Non-Gaussianities in Single Field Inflation and their Optimal Limits from the WMAP 5-year Data

Abstract: Using the recently developed effective field theory of inflation, we argue that the size and the shape of the non-Gaussianities generated by single-field inflation are generically well described by two parameters: f_NL^equil, which characterizes the size of the signal that is peaked on equilateral configurations, and f_NL^orthog, which instead characterizes the size of the signal which is peaked both on equilateral configurations and flat-triangle configurations (with opposite signs). The shape of non-Gaussianities associated with f_NL^orthog is orthogonal to the one associated to f_NL^equil, and former analysis have been mostly blind to it. We perform the optimal analysis of the WMAP 5-year data for both of these parameters. We find no evidence of non-Gaussianity, and we have the following constraints: -125 < f_NL^equil < 435, -369 < f_NL^orthog < 71 at 95% CL. We show that both of these constraints can be translated into limits on parameters of the Lagrangian of single-field inflation. For one of them, the speed of sound of the inflaton fluctuations, we find that it is either bounded to be c_s > 0.011 at 95% CL. or alternatively to be so small that the higher-derivative kinetic term dominate at horizon crossing. We are able to put similar constraints on the other operators of the inflaton Lagrangian.

• The paper presents a detailed effective field theory analysis of non-Gaussianities from single-field inflation, emphasizing key operator interactions.
• The paper applies optimal estimators to WMAP 5-year data to derive constraints on equilateral and orthogonal bispectrum configurations.
• The paper constrains inflationary dynamics by setting limits on parameters like the inflaton’s speed of sound, informing future cosmic microwave background studies.

Overview of Non-Gaussianities in Single Field Inflation and Their Optimal Limits from WMAP 5-year Data

The paper provides a comprehensive analysis of non-Gaussianities generated by single-field inflation models using the framework of effective field theory. The primary goal is to explore the potential presence and constraints of non-Gaussianity signatures from the WMAP 5-year data.

Non-Gaussian Characteristics in Inflationary Models

The theoretical foundation rests upon the effective field theory approach, which highlights that single-field inflationary perturbations are characterized predominantly by two interaction operators: $\dot\pi (\partial_i\pi)^2$ and $\dot\pi^3$. These interactions contribute to bi-dimensional non-Gaussian characteristics that manifest in the cosmic microwave background (CMB) bispectrum. The bispectrum's shape and amplitude provide insight into the inflationary dynamics, especially concerning the inflaton's speed of sound $c_s$ and a parameter $\tilde c_3$ linked to cubic interactions.

Constraints from WMAP 5-Year Data

Utilizing the WMAP 5-year data, the study applies the optimal estimators developed in previous work to extract constraints on the amplitude of these non-Gaussian features, parametrized by $NL$ and $NL$. These parameters are associated with different triangular configurations in Fourier space, notably equilateral and orthogonal shapes, reflecting different inflationary dynamics.

The main empirical result indicates a non-detection of significant non-Gaussianity within the WMAP data, leading to the constraints: $-125 \le NL \le 435$ and $-369 \le NL \le 71$ at a 95% confidence level. These constraints accommodate varying inflationary scenarios, constraining the inflaton perturbations' speed of sound to $c_s \geq 0.011$. Additionally, an alternative possibility is suggested where $c_s$ could be exceedingly small, indicating the prominence of higher-derivative kinetic terms at horizon crossing.

Methodological Approach

The pipeline analyzes for non-Gaussianities using a pair of template shapes—equilateral and orthogonal—demonstrating computational efficiency due to their factorized form in the momentum modes $k_1$, $k_2$, and $k_3$. By employing these templates, the methodology navigates the challenges of non-factorizable shapes, ensuring comprehensive coverage of possible non-Gaussian configurations.

Implications and Future Directions

These findings constrict the parameter space within which potential non-Gaussianities may reside, offering insight into the benign or exotic nature of possible inflationary dynamics. The constraints impact theoretical models by limiting the parameter space, guiding future explorations in more intricate or alternative models of inflation.

Looking forward, improvements in observational data, as anticipated from the Planck satellite, promise sharper resolution and reduced uncertainties in non-Gaussianity constraints. These advancements might potentially illuminate new characteristics of the inflationary epoch and rigorously test the theoretical predictions of non-Gaussian signatures.

In conclusion, the paper establishes a rigorous framework for analyzing these primordial perturbations, systematically investigating the field of single-field inflationary models through the lens of the WMAP dataset and setting a cornerstone for future investigations into the early universe's dynamics.