Abstract. I’ll show the analysis we perform on gravitational microlensing signatures and how we estimate gravitational microlensing parameters to obtain information about several components of the dark matter in our galaxy like free-floating planets, brown dwarfs, primordial black holes, making use of actual and future space-based telescopes: Euclid, THESEUS, Gaia, Roman, etc.

As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform  functions on the eight-dimensional  phase space (x,k) into Hilbertian operators. The x=(x^{\mu}) are space-time variables and the k=(k^{\mu}) are their conjugate wave vector-frequency variables. The procedure is first applied to the variables (x,k) and produces canonically conjugate essentially  self-adjoint operators. It is next applied to the metric field g_{\mu\nu}(x) of general relativity and yields regularised  semi-classical phase space portraits of it.

Astrophysical observations are largely based on electromagnetic signals still read with the Maxwellian massless and linear theory, possibly an approximation of a larger theory, as Newtonian gravity is for Einsteinian gravity in weak fields. Photons are the sole free massless particles in the Standard-Model (SM). Apart from massive formalisms (de Broglie-Proca, Bopp, Stueckelberg and others), the SM Extension dresses the photon of a mass dependent from the Lorentz-Poincaré symmetry violation.

Gravitational wave (GW) standard sirens are well-established probes with which one can measure cosmological parameters, and are complementary to other probes like the cosmic microwave background or supernovae standard candles. I will focus on dark GW sirens, specifically binary black holes (BBHs) for which there is only GW data. Relying on the assumption of a source mass model for the BBH distribution, we consider four models that are representative of the BBH population observed so far.