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To justify the twenty years old distant Ia Supernova observations whichrevealed to us that our universe is experiencing a late time cosmicacceleration, propositions of existence of exotic fluids inside our universeare made. These fluids are assumed to occupy homogeneously the whole space ofthe universe and to exert negative pressure from inside such that the late timeaccelerated expansion is caused. Among the different suggested models of suchexotic matters/ energy popularly coined as dark matter / dark energy, a wellknown and popular process is "introduction of redshift parametrization" of theequation of state parameter of these fluids. We, very particularly, take theparametrization proposed by Barboza and Alcaniz along with the cosmologicalconstant. We use thirty nine data points for Hubble's parameter calculated fordifferent redshifts and try to constrain the dark energy equation of stateparameters for Barboza Alcaniz modelling. We then constrain the dark energyparametrization parameters in the background of Einstein's general relativity,loop quantum gravity and Horava Lifshitz gravity one after another. We find the1$\sigma$, 2$\sigma$ and 3$\sigma$ confidence contours for all these cases andcompare them with each other. We try to speculate which gravity is constrainingthe parameters most and which one is letting the parameters to stay within alarger domain. We tally our results of 557 points Union2 Sample and againcompare them for different gravity theories.

Barboza-Alcaniz Equation of State Parametrization : Constraining the Parameters in Different Gravity Theories