We propose a relativistic gravitational theory leading to modified Newtonian dynamics, a paradigm that explains the observed universal galactic acceleration scale and related phenomenology. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed cosmic microwave background and matter power spectra on linear cosmological scales. We show that its action expanded to second order is free of ghost instabilities and discuss its possible embedding in a more fundamental theory.

7 pages, 2 figures. We separated the CMB and MPS into two figures, displaying for each one the residuals compared to LCDM. We added more references, additional discussion and details, resulting also to structural rearrangements and shortening of text in accordance with referee comments and to fit within PRL page limits. Content matches published version