Quintessence would be a new fundamental force, since it describes distinct gravitational effects from those mediated by the metric-though it wouldn't be the fifth force, but the sixth; the force mediated by the Higgs boson is a new fundamental force, already.

However quintessence and gravity in the form of metric fluctuations are classical notions and it isn't known how to describe the quantum fluctuations of spacetime geometry.

Indeed the metric variations described by metric gravity and the variations described by dark energy are, also, classical. While there has been talk about ``quantum foam'', what isn't known, for the moment, is a consistent quantitative description.

The value of the cosmological constant doesn't depend on the frame of reference. So it doesn't make sense claiming that it does. What Colin et al. want to claim is that its value-as deduced from supernovae measurements-is, in fact, consistent with zero, since they claim that the non-zero value can be accounted for by local effects. However, even were these statements correct, there are, by now, other ways of deducing that the cosmological constant is non-zero, e.g. http://pdg.lbl.gov/2019/reviews/rpp2018-rev-dark-energy.pdf

Can Quintessence be replaced by force of D-Gravity, a fifth fundamental force?

IMO we seem to be always looking for more complicated answers than simple ones. The proposal of Quintessence is based upon the dark energy proposal. Dark Energy is based upon up to a 10% increase in calculated distances up to a redshift of z=.6. The error then reduces to zero at a redshift of z=1.3, where it then starts decreasing in calculated distances over brightness determinations and type 1a supernova thereafter.

Instead of dark energy where 68% percent of the universe is made up of an unknown force, the extremely simple answer is that the Hubble distance formula is somewhat inaccurate at greater distances. In a related paper I and an associate proposed a different distance formula that matches type 1a supernova observations without the existence of dark energy or an expanding universe.

Article An Alternative Universe-Scale Analytic Metrology and Related...

Sir! First of all thank u very much for all of your time and such informing answers. I tried to follow all the papers you referred as far as possible.

And what i think is also in yours side. According to the theory of D-Gravity ,which is incomplete and i'm still working on it, also denies the existence of Dark Energy. And other thing is that Higgs field can be a force but not sure to be a fundamental force. The fact that cosmological constant is not actually constant(i.e.varying) allow us to think of a 5th fundamental force which can explain the need for modification in General Theory of Relativity. From modification, i mean the explanation of variation and fluctuation of space-time curvature as we go from center of Universe to the edge and explanation of space-time coincidence at the center of Black Hole. Now, when we talk about the Hubble parameter which predict greater than speed of light gained by objects near the edge of Universe, the theory of D-Gravity predicts just opposite and space-time coincidence comes into play. This also deny the Big Crunch Theory and predicts the retardation of expansion at the edge of Universe. So, at the edge of Universe there should be some phenomenon similar to that of the center of black hole. And if we could understand this space-time coincidence at the center of black hole, it may then be possible to correctly simulate or analyse the creation of Universe and also of its end as singularity but not as duality which Big Crunch predicts.