a slow-roll inflationary era and then the scalar field rolls into an oscillating phase. The value of the scalar field at the end of the inflation in the Palatini formalism is always larger than that in the metric one, which becomes more and more obvious with the increase of the absolute value of the coupling parameter $|ξ|$. During th…
The $R^2$ term in the Starobinsky inflationary model can be regarded as a leading quantum correction to the gravitational effective action. We assume that parity-preserving and parity-violating (axial) non-minimal couplings between curvature and electromagnetic field are also present in the effective action. In the Einstein frame, they turn into non-trivial couplings of the scalaron and curvature to the electromagnetic field. We make an assessment of inflationary magnetogenesis in this model. In the case of parity-preserving couplings, amplification of magnetic field is negligibly small. In th…
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.
During inflationary preheating, the energy stored in the inflaton field is rapidly converted into excitations of other entropy fields. This stage is characterized by exponential particle production due to parametric resonance and is notoriously difficult to analyze using analytic methods. We develop a detailed numerical simulation to investigate inflationary preheating when the potential of the inflaton is a power-law function with arbitrary power index. To achieve a successful graceful exit from a primordial inflationary phase to a smooth, oscillatory phase during preheating, we assume the in…
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 $p\simeq 1$. 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.
In this work we calculate the tensor power spectrum and the tensor-to-scalar ratio r 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 r using the different approximations, and r is inside the interval reported by observations.
Starobinsky inflation and Higgs inflation in gravity, and their equivalence based on the common inflationary potential are extended to supergravity in the proper framework, where the Starobinsky and Higgs descriptions of inflation arise in two different gauges of the same supergravity model.
Stochastic gravitational wave backgrounds (SGWBs) receive increasing attention and provide a new possibility to directly probe the early Universe. In the preheating process at the end of inflation, parametric resonance can generate large energy density perturbations and efficiently produce gravitational waves (GWs) which carry unique information about inflation. Since the peak frequency of such GWs is approximately proportional to the inflationary energy scale, $Λ_{\mathrm{inf}}$, GWs from preheating are expected to be observed by interferometer GW detectors in low-scale inflationary models. W…
Recently, the nonperturbative quantization scheme of loop quantum gravity has been extended to the Brans-Dicke theory and the corresponding loop quantum Brans-Dicke cosmology has been derived, which provides an essential platform to explore inflationary models in this framework. In this paper, we consider two inflation models, the Starobinsky and $α$-attractor inflation whose cosmological predictions are in excellent agreement with Planck data, and study systematically their pre-inflationary dynamics as well as the slow-roll inflation. We show that for both models, the background evolution of …
In previous work we argued that the correct procedure to predict the gravitational wave signal from preheating after inflation rests on the in-in formalism. We extend here our previous analysis to include the backreaction of the produced matter on the motion of the inflaton and the expansion of the universe, and study how the latter affect the spectrum of the resulting gravitational waves. The addition of backreaction demands the appropriate renormalization of divergent expectation values, which we regularize by preserving diffeomorphism invariance in a manner that is amenable to numerical int…
We consider gravitational wave (GW) production during preheating in hybrid inflation models where an axion-like waterfall field couples to Abelian gauge fields. Based on a linear analysis, we find that the GW signal from such models can be within the reach of a variety of foreseeable GW experiments such as LISA, AEDGE, ET and CE, and is close to that of LIGO A+, both in terms of frequency range and signal strength. Furthermore, the resultant GW signal is helically polarized and thus may distinguish itself from other sources of stochastic GW background. Finally, such models can produce primordi…
Recent cosmic microwave background observations favor low energy scale inflationary models in a closed universe. However, 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 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 n…
In this work, we studied the slow-roll approximation of cosmic inflation within the context of $f(R,T)$ gravity, where $R$ is the scalar curvature, and $T$ is the trace of the energy-momentum tensor. By choosing a minimal coupling between matter and gravity, we obtained the modified slow-roll parameters, the scalar spectral index ($n_s$), the tensor spectral index ($n_{\textrm{T}}$), and the tensor-to-scalar ratio ($r$). We computed these quantities for a general power-law potential, Natural & Quartic Hilltop inflation, and the Starobinsky model, plotting the trajectories on the $(n_s,r)$ plan…
It has been argued that the mixed Higgs-$R^2$ model acts as the UV extension of the Higgs inflation, pushing up its cut-off scale in the vacuum close up to the Planck scale. In this letter, we study the inflaton oscillation stage after inflation, focusing on the effective mass of the phase direction of the Higgs field, which can cause a violent preheating process. We find that the "spikes" in the effective mass of the phase direction observed in the Higgs inflation still appear in the mixed Higgs-$R^2$ model. While the spikes appear above the cut-off scale in the Higgs-only case, they appear b…
We study a model including a real scalar field $ϕ$ non-minimally coupled to $F({\cal R})$ gravity, which is conformally equivalent to an Einstein-Hilbert theory, involving two real scalar fields. We consider three special cases of the potential of the field $ϕ$ in the $F({\cal R})$-frame: a vanishing potential, a mass term and a Higgs potential. All these lead to non-trivial two-field potentials in the Einstein-frame which in particular directions resemble the well-known Starobinsky model. We find, that all these cases can yield viable inflationary models in complete agreement with current obs…
The idea of gauge theories of gravity predicts that there should exist not only the massless graviton but also massive particles carrying the gravitational force. We study the cosmology in a quadratic gravity with dynamical torsion where gravity may be interpreted as a gauge force associated with the Poincaré group. In addition to the massless spin-2 graviton, the model contains four non-ghost massive particle species: a couple of spin-0, a spin-1 and a spin-2. Supposing the restoration of the local Weyl invariance in the UV limit and the parity invariance, we find the most general minisupersp…
We investigate the production of primordial black holes and their contribution to the presently observed dark matter in a dilaton two-field extension of Starobinsky's quadratic $f(R)$ model of inflation. The model features a multi-field amplification mechanism which leads to the generation of a sharp peak in the inflationary power spectrum at small wavelengths responsible for the production of primordial black holes. This mechanism is significantly different from single-field models and requires a stochastic treatment during an intermediate phase of the inflationary dynamics. We find that the …
We investigate non-perturbative production of fermionic dark matter in the early universe. We study analytically the gravitational production mechanism accompanied by the coupling of fermions to the background inflaton field. The latter leads to the variation of effective fermion mass during preheating and makes the resulting spectrum and abundance sensitive to its parameters. Assuming fast preheating that completes in less than the inflationary Hubble time and no oscillations of the inflaton field after inflation, we find an abundant production of particles with energies ranging from the infl…
A note on oscillons: non-negligible metric fluctuations during preheating
Jagiellonian University（雅盖隆大学）；University of Utah（犹他大学）；Institute of Science Tokyo（东京科学大学）；University of Portsmouth（朴茨茅斯大学）；Universidade da Beira Interior（伊比利亚大学）
After the end of inflation, the inflaton field oscillates around a local minimum of its potential and decays into ordinary matter. These oscillations trigger a resonant instability for cosmological perturbations with wavelengths that exit the Hubble radius close to the end of inflation. In this paper, we study the formation of Primordial Black Holes (PBHs) at these enhanced scales. We find that the production mechanism can be so efficient that PBHs subsequently dominate the content of the universe and reheating proceeds from their evaporation. Observational constraints on the PBH abundance als…
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 Schwing…
