Compelling evidence shows that about 80% of the matter in the Universe exists in the form of non-baryonic, electrically neutral, weakly interacting particles from which we can only see their gravitational effects. The nature of this new kind of matter, the so-called Dark Matter (DM), has been puzzling particle physicists, astrophysicists and cosmologists in the last decades.
According to the importance of the DM problem, an astonishing number of experiments are presently dedicating extensive efforts to the investigation of the constituents of DM: searching for DM annihilation products with ground-based telescopes and satellites, looking for DM-baryon collisions in underground detectors, and seeking missing energy from undetectable DM particles produced in colliders. In the last years, these experiments have produced exciting results: among others, the possible direct detection of low-mass WIMPs in DAMA/LIBRA, CoGeNT, CRESST and CDMS, and the excesses measured in indirect detection experiments such as PAMELA or Fermi. The tension with the null results of other experiments stresses the importance of providing complementary approaches, in order to solve the present controversies and help discovering the nature of DM.
Stars provide powerful constraints to the existence of new particles and tests to fundamental theories. The large abundance of WIMP DM particles in the Galactic halo leads to huge quantities of gravitationally captured DM particles inside stars. Concerning the Sun, the additional cooling mechanism provided by the WIMPs leads to a reduction of the solar neutrino fluxes and modifications in the low-degree frequency spacings of the solar oscillations which depend on the DM characteristics. Other stars may also be strongly influenced. In particular, it has been shown that neutron stars and white dwarfs also provide competitive constraints to the DM parameters.
The accumulation of particular types of DM particles inside stars produces modifications in the stellar structure that can be detected by the analysis of the stellar oscillations. This constitutes an innovative and inexpensive approach to efficiently constrain the properties of DM. Solar-like oscillations have already been detected in a hundred of main-sequence and red giant stars by the CoRoT and Kepler asteroseismic missions, including gravity modes probing the core of giant stars. Publicly available photometric data of open, nuclear and globular clusters provides further possibilities.
In the case of the Milky Way's Galactic center, an environment where extremely high DM densities are expected, the role of DM seems to be crucial to understand the properties of the stars. It has been shown that the accumulation of DM particles and their self-annihilation (DM burning) dramatically changes the properties of white dwarfs, neutron stars and main-sequence stars. In addition, the presence of a central massive black hole strongly influences the dynamics, formation history and evolution of the stellar populations in the Galactic center. On the other hand, it has to be noted that the stars observed in the inner parsec of our Galaxy have puzzling characteristics, leading to two unsolved problems: the so-called "paradox of youth" (apparently young stars observed in a region where recent star formation seems impossible) and the "conundrum of old age" (the dearth of late-type stars in the central few arcseconds, meaning that our Galactic center could have a stellar core instead of a stellar cusp, as believed for some decades). A thorough modelling including the mutual influence of the central massive black hole, the dense dark matter halo and the stars may help to shed some light to the complex processes in the centers of galaxies. The gravitational waves emmitted by compact stars inspiraling the central MBH may provide further precious information.
Similar strategies can be applied in other fields of fundamental physics. For instance, solar neutrino measurements and helioseismic data constrain some alternative theories of gravity such as Eddington-inspired Born-Infeld gravity.