The light that we observe that is emitted by far away galaxies travels towards the Earth not through straight trajectories, but rather through perturbed ("curvy") ones as the photons' paths are bent by the gravitational lensing effect caused by the matter that exists between the Earth and the galaxies. This induces tiny distortions in the shapes of the observed galaxies, which can appear more elliptical than what they truly are. Measurements of these distortions are called cosmic shear data, and are one of the most powerful ways to probe the large-scale matter distribution in the Universe.

Like in any analysis of cosmological data, in cosmic shear too one must carefully estimate the statistical errors of the measured quantities. In many areas of Physics this estimation can be done by repeating an experiment over and over again, and then take the statistical error to be the variance (or spread) between the outcome of the different experiments. In cosmology, however, we cannot afford the same luxury since we have only one Universe at our disposal, i.e., one ''experiment''. One way to go about this problem is to run many $N$-body numerical simulations of structure formation in the Universe, and evaluate the variance across this ensemble of simulations. This works in principle, but it is very computationally demanding. In fact, the number of simulations that is thought to be necessary for the analyses of future cosmic shear data makes this method computationally prohibitive, even with current state-of-the-art supercomputing facilities.

Another way to tackle the problem is to calculate directly the expected variance analytically. A problem that existed here was that the ingredients that enter the calculation were not all very well understood theoretically and could not be calculated accurately. This is the problem that I have tackled in a series of papers [8-11] for the most important cosmic shear statistic called the power spectrum. The statistical errors in cosmic shear analyses are encapsulated in a mathematical quantity called the ''covariance matrix'', which has three main physical contributions:

\begin{equation}

\rm{Covariance} = \rm{G} + \rm{SSC} + \rm{cNG},

\end{equation}

- The Gaussian term (G) is a term that is relatively easy to evaluate, and this has been known for a long time.
- I have shown in [11] that the super-sample covariance (SSC) term can be evaluated completely and accurately using a formalism called ''Response Approach to Perturbation Theory'' that I have developed in [9].
- The connected non-Gaussian (cNG) term is the hardest to evaluate completely, but I have shown using the response approach in [10] that it is possible to evaluate at least the majority of its contribution.

These works culminated in the analysis presented in [8], where I have carried out a simulated cosmic shear likelihood analysis of the upcoming Euclid and Vera Rubin surveys to quantify how accurately do we need to know the cNG term. The main finding from this work is that dropping the cNG contribution from the analysis has less than a 6$\%$ impact on the error bar of the cosmological parameters; see Fig.1. This meets already very comfortably the target accuracy requirements for these surveys, and it is quite an aggressive approach in that we completely neglected the cNG contribution: accounting for it with existing analytical calculations, even if approximate, will result in an even better performance. Our work in [8] demonstrated, for the first time, that analytical approaches to the covariance are sufficient and efficient enough for future cosmic shear surveys.

[1] A. Barreira, D. Nelson, A. Pillepich, V. Springel, F. Schmidt, R. Pakmor, L. Hernquist, and M. Vogelsberger, Mon. Not. R. Astron. Soc.488, 2079 (2019), arXiv:1904.02070 [astro-ph.CO].

[2] A. Barreira, G. Cabass, D. Nelson, and F. Schmidt, JCAP, 005 (2020), arXiv:1907.04317 [astro-ph.CO].

[3] A. Barreira, G. Cabass, F. Schmidt, A. Pillepich, and D. Nelson, JCAP, 013 (2020), arXiv:2006.09368 [astro-ph.CO].

[4] A. Halder and A. Barreira, arXiv e-prints, arXiv:2201.05607 (2022), arXiv:2201.05607 [astro-ph.CO].

[5] A. Barreira, G. Cabass, K. D. Lozanov, and F. Schmidt, JCAP, 049 (2020), arXiv:2002.12931 [astro-ph.CO].

[6] A. Barreira, JCAP, 031 (2020), arXiv:2009.06622 [astro-ph.CO].

[7] R. Voivodic and A. Barreira, arXiv e-prints , arXiv:2012.04637 (2020), arXiv:2012.04637 [astro-ph.CO].

[8] A. Barreira, E. Krause, and F. Schmidt, Journal of Cosmology and Astro-Particle Physics, 053 (2018), arXiv:1807.04266 [astroph.

CO].

[9] A. Barreira and F. Schmidt, JCAP, 6, 053 (2017), arXiv:1703.09212.

[10] A. Barreira and F. Schmidt, JCAP, 11, 051 (2017), arXiv:1705.01092.

[11] A. Barreira, E. Krause, and F. Schmidt, JCAP, 6, 015 (2018), arXiv:1711.07467.

[12] T. Baker, A. Barreira, H. Desmond, P. Ferreira, B. Jain, K. Koyama, B. Li, L. Lombriser, A. Nicola, J. Sakstein, and F. Schmidt, arXiv

e-prints (2019), arXiv:1908.03430 [astro-ph.CO].

[13] A. Barreira, B. Li, W. A. Hellwing, C. M. Baugh, and S. Pascoli, JCAP, 027 (2013), arXiv:1306.3219 [astro-ph.CO].

[14] A. Barreira, M. Cautun, B. Li, C. M. Baugh, and S. Pascoli, JCAP, 028 (2015), arXiv:1505.05809 [astro-ph.CO].

[15] A. Barreira, A. G. Sánchez, and F. Schmidt, Phys. Rev. D, 94, 084022 (2016), arXiv:1605.03965 [astro-ph.CO].

[16] J. Renk, M. Zumalacárregui, F. Montanari, and A. Barreira, JCAP, 020 (2017), arXiv:1707.02263 [astro-ph.CO].

[17] A. Barreira, B. Li, A. Sanchez, C. M. Baugh, and S. Pascoli, Phys. Rev. D, 87, 103511 (2013), arXiv:1302.6241 [astro-ph.CO].

[18] A. Barreira, B. Li, C. M. Baugh, and S. Pascoli, JCAP, 059 (2014), arXiv:1406.0485 [astro-ph.CO].