The structures we observe today in the Universe like galaxies and clusters of galaxies formed out of tiny density perturbations generated during the primordial Universe, but the origin of these primordial perturbations remains still a fairly unanswered question. The current most appealing explanation is that they were generated by quantum fluctuations during a period of time called inflation, which lasted the first 10^-34 seconds after the Big Bang. There are two competing classes of inflation models: (i) single-field models, in which only a single scalar field particle species is present during inflation, and (ii) multifield models, in which more than a particle type is present during inflation. These two scenarios can be distinguished by looking for two specific attributes of the inital perturbations. The first is primordial non-Gaussianity (PNG), which describes departures from perfect Gaussianity of the spatial distribution of the perturbations. The second are compensated isocurvature perturbations (CIP), which are regions of the early Universe where there are more baryonic, but less dark matter particles. The single-field models predict zero PNG and CIP, and so any detection (regardless of how small) will immediately rule out these models and tell us that the primordial Universe contained many particle species and was not as simple as it could have been.

Galaxies form through gravitational instability out of the initial density perturbations, and so their spatial distribution is sensitive to whether the initial conditions had PNG or CIP. This dependence can be written mathematically as:

\begin{equation}
\delta_g( \,\, \overrightarrow{x} \,\, ) = b_1 \delta_m(\,\, \overrightarrow{x} \,\,) + b_\phi f_{\rm NL} \phi(\,\, \overrightarrow{x} \,\,) + b_\sigma A_{\rm CIP} \sigma(\,\, \overrightarrow{x} \,\,),
\end{equation}

where $\delta_g$ and $\delta_m$ represent the density contrast (that is, the fluctuations around the mean value) of galaxies and total matter in the Universe, $\phi$ is the primordial gravitational potential and $\sigma$ is a CIP perturbation. The parameters $f_{\rm NL}$ and $A_{\rm CIP}$ quantify the amplitude of PNG and CIP, respectively, and are the parameters we wish to constrain. Finally, the parameters $b_1$, $b_\phi$ and $b_\sigma$ are called galaxy bias parameters, and describe the sensitivity of galaxy formation to the presence of mass fluctuations, gravitational potentials and CIP, respectively. Unlike galaxies $\delta_g$, the $\delta_m$, $\phi$ and $\sigma$ are properties of the Universe that are not directly observable (i.e.~they are dark), which is why {\it galaxy bias} is a description of the connection between the visible and the dark Universe.

Naturally, if we wish to use observations of $\delta_g$ to constrain $f_{\rm NL}$ or $A_{\rm CIP}$, then we need to have a good understanding of the bias parameters. This understanding has been the focus of a series of papers of mine [2-6], in which I have used Separate Universe simulations of galaxy formation to predict the bias parameters, and then forecast the constraints that future surveys may be able to place on PNG and CIP. For example, in [3] I found that the expression $b_\phi = 3.372\left(b_1-p\right)$ with $p\approx 0.55$ seems to describe well the relation between the bias parameters of galaxies selected by their stellar mass, but the value of $p$ has some uncertainties and may vary accross different simulations; see Fig. 1. In another paper [6], I wished to determine the precision with which we should determine the value of $p$ in order to get robust constraints on PNG (i.e., on the parameter $f_{\rm NL}$) using galaxy observations. Figure 2 summarizes one of the main findings.In [2, 5], me and my collaborators carried out similar analyses for the case of CIP.

These works are the first examples of concrete steps being taken towards robustly estimating the bias parameters using self-consistently simulated galaxies. For example, all existing observational tests of PNG using galaxies rely on very rough guesses for the bias parameters, which very likely manifest themselves into incorrect determinations of the parameter $f_{\rm NL}$ from the data. To develop a solid understanding of galaxy bias is therefore crucial to the future of primordial Universe physics studies using galaxy surveys.