The agent causing this expansion is termed as dark energy and it violates the strong

energy condition. Cosmological observations reveal that our universe is approximately homogeneous and isotropic at large scales [1] described by the standard FRW model.

The Null

Energy Condition (NEC) in the bulk imposes some constraints on the class of non-relativistic field theories dual to the hyperscaling violating backgrounds, namely, that the critical exponents must satisfy [72, 75]

From above, it is clear that the energy density of anisotropic fluids ([p.sub.[phi]] = [p.sub.z] = [p.sub.t] tangential stress) violates the weak

energy condition (WEC) [30].

Secondly, the plot of weak

energy condition (WEC), dominant

energy condition (DEC), and strong

energy condition (SEC) for non-interacting and interacting cases is shown in Figures 7 and 8, respectively.

It possesses negatively large pressure which violates the strong

energy condition (p + 3[rho] < 0, where p and [rho] are pressure and energy density, respectively) but its complete characteristics are still not known.

Abreu and Sasaki [24] studied the effects of null

energy condition (NEC) and weak

energy condition (WEC) with noncommutative wormhole.

Yurtsever, "Wormholes, time machines, and the weak

energy condition," Physical Review Letters, vol.

As ordinary matter, DM satisfies the strong

energy condition. Dark energy, instead, is more peculiar still, given that it does not share the clustering properties of ordinary matter or DM, as it violates the strong

energy condition.

The energy density of null dust satisfies the null

energy condition (NEC).

The time machine spacetime discussed in [35-39] violated the weak

energy condition (WEC) and the strong

energy condition (SEC) is violated in [40-43].

Moreover, since [rho]([phi]) = -(3/4)[[beta].sup.2](t) is negative for real nonzero values of [beta](t), the weak

energy condition is not respected by a real nonzero [[phi].sub.[mu]].

Soma, "Lorentzian wormholes in higher-derivative gravity and the weak

energy condition," Physical Review D, vol.