- The paper extends the δN formalism to analyze non-linear adiabatic and isocurvature perturbations, yielding insights into primordial non-Gaussianities.
- It shows how a mixed curvaton-inflaton model can generate significant bispectra where isocurvature perturbations rival adiabatic ones.
- The study examines a double inflation model, revealing that second-order correlations between fluctuations persist despite slow-roll suppression.
Non-linear Isocurvature Perturbations and Non-Gaussianities: An Analytical Inquiry
The paper by Langlois, Vernizzi, and Wands delves deeply into the intricacies of non-linear primordial adiabatic and isocurvature perturbations with an emphasis on examining their non-Gaussian characteristics. Utilizing an extended δN formalism framework, the authors systematically explore two illustrative scenarios: (1) a mixed curvaton-inflaton model, and (2) a double inflation model with two uncoupled scalar fields.
The motivations for this research stem from recent observations of CMB anisotropies, which have highlighted the need for models that offer distinct predictions from traditional single-field slow-roll inflation models. Non-Gaussianity in CMB anisotropies and the potential presence of primordial isocurvature components are critical observables for distinguishing among these models.
Key Findings
- δN Formalism Extension: The authors extend the δN formalism to capture the non-Gaussianities emerging from non-adiabatic fluctuations during inflation, encompassing both primordial adiabatic and isocurvature perturbations. This approach is validated as particularly effective for evaluating large-scale primordial non-Gaussianity.
- Mixed Curvaton-Inflaton Scenario: Within this framework, the bispectrum of primordial isocurvature perturbations may rival that of adiabatic curvature perturbations. This results in notable non-Gaussianity, especially when the curvaton decays well before achieving dominance and the inflaton's contribution remains significant.
- Double Inflation Model: This scenario considers two massive scalar fields during inflation. While the resultant final isocurvature perturbation critically hinges on both scalar field fluctuations, the model allows for analytically tractable results at second order. Despite non-linear interactions, the overall non-Gaussianities are constrained by slow-roll parameters, hinting at primarily Gaussian adiabatic perturbations with limited non-Gaussian impact.
- Interplay Between Adiabatic and Isocurvature Perturbations: Even when adiabatic and entropy perturbations are uncorrelated at first order, they inherently correlate at second order. This intrinsic linkage accentuates potential observational features absent in single-field paradigms.
Implications
Practically, these findings enrich the theoretical landscape of inflationary cosmology by providing models that predict significant non-linear isocurvature perturbations. Theoretically, they propose a mechanism by which isocurvature perturbations might dominate the bispectrum while maintaining a subdominant role in the power spectrum.
Future Prospects
As observational capabilities advance, primarily through enhanced satellite data, there lies significant potential in confirming these models' predictions concerning non-Gaussian isocurvature perturbations. Beyond the currently studied models, this line of inquiry hints at possible extensions towards more complex inflaton-curvaton interactions and applications in different multi-field inflation scenarios.
The portrayal of these interactions through the δN formalism not only clarifies the landscape of primordial cosmological perturbations but also lays a foundation for future models that could extend beyond the constraints of slow-roll parameters. This opens avenues for a deeper understanding of the fundamental nature of the universe through the lens of inflationary perturbation theory.