Escaping the Vacuum Zero-Point Energy Dilemma An Attempt to Locate the Origin of Dark Energy

Starting from three basic hypotheses, this paper rearranges the source structureon the right-hand side of the Einstein equation. The starting point is the Einstein equation without a cosmological term. The three basic hypotheses are:the matter energy-momentum tensor, including vacuum energy, is on equal footingwith its gravitational-field energy-momentum tensor, and both enter the right-handside of the equation as gravitational sources, yielding the equal-footing Einsteinfield equation, hereafter the equal-footing equation; the vacuum zero-point energymomentum tensor and the homogeneous gravitational-field energy-momentum tensor satisfy the Lorentz invariance constraint (the former being an extension of abasic assumption of quantum field theory); and the cosmic zero-energy hypothesisis inherited.It follows that the expectation value of the sum of the vacuum zero-point energymomentum tensor and its gravitational-field energy-momentum tensor is zero. Themagnitude disaster, the fine-tuning problem, and the dynamic-observation challengebrought by treating the vacuum zero-point energy as dark energy are all resolved.The identity problem of the vacuum zero-point energy in the Einstein equation isalso resolved: it enters the equation not as a cosmological term but as a gravitationalsource term. The gravitational field of the large-scale homogeneous distribution ofcosmic matter has an energy-momentum tensor proportional to the metric, withnegative energy density and w = −1, and constitutes the cosmological term thatacts as dark energy. The equal-footing equation naturally yields the form with aneffective cosmological term:Gµν +Λg(t)gµν = 8πGT(m)µν , where Λg(t) = 8πGρDE(t).The cosmological term is not an ad hoc input but a natural output of the equalfooting equation in the large-scale gravitational background of the Universe. Itevolves with time and is structurally compatible with current observational hintsfor dynamic dark energy. On local scales, the matter distribution is more concentrated than its gravitational-field distribution; compared with each other, thegravitational-field contribution tends to zero, and the equal-footing equation returnsto the original Einstein equation without a cosmological term.