Searching for Cosmological Collider in the Planck CMB Data II: collider templates and Modal analysis

TL;DR

The paper tackles testing cosmological collider signals in Planck CMB data by constructing a complete, orthogonalized set of collider templates that cover massive scalars and spinning fields across masses $\mu$ and sound-speed ratios $c_s$. It employs the Modal bispectrum estimator, with cross-validation against the CMB-BEST pipeline and a look-elsewhere correction, to extract constraints on $f_{NL}$ for each template. The strongest hint arises from a massive scalar exchange near $\mu\approx 1.85$ and $c_s\approx 0.012$, yielding a look-elsewhere-adjusted significance of $\tilde{\sigma}_{\rm SNR} \approx 2.35$, but there is no definitive detection; degeneracies with single-field EFT backgrounds are mitigated by the orthogonalization, enabling robust future tests. The methodology is general and applicable to upcoming CMB and LSS data, and sets the stage for tighter cosmological collider tests with future surveys such as the Simons Observatory. Overall, the work provides a systematic framework to isolate genuine collider signals from EFT backgrounds and to interpret potential discoveries in terms of the inflationary particle spectrum.

Abstract

Signatures of massive particles during inflation are highly informative targets for cosmological experiments. With recent progress on both theoretical and observational frontiers, we have reached the point where these novel signals of primordial non-Gaussianities (PNG) can be systematically tested with increasingly precise data. In this paper, we present the results of improved CMB data analysis for cosmological collider signals using Planck CMB data. To set the stage, we first construct a set of simplified but characteristic collider templates which are accurate over a broad range of particle masses, spins and sound speeds. In order to break degeneracies with single-field PNG, we propose an orthogonalization scheme such that the collider templates are uncorrelated with the highly constrained equilateral and orthogonal shapes. On this basis, we deploy the Modal bispectrum estimator for the Planck analysis and perform a systematic scan of parameters to search for the most significant collider signal. The maximum signal-to-noise ratio is found to be $2.35σ$ for massive spin-0 exchange after taking into account the look-elsewhere effect. In addition, we cross-validate the Modal analysis with the CMB-BEST pipeline, which demonstrates the consistency of results across the benchmark examples of collider templates. Given the low signal-to-noise ratio regime we find at the current stage of PNG observations, we believe the orthogonalization procedure provides an optimized strategy for future tests of the cosmological collider with the ability to rule out single field inflation.

Figures (11)

• Figure 1: Shape cosine (correlation) between massive scalars and standard single field templates. Top row: Correlation of scalar-I \ref{['scalarI']} and scalar-II \ref{['scalarIIa']} shapes with the equilateral template \ref{['equil']}. Bottom row: scalar-I and scalar-II correlation with the orthogonal template \ref{['ortho']}. All plots have the same color bar scale to accentuate the fact that massive scalar signals are overall less correlated with the orthogonal shape than with the equilateral.
• Figure 2: Shape cosine between the massive spin-1 \ref{['spin1m_simply']} and standard equilateral and orthogonal templates. One can note a weaker correlation with the latter, a feature common with the scalar field templates.
• Figure 3: Shape cosine between the massive spin-2 \ref{['spin2m']} and standard equilateral and orthogonal templates, with the latter being less correlated as noted previously in other templates. Apparent 'glitch' and asymmetry with respect to the $\log c_s$ stems from the fact that the spin-2 template contains two terms of different powers of $c_s$ which cannot be removed by normalization.
• Figure 4: Illustrations of $1\sigma$ and $2\sigma$ contour plots for joint $f_{\rm NL}$ constraints of two bispectrum shapes. Left: joint constraints on two shapes are shown with varying amounts of correlations between them: 0 (grey), 0.6 (blue), and 0.99 (purple). Independent analysis of $f_{\rm NL}^{(2)}$ corresponds to setting $f_{\rm NL}^{(1)}=0$, and is equivalent to the marginalized constraints if the two shapes are uncorrelated (grey contours). Right: joint constraints on two shapes, where the second shape now includes contributions from the first. Appropriate choice of $x$ effectively orthogonalizes the shape (red contours), making it uncorrelated with the first shape.
• Figure 5: Correlation (shape cosine) between primordial low speed collider and standard shapes: equilateral and local with their mutual correlation added for reference. Note that this plot is slightly different than originally shown in Jazayeri:2023xcj because of different definitions of shape cosine, and different weights in the inner product.