Modified scaling in k-essence model in interacting dark energy–dark matter scenario

It has been shown by Scherrer (Phys Rev Lett 93:011301, 2004. https://doi.org/10.1103/PhysRevLett.93.011301 . arXiv:astro-ph/0402316 [astro-ph]) and de Putter Linder (Astropart Phys 28:263–272, 2007. https://doi.org/10.1016/j.astropartphys.2007.05.011 arXiv:0705.0400 that, when dynamics of dark energy is driven a homogeneous k-essence scalar field $$\phi$$ , with Lagrangian the form $$L = V_0F(X)$$ constant potential $$V_0$$ $$X \frac{{1}}{{2}}\nabla ^\mu \phi \nabla _\mu \frac{{1}}{{2}}{\dot{\phi }}^2$$ one obtains scaling relation $$X(\mathrm{d}F/\mathrm{d}X)^2 Ca^{-6}$$ where C FRW scale factor universe. The separate conservation in sector constancy are instrumental obtaining such scaling. In this paper, we have even considering time-dependent interactions between matter, may lead to modified We obtained for particular class parametrisation source term occurring continuity equation matter interacting scenario. used inputs from JLA analysis luminosity distance redshift data Supernova Ia observations, obtain