Abstract
Abstract We modify Einstein’s theory of gravity, isolating the conformal degree of freedom in a covariant way. This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first derivatives. The resulting equations of motion split into a traceless equation obtained through variation with respect to the auxiliary metric and an additional differential equation for the trace part. As a result the conformal degree of freedom becomes dynamical even in the absence of matter. We show that this extra degree of freedom can mimic cold dark matter.
Highlights
The resulting equations of motion split into a traceless equation obtained through variation with respect to the auxiliary metric and an additional differential equation for the trace part
As a result the conformal degree of freedom becomes dynamical even in the absence of matter. We show that this extra degree of freedom can mimic cold dark matter
Consider a physical metric gμν to be a function of a scalar field φ and an auxiliary metric gμν, defined by gμν = gαβ∂αφ∂βφ gμν ≡ P gμν
Summary
This is done by introducing a physical metric defined in terms of an auxiliary metric and a scalar field appearing through its first derivatives. As a result the conformal degree of freedom becomes dynamical even in the absence of matter. Consider a physical metric gμν to be a function of a scalar field φ and an auxiliary metric gμν, defined by gμν = gαβ∂αφ∂βφ gμν ≡ P gμν .
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