New analytical tools to constrain fundamental physics with astrophysics

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The current paradigms of cosmology and particle physics continue to be tested at always better precision. Still, many fundamental questions remain about the nature of the actors responsible to create the cosmological structures in the Universe and their primeval conditions. This challenge has been embraced by the observational community and the quality and diversity of data is experiencing a revolution. Relevant for this proposal are the missions that map the distribution of matter in the Universe at cosmological large scales (e.g. DES, BOSS, DESI or EUCLID) and the precise observations of very rapidly rotating neutron stars (pulsars) by radiotelescopes, with SKA representing the next step forward. This proposal aims at the development of analytical tools to turn these high-quality observations into quantitative information about Nature. It is divided into two directions representing the PI expertise:I. Dark matter fields and pulsar timingThere is solid evidence that the Universe contains a new form of matter 5 times more abundant than `standard matter' (matter we can manipulate in the laboratory). This new form of matter has not been detected on Earth, hence the name `dark matter'. To directly probe dark matter, one can turn to the Universe and look for processes where the influence of dark matter in well understood phenomena may take place. A natural candidate in this respect are the radio-pulses emitted by pulsars. The accuracy in the determination of the timing of these signals has no equal in astrophysics and may be modified by the presence of new dynamics. In particular, the pulses bring information about the forces responsible of the motions of their sources, the presence of a medium in which the pulsar moves and the possible existence of a background between the pulsar and Earth. Different dark matter models can influence all these aspects and one may wonder to which extend the current and future data can constrain (or detect!) them. This relatively unexplored use of pulsar timing is the objective of this sub-project. The first proposed direction is to study the influence of ultra-light dark matter in the motion of the pulsars, and its possible detection in current and future data. This model of dark matter is very popular due to its connection to quantum chromodynamics and string theory. We will provide strong constraints (or evidence!) on these models, both in the cases where the dark matter candidate is directly coupled or not directly coupled to standard matter. We will also analyze the effects of light dark matter models in the propagation of the radiowave.II. Analytical techniques for large scale structureDark matter and dark energy are key actors in the distribution of mass at the largest scales in the Universe. Still, the `dark sector' is almost unconstrained. The evolution of the mass distribution at cosmological scales is also sensitive to other fundamental aspects of Nature: the value of the mass of the neutrinos (currently unknown) or the primordial distribution of matter during cosmological inflation leave a trace in these observations. The connection of the observations to the fundamental questions is hindered by the non-linear nature of the process of structure formation. A possible strategy is to resort to computer simulations. These simulations are time consuming, and it is not practical to run simulations to answer all fundamental questions. Fortunately, many models leave signatures at mildly non-linear scales which may be described analytically. The aim of this sub-project is to develop new analytical and efficient techniques to understand the process of structure formation. We will first give a precise prediction of the 3-point function of the distribution of matter at dozens of Mpc. This includes parametrizing the effects of very non-linear processes. This will be done for different models of the Universe. These techniques will be then adapted to analyse current or future data.