Relativistic Khronon Theory in agreement with Modified Newtonian Dynamics and Large-Scale Cosmology
arxiv(2024)
摘要
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 τ. 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
ω=0. We find that the deconstrained Hamiltonian is bounded from below
for wavenumbers larger than ∼ 10^-31 eV and unbounded for
smaller wavenumbers.
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