Attractor Inflation Research Articles

E^+e^- annihilation on the stochastic background of primordial gravitational waves with BKP18

The evolution of inflationary primordial gravitational waves with the expansion of the universe is studied while taking into account the e^+e^- annihilation which leads to step correction in the spectrum of primordial gravitational waves which is sim 10% in the amplitude and sim 25% in the energy density. The amplitudes and energy densities are studied for the alpha -attractor inflation models which are in agreement with the recent BICEP/Keck and Planck 2018 joint result. The energy densities are well within the big bang nucleosynthesis bound, but the spectra for these models are very much below the detection range of the currently operating and upcoming detectors.

Non-Gaussianity and secondary gravitational waves from primordial black holes production in alpha -attractor inflation

We study the non-Gaussianity and secondary Gravitational Waves (GWs) in the process of the Primordial Black Holes (PBHs) production from inflation. In our work, we focus on the alpha -attractor inflation model in which a tiny bump in the inflaton potential enhances the amplitude of the curvature perturbations at some scales and consequently leads to the PBHs production with different mass scales. We implement the computational code BINGO which calculates the non-Gaussianity parameter in different triangle configurations. Our examination implies that in this setup, the non-Gaussianity gets amplified significantly in the equilateral shape around the scales in which the power spectrum of the scalar perturbations undergoes a sharp declination. The imprints of these non-Gaussianities can be probed in the scales corresponding to the BBN and mu -distortion events, or in smaller scales, and detection of such signatures in the future observations may confirm the idea of our model for the generation of PBHs or rule it out. Moreover, we investigate the secondary GWs in this framework and show that in our model, the peak of the present fractional energy density is obtained as Omega _{mathrm{GW0}} sim 10^{-8} at different frequencies which depends on the model parameters. These results lie well within the sensitivity region of some GWs detectors at some frequencies, and therefore the observational compatibility of our model can be evaluated by the forthcoming data from these detectors. We further provide some estimations for the tilts of the induced GWs spectrum in the different intervals of frequency, and demonstrate that the spectrum obeys the power-law relation Omega _{mathrm{GW0}}sim f^{n} in those frequency bands.

Preheating constraints in α-attractor inflation and gravitational waves production

We propose a scenario where preheating occurs for a specific duration that is parametrized by an [Formula: see text]-folds number [Formula: see text], our results suggest a direct correlation between the preheating duration and the density of gravitational waves (GWs) produced during this phase. Moreover, we investigate the consequences of the inflationary parameters on the [Formula: see text]-attractor [Formula: see text] model in the small [Formula: see text] limits. In this framework, we perform investigations on the preheating parameters involving the number of [Formula: see text]-folds [Formula: see text], and the temperature of reheating [Formula: see text], then we show that the parameter [Formula: see text] associated with the [Formula: see text] model of [Formula: see text]-attractor inflation has a negligible effect on the preheating duration, and we demonstrate that gravitational wave generation during preheating satisfies the restrictions from Planck’s recent data.

Current and future constraints on single-field α -attractor models

We study here the observational constraints on single-field inflationary models achievable with the next generation of CMB experiments. We particularly focus on a Stage-IV like experiment and forecasts its constraints on inflationary parameters in the context of $\alpha$-attractor inflation comprising a large class of single-field models. To tailor our forecasts we use as a fiducial model the results obtained with current CMB and LSS data, assuming the $\alpha$-model a priori. We found that current CMB data are able to place a tight bound on the ratio of the tensor-to-scalar ratio with the alpha parameter $r/\alpha = 3.87^{+0.78}_{-0.94}\cdot 10^{-3}$ and on the running of the scalar index $\alpha_S = -6.4^{+1.6}_{-1.3}\cdot 10^{-4}$ with a value of the scalar index consistent with current constraints. In the optimistic scenario of detection of primordial gravitational waves in the CMB B-mode polarization power spectra, we found that CMB-S4 will be able to achieve a $15\%$ bound on the value of the parameter $\alpha = 1.01^{+0.14}_{-0.18}$. This bound clearly show the ability of CMB-S4 to constrain not only the energy scale of inflation but also the shape of its potential. Enlarging the baseline model to also include the neutrino sector merely reduce the accuracy of $5\%$ leading to $\alpha = 1.07^{+0.18}_{-0.23}$ so that our main conclusions are still valid.

β-function reconstruction of Palatini inflationary attractors

Attractor inflation is a particularly robust framework for developing inflationary models that are insensitive to the details of the potential. Such models are most often considered in the metric formulation of gravity. However, non-minimal models may not necessarily maintain their attractor nature in the Palatini formalism where the connection is independent of the metric. In this work, we employ the β-function formalism to classify the strong coupling limit of inflationary models in both the metric and the Palatini approaches. Furthermore, we determine the range of values for the non-minimal coupling that lead to theories being observationally indistinguishable in metric and Palatini within current accuracy. Finally, we reconstruct the Jordan frame potential for ξ-attractors by imposing an explicit form for the β-function, demonstrating the effect that the choice of metric or Palatini has on the inflationary observables of the theory.

Preheating from target space curvature and unitarity violation: Analysis in field space

We study particle production and unitarity violation caused by a curved target space right after inflation. We use the inflaton field value instead of cosmic time as the time variable, and derive a semiclassical formula for the spectrum of produced particles. We then derive a simple condition for unitarity violation during preheating, which we confirm by our semiclassical method and numerical solution. This condition depends not only on the target space curvature but also on the height of the inflaton potential at the end of inflation. This condition tells us, for instance, that unitarity is violated in running kinetic inflation and Higgs inflation, while unitarity is conserved in $\alpha$-attractor inflation and Higgs-Palatini inflation.

Superheavy scalar dark matter from gravitational particle production in α -attractor models of inflation

We study the phenomenon of gravitational particle production as applied to a scalar spectator field in the context of $\alpha$-attractor inflation. Assuming that the scalar has a minimal coupling to gravity, we calculate the abundance of gravitationally-produced particles as a function of the spectator's mass $m_\chi$ and the inflaton's $\alpha$ parameter. If the spectator is stable and sufficiently weakly coupled, such that it does not thermalize after reheating, then a population of spin-0 particles is predicted to survive in the universe today, providing a candidate for dark matter. Inhomogeneities in the spatial distribution of dark matter correspond to an isocurvature component, which can be probed by measurements of the cosmic microwave background anisotropies. We calculate the dark matter-photon isocurvature power spectrum and by comparing with upper limits from Planck, we infer constraints on $m_\chi$ and $\alpha$. If the scalar spectator makes up all of the dark matter today, then for $\alpha = 10$ and $T_\text{RH} = 10^4 \ \mathrm{GeV}$ we obtain $m_\chi > 1.8 \times 10^{13} \ \mathrm{GeV} \approx 1.2 \, m_\phi$, where $m_\phi$ is the inflaton's mass.

Revisiting non-Gaussianity in non-attractor inflation models in the light of the cosmological soft theorem

Abstract We revisit the squeezed-limit non-Gaussianity in the single-field non-attractor inflation models from the viewpoint of the cosmological soft theorem. In the single-field attractor models, inflaton’s trajectories with different initial conditions effectively converge into a single trajectory in the phase space, and hence there is only one clock degree of freedom (DoF) in the scalar part. Its long-wavelength perturbations can be absorbed into the local coordinate renormalization and lead to the so-called consistency relation between n- and (n + 1)-point functions. On the other hand, if the inflaton dynamics deviates from the attractor behavior, its long-wavelength perturbations cannot necessarily be absorbed and the consistency relation is expected not to hold any longer. In this work, we derive a formula for the squeezed bispectrum including the explicit correction to the consistency relation, as a proof of its violation in the non-attractor cases. First one must recall that non-attractor inflation needs to be followed by attractor inflation in a realistic case. Then, even if a specific non-attractor phase is effectively governed by a single DoF of phase space (represented by the exact ultra-slow-roll limit) and followed by a single-DoF attractor phase, its transition phase necessarily involves two DoF in dynamics and hence its long-wavelength perturbations cannot be absorbed into the local coordinate renormalization. Thus, it can affect local physics, even taking account of the so-called local observer effect, as shown by the fact that the bispectrum in the squeezed limit can go beyond the consistency relation. More concretely, the observed squeezed bispectrum does not vanish in general for long-wavelength perturbations exiting the horizon during a non-attractor phase.

Production of gravitational waves during preheating in α -attractor inflation

We study the generation of gravitational waves (GWs) during the single-field preheating in the $\ensuremath{\alpha}$-attractor inflation in this paper. We find that the oscillation of the inflaton leads to an intermittent tachyonic instability for certain inflaton fluctuations, which results in that the inflaton quanta become a significant source of GWs. At the beginning of the preheating, the low frequency GW modes grow rapidly, and then nonlinear effects set in and lead to the growth of modes with relatively high frequencies. When the model parameter $\ensuremath{\alpha}$ is chosen to be very small, e.g., ${10}^{\ensuremath{-}5}$, the GW density spectrum increases very fast and the value of model parameter $n$ has negligible effect. However, when $\ensuremath{\alpha}$ becomes relatively large, e.g., ${10}^{\ensuremath{-}4}$ or ${10}^{\ensuremath{-}3}$, the growth of inflaton quanta is inversely proportional to the value of $n$ since a smaller value of $n$ corresponds to a more negative value of the mass square of the inflaton. This effect leads to that the maximum value of the today's total energy density of GWs occurs at $n=1$ and $\ensuremath{\alpha}={10}^{\ensuremath{-}4}$ among different values of model parameters considered in our analysis. Furthermore, we find that the GWs produced during the single-field preheating in the $\ensuremath{\alpha}$-attractor inflation satisfy the constraints from the Planck and those expected from the next-generation CMB experiments.

Inflaton condensate fragmentation: Analytical conditions and application to α -attractor models

We study the stability of an inflaton condensate in the presence of attractive inflaton self-interactions, in order to determine analytical conditions on the self-interaction couplings under which the condensate undergoes fragmentation. As an application of our results, we consider the stability of the inflaton condensate in $\alpha$-attractor inflation. We show that the stability of the condensate depends upon the value of $\alpha$. For the T-model with $n = 1$, we find that it is unstable for $\alpha \lesssim 10^{-4}$. In this case it is expected that inflation will be followed by an oscillon-dominated era.

An alternative attractor in gauged NJL inflation

We have investigated the attractor structure for the CMB fluctuations in a composite inflation scenario within the gauged Nambu–Jona-Lasinio (NJL) model. Such composite inflation represents an attractor which cannot be found in a fundamental scalar model. As is known, the number of inflationary models contains the attractor classified by the α-attractor model. It is found that the attractor inflation in the gauged NJL model corresponds to the case.

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, ns and r, are close to the corresponding ones in the R2 and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.

Effective field theory of non-attractor inflation

We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter η. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.