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In the present work, we study the birth of a homogeneous and isotropicFriedmann Lemaitre Robertson Walker (FLRW) cosmological model, consideringHorava Lifshitz (HL) as the gravitational theory. The matter content of themodel is a radiation perfect fluid. In order to study the birth of the universein the present model, we consider the quantum cosmology mechanism of creationfrom nothing. In that mechanism, the universe appears after the wavefunctionassociated to that universe tunnels through a potential barrier. We startedstudying the classical model. We draw the phase portrait of the model andidentify qualitatively all types of dynamical behaviors associated to it. Then,we write the Hamiltonian of the model and apply the Dirac quantizationprocedure to quantize a constrained theory. We find the appropriateWheeler-DeWitt equation and solve it using the Wentzel Kramers Brillouin (WKB)approximation. Using the WKB solution, to the Wheeler DeWitt equation, wecompute the tunneling probabilities for the birth of that universe (TPWKB).Since the WKB wavefunction depends on the radiation energy (E) and the freeparameters coming from the HL theory (gc, gr, gs, gLambda), we compute thebehavior of TPWKB as a function of E and all the HL parameters gc, gr, gs,gLambda.

Tunneling probability for the birth of an universe with radiation in Horava-Lifshitz theory