Scale-Dependent Galaxy Bias from Massive Particles with Spin during Inflation

TL;DR

This work investigates how upcoming galaxy surveys can constrain the presence of massive particles with spin during inflation by their imprint on primordial non-Gaussianity and the resulting scale-dependent bias in the galaxy power spectrum. It builds a framework linking the squeezed-limit bispectrum, including spins $s=0,1,2$, to a bias expansion with new operators, and uses a 1-loop power-spectrum model with redshift-space distortions and Alcock-Paczynski effects. The authors perform Fisher forecasts for EUCLID and LSST, showing that a two-tracer LSST analysis can dramatically improve constraints on the non-Gaussian amplitudes $C_s$ and the masses $(m_s/H)^2$, especially for spins $0$ and $1$, while spin-2 remains challenging from the power spectrum alone. Gravitational loop corrections modestly affect the results (by factors up to ~1.5–2), and the study highlights the potential gains from combining power-spectrum and bispectrum information in future work. Overall, the paper advances a concrete pathway to probing the particle content of inflation through large-scale structure, with clear guidance on survey design and analysis strategies to maximize sensitivity to spin-dependent PNG signatures.

Abstract

The presence of additional particles during inflation leads to non-Gaussianity in late-time correlators of primordial curvature perturbations. The shape and amplitude of this signal depend on the mass and spin of the extra particles. Constraints on this distinct form of primordial non-Gaussianity, therefore, provide a wealth of information on the particle content during inflation. We investigate the potential of upcoming galaxy surveys in constraining such a signature through its impact on the observed galaxy power spectrum. Primordial non-Gaussianity of various shapes induces a scale-dependent bias on tracers of large-scale structure, such as galaxies. Using this signature we obtain constraints on massive particles during inflation, which can have non-zero spins. In particular, we show that the prospects for constraining particles with spins 0 and 1 are promising, while constraining particles with spin 2 from power spectrum alone seems challenging. We show that the multi-tracer technique can significantly improve the constraints from the power spectrum by at least an order of magnitude. Furthermore, we analyze the effect of non-linearities due to gravitational evolution on the forecasted constraints on the masses of the extra particles and the amplitudes of the imprinted non-Gaussian signal. We find that gravitational evolution affects the constraints by less than a factor of 2.

Figures (8)

• Figure 1: The Gaussian-loop contributions to the galaxy power spectrum as well as contributions from PNG due to additional particles during inflation, at $z=1.5$. "L" refers to the linear power spectrum $P_g^L(k,z) = b_1^2 P_0(k,z)$. The lines labeled ${\rm NG}_{si}$ are contributions due to additional fields with spins 0,1 and 2, while ${\rm NG}_{\rm loc}$ is the contribution from local shape bispectrum, shown for comparison. The other lines correspond to terms in Eq. \ref{['eq:full_1loop_G']} labeled by the bias combinations in front of each term. The solid (dashed) lines indicate positive (negative) values. The value of biases and cosmological parameters are set to the fiducial values described in Section \ref{['sec:Fisher']}. For the non-Gaussian contributions we take $C_s = 1$, $(m_s/H)^2 = 3$ and $f_{\rm NL}^{\rm loc} =1$.
• Figure 1: Constraints on local-shape PNG with the upcoming EUCLID and LSST surveys, marginalizing over the following parameters: ${\boldsymbol\lambda} = \left[{\rm ln} (10^{10}A_s), n_s, H_0,\Omega_{\rm cdm},\Omega_b, \sigma_{{\rm FOG},0}, b_1\right]$. The fiducial value on the amplitude of PNG is taken to be $f_{\rm NL}^{\rm loc} =1$. The numbers in parenthesis are the constraints when using the full 1-loop power spectrum.
• Figure 2: The scale-dependent bias due to additional particles with spins 0, 1 and 2 as a function of $k$, at $z=1.5$. The solid (dashed) lines indicate positive (negative) values. The value of biases and cosmological parameters are set to the fiducial values described in Section \ref{['sec:Fisher']}. For the non-Gaussian contributions we take $C_s = 1$, $(m_s/H)^2 = 3$ and $f_{\rm NL}^{\rm loc} =1$.
• Figure 2: Constraints on amplitudes and masses of the lowest-spin particles (spins $0,1,2$) when $c_\pi = 1$. The 1-loop Gaussian contributions to the galaxy power spectrum are neglected. The fiducial values for the amplitudes are taken to be $C_s = 1$, while for the masses we take $(m_s/H)^2 = 3$. Each spin is considered separately and the constraints are obtained marginalizing over the rest of the parameters, as stated in the text.
• Figure 3: Same as Table \ref{['tab:onlyone_cpi1_tree']}, but for $c_\pi \ll 1$.