Cosmology with Phase Statistics: Parameter Forecasts and Detectability of BAO

We consider an alternative to conventional three-point statistics such as the bispectrum, which is purely based on the Fourier phases of the density field: the line correlation function. This statistic directly probes the non-linear clustering regime and contains information highly complementary to that contained in the power spectrum. In this work, we determine, for the first time, its potential to constrain cosmological parameters and detect baryon acoustic oscillations (hereafter BAOs). We show how to compute the line correlation function for a discrete sampled set of tracers that follow a local Lagrangian biasing scheme and demonstrate how it breaks the degeneracy between the amplitude of density fluctuations and the bias parameters of the model. We then derive analytic expressions for its covariance and show that it can be written as a sum of a Gaussian piece plus non-Gaussian corrections. We compare our predictions with a large ensemble of $N$-body simulations and confirm that BAOs do indeed modulate the signal of the line correlation function for scales $50$-$100\,h^{-1}\,\mathrm{Mpc}$, and that the characteristic S-shape feature would be detectable in upcoming Stage IV surveys at the level of $\sim4\sigma$. We then focus on the cosmological information content and compute Fisher forecasts for an idealized Stage III galaxy redshift survey of volume $V\sim 10\,h^{-3}\,\mathrm{Gpc}^3$ and out to $z=1$. We show that, combining the line correlation function with the galaxy power spectrum and a Planck-like microwave background survey, yields improvements up to a factor of two for parameters such as $\sigma_8$, $b_1$ and $b_2$, compared to using only the two-point information alone.