### Abstract

Cosmic inﬂation is a paradigm that successfully seeds large scale structure in a big bang cosmology whilst causing the Universe to be statistically isotropic. Inﬂation occurred at energy scales that are too high to be accessible with accelerator experiments, thus we have to rely entirely on cosmological observations to rule out classes of inﬂationary models and get insight into the physics of the early Universe. One way to distinguish these models is by measuring how close their predicted primordial ﬂuctuations are to being Gaussian distributed, described at ﬁrst order by the parameter f_{NL}. Local primordial non-Gaussianity alters the biasing law between dark- matter halos and the underlying massdensity ﬁeld at the largest scales [1,2]. Currently, the tightest constraints on the local f

_{NL}= 0.8±5.0 come from the cosmic microwave background experiment Planck [3]. Next generation ground-based experiments will be limited by cosmic variance, and we need a diﬀerent approach to independently conﬁrm these results, and to further narrow down our constraints on the inﬂationary epoch. Galaxy clustering studies so far could not compete with the precision of the f

_{NL}results from the microwave background, but upcoming galaxy surveys will come close to independently conﬁrm the Planck results. Combining future galaxy clustering and Cosmic Microwave Background data will improve f

_{NL}constraints such that they will provide physically interesting results.

This will only be possible if some challenges can be addressed properly, of which two are addressed in this thesis. The ﬁrst problem is that fNL measurements take place at the very largest scales, which are close to maximum scale ﬁtting into the survey volume. This means that we have to rely on a low number of modes and we therefore cannot assume the likelihood of our power spectrum measurement to be Gaussian. The Inverse Cubic Normal distribution is a very good approximation to what we expect for the true likelihood of the Power Spectrum assuming an almost Gaussian galaxy density ﬁeld. On top of that, it has the advantage of absorbing the model dependence of the Power Spectrum covariance matrix into the functional form of the posterior distribution function. Thus, one does not have to run simulations to estimate the covariance matrix for each model to be tested [4].

The other problem addressed in this thesis is that galaxy surveys are plagued by systematic contaminants, especially the eﬀect of foreground stars, at the scales interesting for f

_{NL}measurements. I discuss two contaminant mitigation techniques, mode deprojection and mode subtraction. Mode deprojection needs a covariance based estimator for the Power Spectrum, such as the Quadratic Maximum Likelihood estimator. This however, is computationally infeasible for a 3-dimensional clustering analysis. Applying mode subtraction na¨ıvely using the simpler Feldman-Kaiser-Peacock Power Spectrum estimator leads to a biased measurement. I introduce an additional factor that unbiases this estimate and show that mode deprojection and subtraction are then in fact identical. This allows a fast error mitigation and Power Spectrum estimation trading against a small amount of information loss [5].

This technique is tested using the twelfth data release of the Baryon Acoustic Oscillation Survey. Previously, even after accounting for the stellar contamination, the power spectrum of an f

_{NL }analysis using data of the ninth data release of the Baryon Oscillation Spectroscopic Survey [6] did not agree well with the model for any value f

_{NL}. Interestingly, even using the new methods, and performing a more careful analysis, the resulting Power Spectrum agrees with the Power Spectrum obtained by applying the methods of [6]. This means that there is still some unexplained discrepancy between our measurement and our model. I therefore discuss other sources of systematic data contamination.

Date of Award | May 2018 |
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Original language | English |

Supervisor | Will Percival (Supervisor), Lado Samushia (Supervisor) & David Bacon (Supervisor) |