Dark Energy and Dark Matter in General Relativity With Local Scale Invariance

Abstract

We consider a generalization of Einstein's general theory of relativity such that it respects local scale invariance. This requires the introduction of a scalar and a vector field in the action. We show that the theory naturally displays both dark energy and dark matter. We solve the resulting equations of motion assuming an FRW metric.The solutions are found to be almost identical to those corresponding to the standard ΛCDM model.

Local Scale Invariance and Inflation

“…Earlier, this model has been explored in the context to explain current acceleration of the universe [10][11][12]. This model does not have any dimensionful parameter.…”

“…Some works related to removal of anomaly in conformal invariance and applications of conformal invariance have been discussed in Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

“…In Ref. [11], the background value of temporal part of vector meson S t (= S t ) is taken to be zero as a solution. Under this condition, one obtains the de-Sitter solution if we consider spatial part S i = 0.…”

“…We can also consider S i = 0. The very small background value of S i (= S i ) in early universe epoch as an initial condition [11] explains the cold dark matter of universe today. In Ref.…”

“…In Ref. [11], it is also argued that S i oscillates over time, however, averaging over time, the energy density corresponding to S i drops as 1/a 3 and corresponding pressure is approximately zero. Thus, S i may be a candidate for cold dark matter of the current universe.…”