Sudden Decay Approximation Research Articles

Isocurvature perturbations during two-field inflation and reheating

We use Hamilton–Jacobi formalism to study the curvature and isocurvature perturbations during inflation. This formalism is suitable for going beyond slow roll regime. We solve the equation of fields’ perturbations for some two-field models, and calculate their spectra. We next use $$\delta N$$ formalism to calculate the curvature and isocurvature non-Gaussianity for a non-separable form of the Hubble expansion rate. Finally, using the sudden decay approximation, we obtain the link between the perturbations during inflation and after reheating for noninteracting fields.

Effect of reheating on predictions following multiple-field inflation

We study the sensitivity of cosmological observables to the reheating phase following inflation driven by many scalar fields. We describe a method which allows semi-analytic treatment of the impact of perturbative reheating on cosmological perturbations using the sudden decay approximation. Focusing on $\mathcal{N}$-quadratic inflation, we show how the scalar spectral index and tensor-to-scalar ratio are affected by the rates at which the scalar fields decay into radiation. We find that for certain choices of decay rates, reheating following multiple-field inflation can have a significant impact on the prediction of cosmological observables.

Thermal effects and sudden decay approximation in the curvaton scenario

We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the total entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay approximation prediction.

Modulated curvaton decay

We study primordial density perturbations generated by the late decay of a curvaton field whose decay rate may be modulated by the local value of another isocurvature field, analogous to models of modulated reheating at the end of inflation. We calculate the primordial density perturbation and its local-type non-Gaussianity using the sudden-decay approximation for the curvaton field, recovering standard curvaton and modulated reheating results as limiting cases. We verify the Suyama-Yamaguchi inequality between bispectrum and trispectrum parameters for the primordial density field generated by multiple field fluctuations, and find conditions for the bound to be saturated.

Temporal enhancement of super-horizon curvature perturbations from decays of two curvatons and its cosmological consequences

If more than one curvaton dominate the Universe at different epochs from each other, curvature perturbations can be temporarily enhanced to a value much larger than the observed one 10^{-5}. The traces of the enhancement may be left as higher order correlation functions, that is, as non-Gaussianity, the stochastic gravitational waves that are sourced by scalar-scalar mode couplings, as well as the primordial black holes that are formed by the gravitational collapse of the enhanced curvature perturbations. We first confirm that such a temporal enhancement indeed occurs by solving the linearized perturbation equations both numerically and analytically. We then derive an analytic expression of the full-order curvature perturbation which does not rely on the frequently used sudden decay approximation and is exact on super-horizon scales. By using this analytic formula, we provide expressions of the non-linearity parameters f_nl, tau_nl and g_nl. If both two curvatons contribute to the final curvature perturbations, the strong non-Gaussianity appears in the trispectrum rather than in the bispectrum. We also find a unique consistency relation between tau_nl and g_nl without f_nl. By using the second-order perturbation theory, we numerically show that the spectrum of the induced gravitational waves has a plateau corresponding to duration of the enhancement and such gravitational waves can be probed by ultimate-DECIGO and space-based atomic interferometers. We finally calculate the abundance of the primordial black holes and put a constraint on the amplitude of the enhanced curvature perturbations.

Non-gaussianity with Lagrange multiplier field in the curvaton scenario

In this paper, we will use δ\U0001d4a9-formalism to calculate the primordial curvature perturbation for the curvaton model with a Lagrange multiplier field. We calculate the non-linearity parameters fNL and gNL in the sudden-decay approximation in this kind of model, and we find that one could get a large non-Gaussinity even if the curvaton dominates the total energy density before it decays, and this property will make the curvaton model much richer. We also calculate the probability density function of the primordial curvature perturbation in the sudden-decay approximation, as well as some moments of it.

Non-Gaussianity of the primordial perturbation in the curvaton model

We use the delta N -formalism to investigate the non-Gaussianity of the primordial curvature perturbation in the curvaton scenario for the origin of structure. We numerically calculate the full probability distribution function allowing for the non-instantaneous decay of the curvaton and compare this with analytic results derived in the sudden-decay approximation. We also present results for the leading-order contribution to the primordial bispectrum and trispectrum. In the sudden-decay approximation we derive a fully non-linear expression relating the primordial perturbation to the initial curvaton perturbation. As an example of how non-Gaussianity provides additional constraints on model parameters, we show how the primordial bispectrum on CMB scales can be used to constrain variance on much smaller scales in the curvaton field. Our analytical and numerical results allow for multiple tests of primordial non-Gaussianity, and thus they can offer consistency tests of the curvaton scenario.

A numerical study of non-Gaussianity in the curvaton scenario

We study the curvaton scenario using gauge-invariant second order perturbation theory and solvingthe governing equations numerically. Focusing on large scales we calculate the non-linearity parameterfNL in the two-fluid curvaton model and compare our results with previous analyticalstudies employing the sudden decay approximation. We find good agreement ofthe two approaches for large curvaton energy densities at curvaton decay,Ωσdec, but significantdifferences of up to 10% for small Ωσdec.