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The Mimetic gravity cocktail: Is it healthy and tasty?

KMI Theory Seminar
2018-10-05 16:00
Purnendu Karmakar
KMI Science Symposia (ES635)

The `mimetic dark matter’ model was proposed as a modification of General Relativity (GR) for mimicking the cold dark matter component by performing a non-invertible conformal transformation of the GR metric with a re-scaling parameter being a kinetic term for a (mimetic) scalar field. Later on, such a non-invertible transformation has been applied to wide classes of models including general scalar-tensor theories, f(R) gravity, vector-tensor theories, etc., resulting in mimetic versions of these models. It can source the background evolution of the universe by mimicking any perfect fluid, including radiation, dark matter, and dark energy. From the linear scalar perturbations around a flat Friedmann-Lema^{i}tre-Robertson-Walker (FLRW) background in mimetic Horndeski gravity, we obtain a suitable form of the Poisson equation, which allows us to calculate the effective gravitational constant felt by `ordinary’ matter. By restricting to a minimally coupled model, such an effective gravitational constant is equivalent to that obtained within General Relativity, with cold dark matter plus a perfect fluid dark energy component, with vanishing sound speed. Assuming, further, a $Lambda$CDM background, the effective gravitational constant cannot be distinguished from that of the standard $Lambda$CDM model, at linear order. For the full non-minimally coupled mimetic gravity model we obtain a non-vanishing gravitational slip and an effective gravitational constant which always differs from that of standard $Lambda$CDM. It looks quite promising so far. But is this mimetic dark gravity is as good as the dark matter during the structure formation? Is the mimetic gravity fully healthy? We perform the full non-linear Hamiltonian analysis of several mimetic gravity models. I shall discuss the construction of mimetic gravity, a status report on the mimetic gravity, and some recent exciting results.