Euclid preparation: Testing multi-field inflation with galaxy power spectrum and bispectrum

Primordial non-Gaussianity (PNG) is a powerful probe of the origin of cosmic structure. Stage-IV surveys like \Euclid will measure galaxy $2$- and $3$-point clustering at high signal-to-noise, whose exploitation requires robust joint analysis. We prepare for Euclid's spectroscopic sample by validating a redshift-space power-spectrum and bispectrum pipeline (one-loop $P_\ell$, tree-level $B_\ell$) on Euclid-like mocks from Abacus-PNG $N$-body simulations with Gaussian and local-PNG initial conditions, using a halo occupation distribution (HOD) tuned to Euclid Flagship 2. We stress-test analysis choices -- PNG-bias parametrisation, priors, and scale cuts -- and perform null tests without PNG. In a `prior-agnostic setup', detection of the dominant PNG term $\propto f_{\rm NL} \, b_\phi$ in single redshift bins is difficult; nevertheless, the bispectrum provides constraints on other PNG combinations that partially lift degeneracies. We propose a physically motivated prior on $b_\phi$ that yields unbiased $f_{\rm NL}$ while accounting for theory uncertainty, and determine scale cuts that give unbiased $\Lambda$CDM and $f_{\rm NL}$. With $V_{\rm eff}=16\,h^{-3}\,{\rm Gpc}^3$ across four snapshots ($0.8\le z\le1.7$), our likelihood analyses recover $<1\sigma$ bias in $f_{\rm NL}$ and $\Lambda$CDM. At fixed cuts, $B_\ell$ alone reduces $\sigma({f_{\rm NL}})$ by $\sim29$--$46\%$ relative to $P_\ell$, and joint power spectrum-bispectrum analysis tightens a further $\sim8$--$13\%$; the cumulative gain from $z=0.8$ to $1.7$ is $\sim2.3$ for the joint case. The bispectrum quadrupole is key. Our strongest results are at $z=1.7$: $1.9\sigma$ for $f_{\rm NL} \, b_\phi$ (prior-agnostic) and $2.35\sigma$ for $f_{\rm NL}$ (prior-based). Joint analyses thus offer strong prospects for testing multi-field inflation, pending end-to-end validation in the full Euclid geometry with observational systematics.