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arXiv · 2404.06584

Relativistic Khronon Theory in agreement with Modified Newtonian Dynamics and Large-Scale Cosmology

Luc Blanchet·Constantinos Skordis
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Abstract

We propose an extension of General Relativity (GR) based on a space-time foliation by three-dimensional space-like hypersurfaces labeled by the Khronon scalar field $\tau$. We show that this theory (i) leads to modified Newtonian dynamics (MOND) at galactic scales for stationary systems; (ii) recovers GR plus a cosmological constant in the strong field regime; (iii) is in agreement with the standard cosmological model and the observed cosmic microwave background anisotropies at linear cosmological scales, where the theory reduces to a subset of the generalized dark matter (GDM) model. We compute the second order action on a Minkowski background and show that it contains the usual tensor modes of GR and a scalar degree of freedom with dispersion relation $\omega=0$. We find that the deconstrained Hamiltonian is bounded from below for wavenumbers larger than $\sim 10^{-31}\,\text{eV}$ and unbounded for smaller wavenumbers.

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Luc Blanchet, Constantinos Skordis. 2024-04-09. Relativistic Khronon Theory in agreement with Modified Newtonian Dynamics and Large-Scale Cosmology. https://doi.org/10.1088/1475-7516%2F2024%2F11%2F040

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