Nozari and Asadi (Phys. Rev. D 93, 103511 (2016)) studied a two-field Dirac-Born-Infeld (DBI) inflation model beyond the slow-roll approximation and found parameter regimes — consistent with Planck 2015 constraints on the tensor-to-scalar ratio rr and spectral index nsn_s — in which the model produces large primordial non-Gaussianity (NG) that would be observable by future improvements in CMB experiments. They framed the actual detection of such enhanced NG as an open observational challenge that would test the viability of this two-field DBI scenario. This problem asks for the observational determination of that prediction: reconstruct the model's predicted equilateral- and orthogonal-type amplitudes fNLf_{\mathrm{NL}} across its viable parameter band, and either detect primordial NG at those amplitudes in CMB data, exclude the viable large-NG band with current or next-generation bispectrum constraints, or establish from actual CMB bispectrum data that current constraints neither detect the predicted NG nor yet exclude the viable large-NG band.

Background

Inflation — a period of accelerated expansion in the very early universe — generates the primordial curvature perturbation whose imprint is the cosmic microwave background (CMB) temperature and polarization anisotropy. If the perturbation were exactly Gaussian, its statistics would be fully captured by the two-point function (power spectrum); the leading statistic beyond it is the bispectrum, the three-point function of Fourier modes, customarily parametrized by a dimensionless amplitude fNLf_{\mathrm{NL}}. Its shape as a function of the three wavenumbers encodes the physics of inflation: a 'local' shape (maximal in squeezed triangles, k1≪k2≈k3k_1 \ll k_2 \approx k_3) signals multi-source super-horizon evolution, while 'equilateral' (maximal for k1≈k2≈k3k_1 \approx k_2 \approx k_3) and 'orthogonal' (sign-changing, anti-correlated with both) shapes signal non-canonical kinetic terms with a reduced sound speed. DBI inflation realizes the latter: in type IIB string compactifications, the inflaton describes the position of a brane falling down a warped 'throat', and the Dirac–Born–Infeld action induces a field-dependent sound speed cs≤1c_s \le 1, which generically enhances equilateral-type NG to amplitudes fNL∼cs−2f_{\mathrm{NL}} \sim c_s^{-2} — potentially orders of magnitude above the slow-roll single-field expectation. In two-field DBI models a second field ('entropy' perturbation, orthogonal to the inflaton trajectory) further modifies the bispectrum and weakens the usual single-field consistency relations. Nozari and Asadi (arXiv:1605.00823) analyzed a two-field DBI model with H=H0+H1φ+H2χH = H_0 + H_1\varphi + H_2\chi (H0=10−6H_0 = 10^{-6}, H1=H2=0.01H_1 = H_2 = 0.01, φ0=10\varphi_0 = 10, χ0=1\chi_0 = 1) and DBI function f(χ)=λ/χ4f(\chi) = \lambda/\chi^4, computing the scalar spectral index, tensor-to-scalar ratio, and the equilateral- and orthogonal-type fNLf_{\mathrm{NL}} expressions (their Eqs. (51)–(52)) beyond the slow-roll approximation. Comparing with Planck 2015 constraints, they found the rr–nsn_s data compatible at 95% CL only in narrow bands (e.g. 88200<λ<9500088200 < \lambda < 95000 for N=60N = 60 e-folds), while the Planck 2015 bispectrum bounds admitted large NG in wider bands (e.g. λ<911800\lambda < 911800 for N=60N = 60, with λ<2102800\lambda < 2102800 for N=50N = 50 and λ<357260\lambda < 357260 for N=70N = 70 against the orthogonal bounds); overlapping these, they concluded the model can realize large NG observable by future experiments. At the time, Planck 2015 reported fNLequil=−4±43f_{\mathrm{NL}}^{\mathrm{equil}} = -4 \pm 43 and fNLortho=−26±21f_{\mathrm{NL}}^{\mathrm{ortho}} = -26 \pm 21 (68% CL, temperature plus polarization) — no detection. Forecast sensitivities — Simons Observatory (SO) σ(fNLequil)≈24\sigma(f_{\mathrm{NL}}^{\mathrm{equil}}) \approx 24–2727, σ(fNLortho)≈13\sigma(f_{\mathrm{NL}}^{\mathrm{ortho}}) \approx 13–1414; CMB-HD targeting σ(fNL)<1\sigma(f_{\mathrm{NL}}) < 1 — define the experimental window in which the model's prediction becomes decisively testable.

Problem Statement

Determine, observationally, the status of the large primordial non-Gaussianity predicted by the two-field DBI inflation model of Nozari and Asadi (arXiv:1605.00823) in its observationally viable parameter regime. Concretely: (i) reconstruct the model's predictions fNLequil(λ,N)f_{\mathrm{NL}}^{\mathrm{equil}}(\lambda, N) and fNLortho(λ,N)f_{\mathrm{NL}}^{\mathrm{ortho}}(\lambda, N) from the model's bispectrum expressions (beyond the slow-roll approximation, with H=H0+H1φ+H2χH = H_0 + H_1\varphi + H_2\chi and f(χ)=λ/χ4f(\chi) = \lambda/\chi^4) throughout the band compatible with CMB constraints on rr and nsn_s (e.g. 88200<λ<9500088200 < \lambda < 95000 at N=60N = 60, including its overlap with the large-NG band λ<911800\lambda < 911800); and (ii) decide the observational question with current or next-generation CMB bispectrum data — either a detection of primordial equilateral/orthogonal non-Gaussianity at the amplitudes this regime predicts, which would constitute the first detection of primordial NG and directly test the viability of this two-field DBI scenario, or an observational constraint from actual CMB bispectrum data tight enough (e.g. measured σ(fNLequil)\sigma(f_{\mathrm{NL}}^{\mathrm{equil}}) and σ(fNLortho)\sigma(f_{\mathrm{NL}}^{\mathrm{ortho}}) reaching the SO/CMB-S4/CMB-HD sensitivity levels) to exclude the model's viable large-NG band, together with the resulting revision of the model's allowed λ\lambda–NN parameter space, or a demonstration from actual CMB bispectrum data that current constraints neither detect the predicted NG nor yet exclude the viable large-NG band. Notation caveat for the reconstruction: in arXiv:1605.00823 the symbol λ\lambda appearing inside the bispectrum expressions (Eqs. (51)–(52)) is a dynamical combination of ff and χ˙\dot{\chi} defined in the paper's Eq. (33), distinct from the warp (geometric) parameter λ\lambda of f(χ)=λ/χ4f(\chi) = \lambda/\chi^4 that the observational bands above bound; the predictions fNL(λ,N)f_{\mathrm{NL}}(\lambda, N) are functions of the warp λ\lambda, obtained by evaluating Eqs. (51)–(52) — with the sound speed csc_s and Σ\Sigma (the paper's Eq. (34)) — along the model's numerically integrated trajectory. The completion boundary is the observational verdict on the model's enhanced-NG prediction from actual CMB bispectrum data — a detection, an exclusion of the viable large-NG band, or a data-based finding that current constraints neither detect the predicted NG nor yet exclude that band — not merely a re-derivation of the predictions, and not a comparison of the reconstructed amplitudes against published forecast sensitivities in place of a data-based verdict.

References

  1. Kourosh Nozari, Kosar Asadi, 'Testing a Two Field Inflation Beyond the Slow-Roll Approximation', Physical Review D 93, 103511 (2016), arXiv:1605.00823, DOI 10.1103/PhysRevD.93.103511, https://doi.org/10.1103/PhysRevD.93.103511
  2. Planck Collaboration (P. A. R. Ade, N. Aghanim, M. Arnaud, et al.), 'Planck 2015 results. XVII. Constraints on primordial non-Gaussianity', Astronomy & Astrophysics 594, A17 (2016), arXiv:1502.01592, DOI 10.1051/0004-6361/201525836, https://doi.org/10.1051/0004-6361/201525836
  3. Planck Collaboration (Y. Akrami, F. Arroja, M. Ashdown, et al.), 'Planck 2018 results. IX. Constraints on primordial non-Gaussianity', Astronomy & Astrophysics 641, A9 (2020), arXiv:1905.05697, DOI 10.1051/0004-6361/201935891, https://doi.org/10.1051/0004-6361/201935891
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  5. Neelima Sehgal, Simone Aiola, Yashar Akrami, et al., 'CMB-HD: An Ultra-Deep, High-Resolution Millimeter-Wave Survey Over Half the Sky', Bulletin of the American Astronomical Society 51(7), 6 (2019), arXiv:1906.10134, https://arxiv.org/abs/1906.10134
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  7. Oliver H. E. Philcox, Maresuke Shiraishi, 'Non-Gaussianity Beyond the Scalar Sector: A Search for Tensor and Mixed Tensor-Scalar Bispectra with Planck Data', Physical Review D 111, 123502 (2025), arXiv:2409.10595, DOI 10.1103/pb7x-lp19, https://doi.org/10.1103/pb7x-lp19