Influences of dark energy and dark matter on gravitational time advancement

The effect of dark matter/energy on the gravitational time advancement (negative effective time delay) has been investigated considering a few dark energy/matter models including cosmological constant. It is found that dark energy gives only a (positive) gravitational time delay, irrespective of the position of the observer, whereas a pure Schwarzschild geometry leads to a gravitational time advancement when the observer is situated at a relatively stronger gravitational field point in the light trajectory. Consequently, there will be no time advancement effect at all at radial distances where the gravitational field due to dark energy is stronger than the gravitational field of the Schwarzschild geometry.