Dark matter, the Equivalence Principle and modified gravity

• I discuss to what extent gravitational lensing is evidence of dark matter (DM).
• Einstein Equivalence Principle does not indicate presence of DM in a space-time region.
• Not every metric theory sees lensing as confirming the dark matter hypothesis.
• Details of modified theories of gravity must be taken into account.

Dark matter (DM) is an essential ingredient of the present Standard Cosmological Model, according to which only 5% of the mass/energy content of our universe is made of ordinary matter. In recent times, it has been argued that certain cases of gravitational lensing represent a new type of evidence for the existence of DM. In a recent paper, Peter Kosso attempts to substantiate that claim. His argument is that, although in such cases DM is only detected by its gravitational effects, gravitational lensing is a direct consequence of Einstein's Equivalence Principle (EEP) and therefore the complete gravitational theory is not needed in order to derive such lensing effects. In this paper I critically examine Kosso's argument: I confront the notion of empirical evidence involved in the discussion and argue that EEP does not have enough power by itself to sustain the claim that gravitational lensing in the Bullet Cluster constitutes evidence for the DM Hypothesis. As a consequence of this, it is necessary to examine the details of alternative theories of gravity to decide whether certain empirical situations are indeed evidence for the existence of DM. It may well be correct that gravitational lensing does constitute evidence for the DM Hypothesis—at present it is controversial whether the proposed modifications of gravitation all need DM to account for the phenomenon of gravitational lensing and if so, of which kind—but this will not be a direct consequence of EEP.