Extending the Cosmological Collider: New Scaling Regimes and Constraints from BOSS

TL;DR

The paper expands the cosmological collider program by allowing a complex scaling dimension Δ = α + iν for extra fields coupled to the inflaton, enabling a hybrid of light- and heavy-field signatures that imprint oscillatory log k patterns in the large-scale structure. It develops a two-field model showing that large oscillation frequencies ν can coexist with small α under inflaton–field mixing and non-de Sitter dynamics, and translates these primordial signals into a modulated scale-dependent bias in galaxy clustering. The authors provide a practical galaxy-power spectrum framework with oscillatory components parameterized by A_cos and A_sin, and perform Fisher forecasts for current and near-future surveys, finding enhanced sensitivity for α ≳ 0 and ν ≳ 1 due to the oscillations breaking degeneracies with nonlinearities. Applying the approach to BOSS DR12 data yields the first constraints on this extended oscillatory PNG parameter space, with no detection but results broadly consistent with forecasts and highlighting strong potential for DESI, SPHEREx, and future surveys to explore these signatures. Overall, the work demonstrates that oscillatory primordial non-Gaussianity from extended inflationary sectors can be robustly constrained with near-term LSS data and motivates continued exploration of high-frequency, log-oscillatory signals in cosmology.

Abstract

Primordial non-Gaussianity generated by additional fields during inflation offers a compelling observational target. Heavy fields imprint characteristic oscillatory signals in non-Gaussian correlation functions of the inflaton, a process sometimes referred to as cosmological-collider physics. These distinct signatures are compelling windows into ultra-high-energy physics, but are often suppressed, making standard equilateral non-Gaussianity the most promising discovery channel in many scenarios. In this paper, we show that direct couplings between the inflaton and additional fields can lead to a wide variety of novel, observationally relevant signals which open new parameter regimes that simultaneously exhibit the characteristics of light and heavy fields. We identify these primordial signatures in the late-time observables of the large-scale structure of the Universe, where they most significantly modify the scale-dependent bias of the galaxy power spectrum to include an oscillatory modulation around a non-trivial power law. We explore the full range of parameters that phenomenologically arise in these models and study the sensitivity of current and future galaxy surveys, finding that this new class of primordial non-Gaussianity is particularly accessible in near-term surveys due to its oscillatory feature. Finally, we perform an analysis of existing data from the final release of the Baryon Oscillation Spectroscopic Survey (BOSS DR12). While we find no evidence for a signal, we demonstrate significant improvements in sensitivity over respective non-oscillatory scenarios and place the first constraints on this extended parameter space of oscillatory non-Gaussianity.

Figures (20)

• Figure 1: Illustration of the effect of oscillatory primordial non-Gaussianity on the linear galaxy power spectrum through the scale-dependent bias for different scaling dimensions $\Delta = \alpha + \mathrm{i}\nu$. In addition to the standard cosmological collider with $\alpha = 3/2$ as in \ref{['eq:squeezed_bispectrum']}, we also show examples for the wider range of values considered in this work. The employed non-Gaussian amplitudes are $f_\mathrm{NL}^{\alpha, \nu} = 3, 500, 2000\text{ and }2000$ for the shown cases (with absorbed suppression factors; see especially Section \ref{['sec:forecasts']} for its definition and details). We observe that the oscillatory imprint with logarithmic frequency $\nu$ moves from large to small scales as we increase the scaling exponent $\alpha$, which also sets the envelope of the oscillations. The horizontal dashed lines indicate the effective shot noise level for BOSS, DESI and SPHEREx after scaling them to the displayed redshift $z = 0$ and linear bias $b_1 = 1.6$. The gray-shaded regions on large scales indicate the wavenumbers below the minimum wavenumber of these surveys, $k < k_\mathrm{min}$, computed based on their entire spherical volume. The gray-shaded regions for large wavenumbers indicate the regimes where the scales exceed the nonlinear scale, $k > k_\mathrm{NL}$, for the maximum redshift of BOSS and DESI, respectively.
• Figure 2: Comparison of the numerical and analytical solutions for the dimensionless mode function $\tilde{\sigma}(u)$ (top) and its respective power spectrum $H^{-2} k^3 P_{\sigma}(u)$ (bottom) as a function of $u = k \tau$ for the case of no mixing, $\rho = 0$, and equal masses of the two fields, $m_1 = m_2$. We display both the real and imaginary parts of $\tilde{\sigma}$, and note that $\tilde{\sigma} \equiv \tilde{\sigma}_A^{(+)} = -\tilde{\sigma}_A^{(-)} = \mathrm{i}\tilde{\sigma}_B^{(\pm)}$ [cf. \ref{['eq:wkb-mf']} since $\sigma_1 = \sigma_2$]. The left and right panels illustrate the massless scenario and an example for the massive case with $m = 10H$, respectively. The numerical solution is computed using the Dormand-Prince method with initial step size $\Delta u = 0.01$ and initial point $u_0 = -5000$ to minimize the phase error, and exhibits very good agreement with the analytic result.
• Figure 3: Numerical solutions for the mode functions $\tilde{\sigma}^{(\pm)}(u) \equiv \pm\tilde{\sigma}_A^{(\pm)}(u) = \mathrm{i}\tilde{\sigma}_B^{(\pm)}(u)$ for six different cases of non-zero mixing, $\rho \neq 0$. We show the real (blue) and imaginary (green) parts for a few different scenarios, taking the masses to be equal for simplicity. Fitting the parametrization \ref{['eq:sig_powers']} to these curves over the shown range of $u$ leads to excellent agreement, with differences being at most at the sub-percent level. We explicitly highlight the dominant scaling solution as parameterized by $\Delta = \alpha + \mathrm{i}\nu$ in each panel. We observe that the oscillatory mode functions are not only non-zero in all cases, but may in fact have an appreciably large amplitude, especially for tachyonic masses in the new regime of interest with small scaling exponent $\alpha$ and large frequency $\nu$.
• Figure 4: Suppression of the overall amplitude of the oscillatory PNG signal in the galaxy power spectrum as captured by $|\Sigma_M^2(\alpha, \nu)|$ in \ref{['eq:Pg']} for a halo mass of $M = e13 M_\odot$. For all values of the scaling exponent $\alpha$, $|\Sigma_M^2|$ sharply decreases at large frequencies $\nu$ since we integrate over the highly oscillatory signal. It approaches a constant for small frequencies which is (close to) unity for (around) $\alpha = 0$, as expected, but is $O(100)$ for $\alpha = 3$ since the integrand in \ref{['eq:sigma2_M_integral']} peaks around the scale of matter-radiation equality and is additionally enhanced by $(q R_M)^{-\alpha} \gg 1$ at that scale. We note that we absorb this suppression factor into the PNG amplitude $f_\mathrm{NL}^{\alpha, \nu}$ for the rest of our discussion, forecasts and data analysis. This is because we are mostly interested in investigating the sensitivity to a potential signal in this new PNG class and this suppression factor can easily be reinstated to get specific model predictions and results.
• Figure 5: Illustration of the effect of the oscillatory scale-dependent bias on the linear BOSS galaxy power spectrum at $z = 0.35$, with the phase chosen so that $A_\mathrm{sin} = 0$. The top panels display the power spectra $P_g(k)$ for different values of the scaling exponent $\alpha$ and frequency $\nu$, while the bottom panels show the non-Gaussian bias $b_\mathrm{NG}(k)$. We observe how the non-Gaussian signature moves from the largest to the smallest scales as we increase the scaling exponent $\alpha$ from the leftmost to the rightmost panels. (Note that the PNG amplitude $f_\mathrm{NL}^{\alpha, \nu}$ also increases between the panels and we have already absorbed the suppression factor $|\Sigma_M^2|$ into its normalization as explained in the main text.) We can also see how the logarithmic oscillations with frequency $\nu$ are modulated by the power-law contribution, which is governed by $\alpha$, and that we would only measure part of an oscillation for small frequencies given the limited range of wavenumbers (see main text).