<figure><img src="image_17.png" /><figcaption>Figure 13. The schematic diagram illustrates the triple-exchange bootstrap equations. a, b, c and d are the SK indices. When the two SK indices of one massive propagator are opposite, applying the corresponding differential operator results in homogeneous equations. Conversely, if the two indices are the same, an additional δ-term introduces a source term, which can be expressed using the seed integral of the double-exchange diagram.</figcaption></figure>

where the function $F_C[\cdots]$ is Lauricella's hypergeometric function with three variables defined in (A.12). The eight coefficients $c_{\pm\pm\pm\mp,abc}$ could be determined by proper boundary conditions.

As a next example, let us see $\hat{\mathcal{I}}_{\mp\pm\pm\mp}$ including a single time-ordered propagator for $\sigma^\alpha$, $\hat{D}_{\mp\mp}(z_1, r_1 z_4)$. In this case, we obtain an inhomogeneous term in the bootstrap equation after acting with the differential operator $\mathcal{D}_{w_1}^{(3)}$,

$$ \mathcal{D}_{w_1}^{(3)} \hat{\mathcal{I}}_{\mp\pm\pm\mp,\alpha\beta\gamma}^{p_1 p_2 p_3 p_4} = \frac{w_1^{4+p_1} w_2^{4+p_2} w_3^{4+p_3}}{(1+w_1)^{p_{1234}+13}} \mathcal{I}_{\pm\mp}^{p_2, p_{14}+4, p_3} \left( u = \frac{w_2}{1+w_1}, v = \frac{w_3}{1+w_1} \right), \quad (D.9) $$

while the other equations with $\mathcal{D}_{w_2}^{(3)}$ and $\mathcal{D}_{w_3}^{(3)}$ still satisfy the homogeneous ones,

$$ \mathcal{D}_{w_2}^{(3)} \hat{\mathcal{I}}_{\mp\pm\pm\mp,\alpha\beta\gamma}^{p_1 p_2 p_3 p_4} = \mathcal{D}_{w_3}^{(3)} \hat{\mathcal{I}}_{\mp\pm\pm\mp,\alpha\beta\gamma}^{p_1 p_2 p_3 p_4} = 0. \quad (D.10) $$

Note that the right-hand side of the first equation (D.9) is written as the seed integral of double-exchange diagram, which we obtained analytic forms in the main text. This structure is generic: the seed integral with n-massive field exchange, denoted as $\mathcal{I}_n$, emerges as a source term in the bootstrap equations of $\mathcal{I}_{n+1}$. Consequently, we can systematically solve more complex tree-level diagrams, although the detailed calculations remain non-trivial tasks: as shown in (D.8), the homogeneous solutions can be written down as known special functions, which is true even for more general diagram with n-massive exchanges. However, determining particular solutions would be a non-trivial task since the source term (the right-hand side of (D.9) for triple exchange) becomes more and more complicated as n increases, and we leave the detailed derivation for future work.
Similarly, deriving the remaining bootstrap equations for other seed integrals follows a straightforward procedure. However, we do not intend to delve into all the tedious details within this work. Instead, we illustrate the structure of the bootstrap equations in figure 13.

**Open Access.** This article is distributed under the terms of the Creative Commons Attribution License (CC-BY4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

## References

[1] X. Chen and Y. Wang, *Quasi-Single Field Inflation and Non-Gaussianities*, JCAP 04 (2010) 027 [arXiv:0911.3380] [INSPIRE].

[2] D. Baumann and D. Green, *Signatures of Supersymmetry from the Early Universe*, Phys. Rev. D 85 (2012) 103520 [arXiv:1109.0292] [INSPIRE].

[3] T. Noumi, M. Yamaguchi and D. Yokoyama, *Effective field theory approach to quasi-single field inflation and effects of heavy fields*, JHEP 06 (2013) 051 [arXiv:1211.1624] [INSPIRE].

[4] N. Arkani-Hamed and J. Maldacena, *Cosmological Collider Physics*, arXiv:1503.08043 [INSPIRE].

[5] X. Chen and Y. Wang, *Large non-Gaussianities with Intermediate Shapes from Quasi-Single Field Inflation*, Phys. Rev. D 81 (2010) 063511 [arXiv:0909.0496] [INSPIRE].

[6] E. Sefusatti, J.R. Fergusson, X. Chen and E.P.S. Shellard, *Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background*, JCAP 08 (2012) 033 [arXiv:1204.6318] [INSPIRE].

[7] J. Norena, L. Verde, G. Barenboim and C. Bosch, *Prospects for constraining the shape of non-Gaussianity with the scale-dependent bias*, JCAP 08 (2012) 019 [arXiv:1204.6324] [INSPIRE].

[8] X. Chen and Y. Wang, *Quasi-Single Field Inflation with Large Mass*, JCAP 09 (2012) 021 [arXiv:1205.0160] [INSPIRE].

[9] S. Pi and M. Sasaki, *Curvature Perturbation Spectrum in Two-field Inflation with a Turning Trajectory*, JCAP 10 (2012) 051 [arXiv:1205.0161] [INSPIRE].

[10] S. Céspedes and G.A. Palma, *Cosmic inflation in a landscape of heavy-fields*, JCAP 10 (2013) 051 [arXiv:1303.4703] [INSPIRE].

[11] J.-O. Gong, S. Pi and M. Sasaki, *Equilateral non-Gaussianity from heavy fields*, JCAP 11 (2013) 043 [arXiv:1306.3691] [INSPIRE].

[12] R. Emami, *Spectroscopy of Masses and Couplings during Inflation*, JCAP 04 (2014) 031 [arXiv:1311.0184] [INSPIRE].

[13] A. Kehagias and A. Riotto, *High Energy Physics Signatures from Inflation and Conformal Symmetry of de Sitter*, Fortsch. Phys. 63 (2015) 531 [arXiv:1501.03515] [INSPIRE].

[14] J. Liu, Y. Wang and S. Zhou, *Inflation with Massive Vector Fields*, JCAP 08 (2015) 033 [arXiv:1502.05138] [INSPIRE].

[15] E. Dimastrogiovanni, M. Fasiello and M. Kamionkowski, *Imprints of Massive Primordial Fields on Large-Scale Structure*, JCAP 02 (2016) 017 [arXiv:1504.05993] [INSPIRE].
[16] F. Schmidt, N.E. Chisari and C. Dvorkin, Imprint of inflation on galaxy shape correlations, JCAP 10 (2015) 032 [arXiv:1506.02671] [INSPIRE].

[17] X. Chen, M.H. Namjoo and Y. Wang, Quantum Primordial Standard Clocks, JCAP 02 (2016) 013 [arXiv:1509.03930] [INSPIRE].

[18] L.V. Delacretaz, T. Noumi and L. Senatore, Boost Breaking in the EFT of Inflation, JCAP 02 (2017) 034 [arXiv:1512.04100] [INSPIRE].

[19] B. Bonga, S. Brahma, A.-S. Deutsch and S. Shandera, Cosmic variance in inflation with two light scalars, JCAP 05 (2016) 018 [arXiv:1512.05365] [INSPIRE].

[20] X. Chen, Y. Wang and Z.-Z. Xianyu, Loop Corrections to Standard Model Fields in Inflation, JHEP 08 (2016) 051 [arXiv:1604.07841] [INSPIRE].

[21] R. Flauger, M. Mirbabayi, L. Senatore and E. Silverstein, Productive Interactions: heavy particles and non-Gaussianity, JCAP 10 (2017) 058 [arXiv:1606.00513] [INSPIRE].

[22] H. Lee, D. Baumann and G.L. Pimentel, Non-Gaussianity as a Particle Detector, JHEP 12 (2016) 040 [arXiv:1607.03735] [INSPIRE].

[23] L.V. Delacretaz, V. Gorbenko and L. Senatore, The Supersymmetric Effective Field Theory of Inflation, JHEP 03 (2017) 063 [arXiv:1610.04227] [INSPIRE].

[24] P.D. Meerburg, M. Münchmeyer, J.B. Muñoz and X. Chen, Prospects for Cosmological Collider Physics, JCAP 03 (2017) 050 [arXiv:1610.06559] [INSPIRE].

[25] X. Chen, Y. Wang and Z.-Z. Xianyu, Standard Model Background of the Cosmological Collider, Phys. Rev. Lett. 118 (2017) 261302 [arXiv:1610.06597] [INSPIRE].

[26] X. Chen, Y. Wang and Z.-Z. Xianyu, Standard Model Mass Spectrum in Inflationary Universe, JHEP 04 (2017) 058 [arXiv:1612.08122] [INSPIRE].

[27] A. Kehagias and A. Riotto, On the Inflationary Perturbations of Massive Higher-Spin Fields, JCAP 07 (2017) 046 [arXiv:1705.05834] [INSPIRE].

[28] H. An, M. McAneny, A.K. Ridgway and M.B. Wise, Quasi Single Field Inflation in the non-perturbative regime, JHEP 06 (2018) 105 [arXiv:1706.09971] [INSPIRE].

[29] X. Tong, Y. Wang and S. Zhou, On the Effective Field Theory for Quasi-Single Field Inflation, JCAP 11 (2017) 045 [arXiv:1708.01709] [INSPIRE].

[30] A. Moradinezhad Dizgah and C. Dvorkin, Scale-Dependent Galaxy Bias from Massive Particles with Spin during Inflation, JCAP 01 (2018) 010 [arXiv:1708.06473] [INSPIRE].

[31] A.V. Iyer et al., Strongly Coupled Quasi-Single Field Inflation, JCAP 01 (2018) 041 [arXiv:1710.03054] [INSPIRE].

[32] H. An, M. McAneny, A.K. Ridgway and M.B. Wise, Non-Gaussian Enhancements of Galactic Halo Correlations in Quasi-Single Field Inflation, Phys. Rev. D 97 (2018) 123528 [arXiv:1711.02667] [INSPIRE].

[33] S. Kumar and R. Sundrum, Heavy-Lifting of Gauge Theories By Cosmic Inflation, JHEP 05 (2018) 011 [arXiv:1711.03988] [INSPIRE].

[34] G. Franciolini, A. Kehagias and A. Riotto, Imprints of Spinning Particles on Primordial Cosmological Perturbations, JCAP 02 (2018) 023 [arXiv:1712.06626] [INSPIRE].

[35] S. Riquelme M., Non-Gaussianities in a two-field generalization of Natural Inflation, JCAP 04 (2018) 027 [arXiv:1711.08549] [INSPIRE].
[36] X. Tong, Y. Wang and S. Zhou, *Unsuppressed primordial standard clocks in warm quasi-single field inflation*, JCAP 06 (2018) 013 [arXiv:1801.05688 [INSPIRE]].

[37] X. Chen et al., *Quantum Standard Clocks in the Primordial Trispectrum*, JCAP 05 (2018) 049 [arXiv:1803.04412 [INSPIRE]].

[38] R. Saito and T. Kubota, *Heavy Particle Signatures in Cosmological Correlation Functions with Tensor Modes*, JCAP 06 (2018) 009 [arXiv:1804.06974 [INSPIRE]].

[39] G. Cabass, E. Pajer and F. Schmidt, *Imprints of Oscillatory Bispectra on Galaxy Clustering*, JCAP 09 (2018) 003 [arXiv:1804.07295 [INSPIRE]].

[40] A. Moradinezhad Dizgah, H. Lee, J.B. Muñoz and C. Dvorkin, *Galaxy Bispectrum from Massive Spinning Particles*, JCAP 05 (2018) 013 [arXiv:1801.07265 [INSPIRE]].

[41] Y. Wang, Y.-P. Wu, J. Yokoyama and S. Zhou, *Hybrid Quasi-Single Field Inflation*, JCAP 07 (2018) 068 [arXiv:1804.07541 [INSPIRE]].

[42] X. Chen, Y. Wang and Z.-Z. Xianyu, *Neutrino Signatures in Primordial Non-Gaussianities*, JHEP 09 (2018) 022 [arXiv:1805.02656 [INSPIRE]].

[43] N. Bartolo et al., *Supergravity, $\alpha$-attractors and primordial non-Gaussianity*, JCAP 10 (2018) 017 [arXiv:1805.04269 [INSPIRE]].

[44] E. Dimastrogiovanni, M. Fasiello and G. Tasinato, *Probing the inflationary particle content: extra spin-2 field*, JCAP 08 (2018) 016 [arXiv:1806.00850 [INSPIRE]].

[45] L. Bordin, P. Creminelli, A. Khmelnitsky and L. Senatore, *Light Particles with Spin in Inflation*, JCAP 10 (2018) 013 [arXiv:1806.10587 [INSPIRE]].

[46] X. Chen, A. Loeb and Z.-Z. Xianyu, *Unique Fingerprints of Alternatives to Inflation in the Primordial Power Spectrum*, Phys. Rev. Lett. 122 (2019) 121301 [arXiv:1809.02603 [INSPIRE]].

[47] A. Achúcarro, S. Céspedes, A.-C. Davis and G.A. Palma, *Constraints on Holographic Multifield Inflation and Models Based on the Hamilton-Jacobi Formalism*, Phys. Rev. Lett. 122 (2019) 191301 [arXiv:1809.05341 [INSPIRE]].

[48] W.Z. Chua, Q. Ding, Y. Wang and S. Zhou, *Imprints of Schwinger Effect on Primordial Spectra*, JHEP 04 (2019) 066 [arXiv:1810.09815 [INSPIRE]].

[49] S. Kumar and R. Sundrum, *Seeing Higher-Dimensional Grand Unification In Primordial Non-Gaussianities*, JHEP 04 (2019) 120 [arXiv:1811.11200 [INSPIRE]].

[50] G. Goon, K. Hinterbichler, A. Joyce and M. Trodden, *Shapes of gravity: Tensor non-Gaussianity and massive spin-2 fields*, JHEP 10 (2019) 182 [arXiv:1812.07571 [INSPIRE]].

[51] Y.-P. Wu, *Higgs as heavy-lifted physics during inflation*, JHEP 04 (2019) 125 [arXiv:1812.10654 [INSPIRE]].

[52] D. Anninos et al., *Cosmological Shapes of Higher-Spin Gravity*, JCAP 04 (2019) 045 [arXiv:1902.01251 [INSPIRE]].

[53] L. Li et al., *Gravitational Production of Superheavy Dark Matter and Associated Cosmological Signatures*, JHEP 07 (2019) 067 [arXiv:1903.08842 [INSPIRE]].

[54] M. McAneny and A.K. Ridgway, *New Shapes of Primordial Non-Gaussianity from Quasi-Single Field Inflation with Multiple Isocurvatons*, Phys. Rev. D 100 (2019) 043534 [arXiv:1903.11607 [INSPIRE]].
[55] S. Kim, T. Noumi, K. Takeuchi and S. Zhou, Heavy Spinning Particles from Signs of Primordial Non-Gaussianities: Beyond the Positivity Bounds, JHEP 12 (2019) 107 [arXiv:1906.11840] [INSPIRE].

[56] S. Alexander et al., Higher Spin Supersymmetry at the Cosmological Collider: Sculpting SUSY Rilles in the CMB, JHEP 10 (2019) 156 [arXiv:1907.05829] [INSPIRE].

[57] S. Lu, Y. Wang and Z.-Z. Xianyu, A Cosmological Higgs Collider, JHEP 02 (2020) 011 [arXiv:1907.07390] [INSPIRE].

[58] A. Hook, J. Huang and D. Racco, Searches for other vacua. Part II. A new Higgs story at the cosmological collider, JHEP 01 (2020) 105 [arXiv:1907.10624] [INSPIRE].

[59] A. Hook, J. Huang and D. Racco, Minimal signatures of the Standard Model in non-Gaussianities, Phys. Rev. D 101 (2020) 023519 [arXiv:1908.00019] [INSPIRE].

[60] S. Kumar and R. Sundrum, Cosmological Collider Physics and the Curvaton, JHEP 04 (2020) 077 [arXiv:1908.11378] [INSPIRE].

[61] T. Liu, X. Tong, Y. Wang and Z.-Z. Xianyu, Probing P and CP Violations on the Cosmological Collider, JHEP 04 (2020) 189 [arXiv:1909.01819] [INSPIRE].

[62] L.-T. Wang and Z.-Z. Xianyu, In Search of Large Signals at the Cosmological Collider, JHEP 02 (2020) 044 [arXiv:1910.12876] [INSPIRE].

[63] Y. Welling, Simple, exact model of quasisingle field inflation, Phys. Rev. D 101 (2020) 063535 [arXiv:1907.02951] [INSPIRE].

[64] D.-G. Wang, On the inflationary massive field with a curved field manifold, JCAP 01 (2020) 046 [arXiv:1911.04459] [INSPIRE].

[65] Y. Wang and Y. Zhu, Cosmological Collider Signatures of Massive Vectors from Non-Gaussian Gravitational Waves, JCAP 04 (2020) 049 [arXiv:2001.03879] [INSPIRE].

[66] L. Li, S. Lu, Y. Wang and S. Zhou, Cosmological Signatures of Superheavy Dark Matter, JHEP 07 (2020) 231 [arXiv:2002.01131] [INSPIRE].

[67] L.-T. Wang and Z.-Z. Xianyu, Gauge Boson Signals at the Cosmological Collider, JHEP 11 (2020) 082 [arXiv:2004.02887] [INSPIRE].

[68] J.J. Fan and Z.-Z. Xianyu, A Cosmic Microscope for the Preheating Era, JHEP 01 (2021) 021 [arXiv:2005.12278] [INSPIRE].

[69] K. Kogai, K. Akitsu, F. Schmidt and Y. Urakawa, Galaxy imaging surveys as spin-sensitive detector for cosmological colliders, JCAP 03 (2021) 060 [arXiv:2009.05517] [INSPIRE].

[70] A. Bodas, S. Kumar and R. Sundrum, The Scalar Chemical Potential in Cosmological Collider Physics, JHEP 02 (2021) 079 [arXiv:2010.04727] [INSPIRE].

[71] S. Aoki and M. Yamaguchi, Disentangling mass spectra of multiple fields in cosmological collider, JHEP 04 (2021) 127 [arXiv:2012.13667] [INSPIRE].

[72] N. Maru and A. Okawa, Non-Gaussianity from X, Y gauge bosons in Cosmological Collider Physics, arXiv:2101.10634 [INSPIRE].

[73] S. Kim, T. Noumi, K. Takeuchi and S. Zhou, Perturbative unitarity in quasi-single field inflation, JHEP 07 (2021) 018 [arXiv:2102.04101] [INSPIRE].

[74] S. Lu, Axion isocurvature collider, JHEP 04 (2022) 157 [arXiv:2103.05958] [INSPIRE].

[75] C.M. Sou, X. Tong and Y. Wang, Chemical-potential-assisted particle production in FRW spacetimes, JHEP 06 (2021) 129 [arXiv:2104.08772] [INSPIRE].
[76] Q. Lu, M. Reece and Z.-Z. Xianyu, *Missing scalars at the cosmological collider*, JHEP 12 (2021) 098 [arXiv:2108.11385] [INSPIRE].

[77] L. Pinol, S. Aoki, S. Renaux-Petel and M. Yamaguchi, *Inflationary flavor oscillations and the cosmic spectroscopy*, Phys. Rev. D 107 (2023) L021301 [arXiv:2112.05710] [INSPIRE].

[78] Y. Cui and Z.-Z. Xianyu, *Probing Leptogenesis with the Cosmological Collider*, Phys. Rev. Lett. 129 (2022) 111301 [arXiv:2112.10793] [INSPIRE].

[79] X. Tong and Z.-Z. Xianyu, *Large spin-2 signals at the cosmological collider*, JHEP 10 (2022) 194 [arXiv:2203.06349] [INSPIRE].

[80] M. Reece, L.-T. Wang and Z.-Z. Xianyu, *Large-field inflation and the cosmological collider*, Phys. Rev. D 107 (2023) L101304 [arXiv:2204.11869] [INSPIRE].

[81] X. Chen, R. Ebadi and S. Kumar, *Classical cosmological collider physics and primordial features*, JCAP 08 (2022) 083 [arXiv:2205.01107] [INSPIRE].

[82] Z. Qin and Z.-Z. Xianyu, *Phase information in cosmological collider signals*, JHEP 10 (2022) 192 [arXiv:2205.01692] [INSPIRE].

[83] G. Cabass, S. Jazayeri, E. Pajer and D. Stefanyszyn, *Parity violation in the scalar trispectrum: no-go theorems and yes-go examples*, JHEP 02 (2023) 021 [arXiv:2210.02907] [INSPIRE].

[84] G. Cabass, M.M. Ivanov and O.H.E. Philcox, *Colliders and ghosts: Constraining inflation with the parity-odd galaxy four-point function*, Phys. Rev. D 107 (2023) 023523 [arXiv:2210.16320] [INSPIRE].

[85] X. Niu, M.H. Rahat, K. Srinivasan and W. Xue, *Gravitational wave probes of massive gauge bosons at the cosmological collider*, JCAP 02 (2023) 013 [arXiv:2211.14331] [INSPIRE].

[86] X. Niu, M.H. Rahat, K. Srinivasan and W. Xue, *Parity-odd and even trispectrum from axion inflation*, JCAP 05 (2023) 018 [arXiv:2211.14324] [INSPIRE].

[87] D.H. Tran, Y. Wang, J. Yang and Y. Zhu, *Numerical prescriptions of early-time divergences of the in-in formalism*, JCAP 07 (2022) 014 [arXiv:2202.06350] [INSPIRE].

[88] S. Aoki, *Continuous spectrum on cosmological collider*, JCAP 04 (2023) 002 [arXiv:2301.07920] [INSPIRE].

[89] X. Tong, Y. Wang, C. Zhang and Y. Zhu, *BCS in the sky: signatures of inflationary fermion condensation*, JCAP 04 (2024) 022 [arXiv:2304.09428] [INSPIRE].

[90] S. Jazayeri, S. Renaux-Petel and D. Werth, *Shapes of the cosmological low-speed collider*, JCAP 12 (2023) 035 [arXiv:2307.01751] [INSPIRE].

[91] Y. Yin, *Cosmological collider signal from non-Bunch-Davies initial states*, Phys. Rev. D 109 (2024) 043535 [arXiv:2309.05244] [INSPIRE].

[92] P. Chakraborty and J. Stout, *Light scalars at the cosmological collider*, JHEP 02 (2024) 021 [arXiv:2310.01494] [INSPIRE].

[93] X. Chen, J.J. Fan and L. Li, *New inflationary probes of axion dark matter*, JHEP 12 (2023) 197 [arXiv:2303.03406] [INSPIRE].

[94] S. Jazayeri et al., *Parity violation from emergent nonlocality during inflation*, Phys. Rev. D 108 (2023) 123523 [arXiv:2308.11315] [INSPIRE].

[95] P. Chakraborty and J. Stout, *Compact scalars at the cosmological collider*, JHEP 03 (2024) 149 [arXiv:2311.09219] [INSPIRE].
[96] Y. Ema and S. Verner, Cosmological collider signatures of Higgs-R² inflation, JCAP 04 (2024) 039 [arXiv:2309.10841] [INSPIRE].

[97] C. McCulloch, E. Pajer and X. Tong, A cosmological tachyon collider: enhancing the long-short scale coupling, JHEP 05 (2024) 262 [arXiv:2401.11009] [INSPIRE].

[98] N. Craig, S. Kumar and A. McCune, An effective cosmological collider, JHEP 07 (2024) 108 [arXiv:2401.10976] [INSPIRE].

[99] Y.-P. Wu, The cosmological collider in R² inflation, JCAP 07 (2024) 010 [arXiv:2404.05031] [INSPIRE].

[100] J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation, JHEP 09 (2011) 045 [arXiv:1104.2846] [INSPIRE].

[101] V. Assassi, D. Baumann and D. Green, On Soft Limits of Inflationary Correlation Functions, JCAP 11 (2012) 047 [arXiv:1204.4207] [INSPIRE].

[102] D. Baumann, G. Goon, H. Lee and G.L. Pimentel, Partially Massless Fields During Inflation, JHEP 04 (2018) 140 [arXiv:1712.06624] [INSPIRE].

[103] N. Arkani-Hamed and P. Benincasa, On the Emergence of Lorentz Invariance and Unitarity from the Scattering Facet of Cosmological Polytopes, arXiv:1811.01125 [INSPIRE].

[104] C. Sleight, A Mellin Space Approach to Cosmological Correlators, JHEP 01 (2020) 090 [arXiv:1906.12302] [INSPIRE].

[105] C. Sleight and M. Taronna, Bootstrapping Inflationary Correlators in Mellin Space, JHEP 02 (2020) 098 [arXiv:1907.01143] [INSPIRE].

[106] N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities, JHEP 04 (2020) 105 [arXiv:1811.00024] [INSPIRE].

[107] D. Baumann et al., The cosmological bootstrap: weight-shifting operators and scalar seeds, JHEP 12 (2020) 204 [arXiv:1910.14051] [INSPIRE].

[108] D. Baumann et al., The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization, SciPost Phys. 11 (2021) 071 [arXiv:2005.04234] [INSPIRE].

[109] E. Pajer, D. Stefanyszyn and J. Supeł, The Boostless Bootstrap: Amplitudes without Lorentz boosts, JHEP 12 (2020) 198 [Erratum ibid. 04 (2022) 023] [arXiv:2007.00027] [INSPIRE].

[110] H. Goodhew, S. Jazayeri and E. Pajer, The Cosmological Optical Theorem, JCAP 04 (2021) 021 [arXiv:2009.02898] [INSPIRE].

[111] D. Meltzer, The inflationary wavefunction from analyticity and factorization, JCAP 12 (2021) 018 [arXiv:2107.10266] [INSPIRE].

[112] H. Goodhew, S. Jazayeri, M.H.G. Lee and E. Pajer, Cutting cosmological correlators, JCAP 08 (2021) 003 [arXiv:2104.06587] [INSPIRE].

[113] S. Jazayeri, E. Pajer and D. Stefanyszyn, From locality and unitarity to cosmological correlators, JHEP 10 (2021) 065 [arXiv:2103.08649] [INSPIRE].

[114] D. Baumann et al., Linking the singularities of cosmological correlators, JHEP 09 (2022) 010 [arXiv:2106.05294] [INSPIRE].

[115] S. Melville and E. Pajer, Cosmological Cutting Rules, JHEP 05 (2021) 249 [arXiv:2103.09832] [INSPIRE].
[116] L. Di Pietro, V. Gorbenko and S. Komatsu, Analyticity and unitarity for cosmological correlators, JHEP 03 (2022) 023 [arXiv:2108.01695] [INSPIRE].

[117] H. Gomez, R.L. Jusinskas and A. Lipstein, Cosmological Scattering Equations, Phys. Rev. Lett. 127 (2021) 251604 [arXiv:2106.11903] [INSPIRE].

[118] A. Premkumar, Regulating loops in de Sitter spacetime, Phys. Rev. D 109 (2024) 045003 [arXiv:2110.12504] [INSPIRE].

[119] J. Bonifacio, E. Pajer and D.-G. Wang, From amplitudes to contact cosmological correlators, JHEP 10 (2021) 001 [arXiv:2106.15468] [INSPIRE].

[120] M. Hogervorst, J. Penedones and K.S. Vaziri, Towards the non-perturbative cosmological bootstrap, JHEP 02 (2023) 162 [arXiv:2107.13871] [INSPIRE].

[121] C. Sleight and M. Taronna, From AdS to dS exchanges: Spectral representation, Mellin amplitudes, and crossing, Phys. Rev. D 104 (2021) L081902 [arXiv:2007.09993] [INSPIRE].

[122] C. Sleight and M. Taronna, From dS to AdS and back, JHEP 12 (2021) 074 [arXiv:2109.02725] [INSPIRE].

[123] C. Sleight and M. Taronna, On the consistency of (partially-)massless matter couplings in de Sitter space, JHEP 10 (2021) 156 [arXiv:2106.00366] [INSPIRE].

[124] G. Cabass, E. Pajer, D. Stefanyszyn and J. Supeł, Bootstrapping large graviton non-Gaussianities, JHEP 05 (2022) 077 [arXiv:2109.10189] [INSPIRE].

[125] X. Tong, Y. Wang and Y. Zhu, Cutting rule for cosmological collider signals: a bulk evolution perspective, JHEP 03 (2022) 181 [arXiv:2112.03448] [INSPIRE].

[126] L.-T. Wang, Z.-Z. Xianyu and Y.-M. Zhong, Precision calculation of inflation correlators at one loop, JHEP 02 (2022) 085 [arXiv:2109.14635] [INSPIRE].

[127] H. Gomez, R. Lipinski Jusinskas and A. Lipstein, Cosmological scattering equations at tree-level and one-loop, JHEP 07 (2022) 004 [arXiv:2112.12695] [INSPIRE].

[128] D. Baumann et al., Snowmass White Paper: The Cosmological Bootstrap, in the proceedings of the Snowmass 2021, Seattle, U.S.A., July 17–26 (2022) [arXiv:2203.08121] [INSPIRE].

[129] T. Heckelbacher, I. Sachs, E. Skvortsov and P. Vanhove, Analytical evaluation of cosmological correlation functions, JHEP 08 (2022) 139 [arXiv:2204.07217] [INSPIRE].

[130] E. Pajer, Building a Boostless Bootstrap for the Bispectrum, JCAP 01 (2021) 023 [arXiv:2010.12818] [INSPIRE].

[131] G.L. Pimentel and D.-G. Wang, Boostless cosmological collider bootstrap, JHEP 10 (2022) 177 [arXiv:2205.00013] [INSPIRE].

[132] S. Jazayeri and S. Renaux-Petel, Cosmological bootstrap in slow motion, JHEP 12 (2022) 137 [arXiv:2205.10340] [INSPIRE].

[133] J. Bonifacio et al., The graviton four-point function in de Sitter space, JHEP 06 (2023) 212 [arXiv:2212.07370] [INSPIRE].

[134] H. Lee and X. Wang, Cosmological double-copy relations, Phys. Rev. D 108 (2023) L061702 [arXiv:2212.11282] [INSPIRE].

[135] Z. Qin and Z.-Z. Xianyu, Helical inflation correlators: partial Mellin-Barnes and bootstrap equations, JHEP 04 (2023) 059 [arXiv:2208.13790] [INSPIRE].

[136] Z.-Z. Xianyu and H. Zhang, Bootstrapping one-loop inflation correlators with the spectral decomposition, JHEP 04 (2023) 103 [arXiv:2211.03810] [INSPIRE].
[137] D.-G. Wang, G.L. Pimentel and A. Achúcarro, Bootstrapping multi-field inflation: non-Gaussianities from light scalars revisited, JCAP 05 (2023) 043 [arXiv:2212.14035] [INSPIRE].

[138] Z. Qin and Z.-Z. Xianyu, Closed-form formulae for inflation correlators, JHEP 07 (2023) 001 [arXiv:2301.07047] [INSPIRE].

[139] Z. Qin and Z.-Z. Xianyu, Inflation correlators at the one-loop order: nonanalyticity, factorization, cutting rule, and OPE, JHEP 09 (2023) 116 [arXiv:2304.13295] [INSPIRE].

[140] Z. Qin and Z.-Z. Xianyu, Nonanalyticity and on-shell factorization of inflation correlators at all loop orders, JHEP 01 (2024) 168 [arXiv:2308.14802] [INSPIRE].

[141] Z.-Z. Xianyu and J. Zang, Inflation correlators with multiple massive exchanges, JHEP 03 (2024) 070 [arXiv:2309.10849] [INSPIRE].

[142] D. Green, Y. Huang, C.-H. Shen and D. Baumann, Positivity from Cosmological Correlators, JHEP 04 (2024) 034 [arXiv:2310.02490] [INSPIRE].

[143] C. Duaso Pueyo and E. Pajer, A cosmological bootstrap for resonant non-Gaussianity, JHEP 03 (2024) 098 [arXiv:2311.01395] [INSPIRE].

[144] S. De and A. Pokraka, Cosmology meets cohomology, JHEP 03 (2024) 156 [arXiv:2308.03753] [INSPIRE].

[145] M. Loparco, J. Penedones, K. Salehi Vaziri and Z. Sun, The Källén-Lehmann representation in de Sitter spacetime, JHEP 12 (2023) 159 [arXiv:2306.00090] [INSPIRE].

[146] M.H.G. Lee, C. McCulloch and E. Pajer, Leading loops in cosmological correlators, JHEP 11 (2023) 038 [arXiv:2305.11228] [INSPIRE].

[147] S. Aoki, T. Noumi, F. Sano and M. Yamaguchi, Analytic formulae for inflationary correlators with dynamical mass, JHEP 03 (2024) 073 [arXiv:2312.09642] [INSPIRE].

[148] N. Arkani-Hamed et al., Differential Equations for Cosmological Correlators, arXiv:2312.05303 [INSPIRE].

[149] N. Arkani-Hamed et al., Kinematic Flow and the Emergence of Time, arXiv:2312.05300 [INSPIRE].

[150] D. Stefanyszyn, X. Tong and Y. Zhu, Cosmological correlators through the looking glass: reality, parity, and factorisation, JHEP 05 (2024) 196 [arXiv:2309.07769] [INSPIRE].

[151] Y. Donath and E. Pajer, The in-out formalism for in-in correlators, JHEP 07 (2024) 064 [arXiv:2402.05999] [INSPIRE].

[152] B. Fan and Z.-Z. Xianyu, Cosmological Amplitudes in Power-Law FRW Universe, arXiv:2403.07050 [INSPIRE].

[153] T.W. Grimm, A. Hoefnagels and M. van Vliet, Structure and Complexity of Cosmological Correlators, arXiv:2404.03716 [INSPIRE].

[154] Z.-Z. Du and D. Stefanyszyn, Soft theorems for boostless amplitudes, JHEP 07 (2024) 011 [arXiv:2403.05459] [INSPIRE].

[155] S. Melville and G.L. Pimentel, A de Sitter S-matrix from amputated cosmological correlators, JHEP 08 (2024) 211 [arXiv:2404.05712] [INSPIRE].

[156] G. Cabass et al., BOSS Constraints on Massive Particles during Inflation: The Cosmological Collider in Action, arXiv:2404.01894 [INSPIRE].
[157] W. Sohn, D.-G. Wang, J.R. Fergusson and E.P.S. Shellard, *Searching for Cosmological Collider in the Planck CMB Data*, JCAP 09 (2024) 016 [arXiv:2404.07203 [insPIRE]].

[158] X. Chen, *Primordial Non-Gaussianities from Inflation Models*, Adv. Astron. 2010 (2010) 638979 [arXiv:1002.1416 [insPIRE]].

[159] Y. Wang, *Inflation, Cosmic Perturbations and Non-Gaussianities*, Commun. Theor. Phys. 62 (2014) 109 [arXiv:1303.1523 [insPIRE]].

[160] X. Chen, Y. Wang and Z.-Z. Xianyu, *Schwinger-Keldysh Diagrammatics for Primordial Perturbations*, JCAP 12 (2017) 006 [arXiv:1703.10166 [insPIRE]].

[161] D. Anninos, T. Anous, D.Z. Freedman and G. Konstantinidis, *Late-time Structure of the Bunch-Davies De Sitter Wavefunction*, JCAP 11 (2015) 048 [arXiv:1406.5490 [insPIRE]].

[162] N. Arkani-Hamed, P. Benincasa and A. Postnikov, *Cosmological Polytopes and the Wavefunction of the Universe*, arXiv:1709.02813 [insPIRE].

[163] A. Hillman, *Symbol Recursion for the dS Wave Function*, arXiv:1912.09450 [insPIRE].

[164] S. Céspedes, A.-C. Davis and S. Melville, *On the time evolution of cosmological correlators*, JHEP 02 (2021) 012 [arXiv:2009.07874 [insPIRE]].

[165] A. Hillman and E. Pajer, *A differential representation of cosmological wavefunctions*, JHEP 04 (2022) 012 [arXiv:2112.01619 [insPIRE]].

[166] S.A. Salcedo, M.H.G. Lee, S. Melville and E. Pajer, *The Analytic Wavefunction*, JHEP 06 (2023) 020 [arXiv:2212.08009 [insPIRE]].

[167] S. Albayrak, P. Benincasa and C. Duaso Pueyo, *Perturbative unitarity and the wavefunction of the Universe*, SciPost Phys. 16 (2024) 157 [arXiv:2305.19686 [insPIRE]].

[168] S. Agui Salcedo and S. Melville, *The cosmological tree theorem*, JHEP 12 (2023) 076 [arXiv:2308.00680 [insPIRE]].

[169] S. Céspedes, A.-C. Davis and D.-G. Wang, *On the IR divergences in de Sitter space: loops, resummation and the semi-classical wavefunction*, JHEP 04 (2024) 004 [arXiv:2311.17990 [insPIRE]].

[170] D. Werth, L. Pinol and S. Renaux-Petel, *Cosmological Flow of Primordial Correlators*, arXiv:2302.00655 [insPIRE].

[171] L. Pinol, S. Renaux-Petel and D. Werth, *The Cosmological Flow: A Systematic Approach to Primordial Correlators*, arXiv:2312.06559 [insPIRE].

[172] D. Werth, L. Pinol and S. Renaux-Petel, *CosmoFlow: Python Package for Cosmological Correlators*, Class. Quant. Grav. 41 (2024) 175015 [arXiv:2402.03693 [insPIRE]].

[173] NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov/.

[174] S. Garcia-Saenz, L. Pinol and S. Renaux-Petel, *Revisiting non-Gaussianity in multifield inflation with curved field space*, JHEP 01 (2020) 073 [arXiv:1907.10403 [insPIRE]].

[175] L. Pinol, *Multifield inflation beyond $N_{field} = 2$: non-Gaussianities and single-field effective theory*, JCAP 04 (2021) 002 [arXiv:2011.05930 [insPIRE]].

[176] A. Bzowski, P. McFadden and K. Skenderis, *Implications of conformal invariance in momentum space*, JHEP 03 (2014) 111 [arXiv:1304.7760 [insPIRE]].

[177] B.M. Minton, *Generalized Hypergeometric Function of Unit Argument*, J. Math. Phys. 11 (1970) 1375.
[178] R. Holman and A.J. Tolley, *Enhanced Non-Gaussianity from Excited Initial States*, JCAP 05 (2008) 001 [arXiv:0710.1302] [INSPIRE].

[179] R. Flauger, D. Green and R.A. Porto, *On squeezed limits in single-field inflation. Part I*, JCAP 08 (2013) 032 [arXiv:1303.1430] [INSPIRE].

[180] PLANCK collaboration, *Planck 2018 results. X. Constraints on inflation*, Astron. Astrophys. 641 (2020) A10 [arXiv:1807.06211] [INSPIRE].

[181] P. Creminelli, M.A. Luty, A. Nicolis and L. Senatore, *Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies*, JHEP 12 (2006) 080 [hep-th/0606090] [INSPIRE].

[182] C. Cheung et al., *The Effective Field Theory of Inflation*, JHEP 03 (2008) 014 [arXiv:0709.0293] [INSPIRE].

[183] L. Senatore and M. Zaldarriaga, *The Effective Field Theory of Multifield Inflation*, JHEP 04 (2012) 024 [arXiv:1009.2093] [INSPIRE].

[184] A.J. Tolley and M. Wyman, *The Gelaton Scenario: Equilateral non-Gaussianity from multi-field dynamics*, Phys. Rev. D 81 (2010) 043502 [arXiv:0910.1853] [INSPIRE].

[185] S. Cremonini, Z. Lalak and K. Turzynski, *Strongly Coupled Perturbations in Two-Field Inflationary Models*, JCAP 03 (2011) 016 [arXiv:1010.3021] [INSPIRE].

[186] A. Achúcarro et al., *Features of heavy physics in the CMB power spectrum*, JCAP 01 (2011) 030 [arXiv:1010.3693] [INSPIRE].

[187] D. Babich, P. Creminelli and M. Zaldarriaga, *The Shape of non-Gaussianities*, JCAP 08 (2004) 009 [astro-ph/0405356] [INSPIRE].

[188] J.R. Fergusson and E.P.S. Shellard, *The shape of primordial non-Gaussianity and the CMB bispectrum*, Phys. Rev. D 80 (2009) 043510 [arXiv:0812.3413] [INSPIRE].

[189] PLANCK collaboration, *Planck 2018 results. IX. Constraints on primordial non-Gaussianity*, Astron. Astrophys. 641 (2020) A9 [arXiv:1905.05697] [INSPIRE].

[190] T. Suyama and M. Yamaguchi, *Non-Gaussianity in the modulated reheating scenario*, Phys. Rev. D 77 (2008) 023505 [arXiv:0709.2545] [INSPIRE].

[191] K. Matsumoto, *Appell and Lauricella Hypergeometric Functions*, in *Encyclopedia of Special Functions: The Askey-Bateman Project*, T.H. Koornwinder and J.V. Stokman eds., Cambridge University Press (2020), p. 79–100 [DOI:10.1017/9780511777165.004].