What Planck does not tell us about inflation (1307.7095v1)

Abstract: Planck data has not found the 'smoking gun' of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single field scenarios. This raises the important question of what these results do imply for more general models, and in particular, multi-field inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single field models; two-field slow-roll dynamics, curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behaviour, focusing on the latter two which have been least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.

• The paper demonstrates that multi-field inflation models require finely tuned initial conditions to generate detectable non-Gaussian signals.
• It evaluates four scenarios—two-field slow-roll, curvaton-type behavior, inhomogeneous end of inflation, and modulated reheating—to map constraints on Gaussian curvature and bispectrum features.
• The analysis suggests that while Planck data marginally limits these models, complex inflationary scenarios remain viable, prompting further theoretical investigation.

Insights from "What Planck Does Not Tell Us About Inflation"

The paper titled "What Planck Does Not Tell Us About Inflation" addresses pivotal questions in the context of inflationary cosmology, particularly focusing on the insights obtained—or not obtained—from Planck satellite observations. The authors delve into multi-field inflationary models, particularly emphasizing the implications of Planck data on these models, and explore scenarios not captured by simple single-field models.

Overview of Analysis

The paper explores several categories of two-field inflationary models known for their potential to generate non-Gaussianity, which is a statistical deviation of cosmic microwave background (CMB) perturbations from a Gaussian distribution. The authors revisit four specific scenarios: two-field slow-roll dynamics, curvaton-type behavior, inhomogeneous end of inflation (IEI), and modulated reheating (MR).

1. Two-field Slow-roll Dynamics:
   • The dynamical richness of multiple light fields introduces isocurvature modes, potentially enhancing non-Gaussianity beyond the typical single-field predictions.
   • The analysis indicates that obtaining significant non-Gaussianity involves narrow initial condition tuning, aligning with previous studies on the necessity of specific initial conditions.
2. Curvaton-type Behavior:
   • This scenario considers a secondary field that may dominate energy density later in cosmic evolution, affecting inflation-generated perturbations.
   • As with slow-roll dynamics, the model's ability to produce substantial non-Gaussian signals is contingent upon particularly fine-tuned initial conditions, which restricts the parameter space affected by Planck constraints.
3. Inhomogeneous End of Inflation:
   • The IEI scenario explores scenarios where inflation concludes on a spatially variable surface, inducing perturbations.
   • An innovative contribution of this paper is the geometric evaluation of this hypersurface, providing insights into factors like Gaussian curvature and its impact on predicted CMB bispectrum, thereby affecting non-Gaussianity.
4. Modulated Reheating:
   • MR involves conditions where reheating depends on a field modulation, introducing a time-variable decay rate.
   • A parallel is drawn between MR and IEI scenarios, noting their similarities in interpretation but also emphasizing distinct differences in phenomenological outcomes.

Key Findings and Constraints

The investigation into these scenarios reveals that, despite Planck's lack of evidence for strong non-Gaussianity, multi-field models remain plausible. The Planck data constrains these models only in isolated regions of their parameter space where significant non-Gaussian signals might emerge. The authors provide quantitative constraints on scenario parameters such as Gaussian curvature, utilizing Planck results indirectly for model refinement within allowable ranges.

1. Numerical Results:
   • The analysis highlighted constraints on Gaussian curvature (denoted K), presenting bounds for scenarios that envision a substantial bispectrum signal.
   • The attention to parameter ranges, specifically where IEI and MR might show substantial bispectral peaks, showcases a rigorous computational effort matching Planck's sensitivity limits.
2. Implications and Future Directions:
   • The authors argue against the notion that Planck’s findings suffice to dismiss multi-field inflation. The mathematical tuning necessitated to violate Planck’s constraints exemplifies the feasibility and continued viability of complex inflationary models involving multiple degrees of freedom.
   • Future work could benefit from examining more nuanced model connections across theoretical frameworks such as supergravity or string theory, potentially accommodating a broader parameter space explored within this paper.

In conclusion, "What Planck Does Not Tell Us About Inflation" contributes significantly to inflationary cosmology discourse by complementing observational data with complex model analysis. The theoretical exploration confirms multi-field inflation's persistence as a competitive hypothesis, emphasizing its compatibility with current data while identifying nuanced parameter constraints that guide future research trajectories.