Tachyonic Field Coupled with Global Monopole

As the early universe expanded, phase transitions occurred which resulted in the formation of different types of topological defects. Specifically, the self-coupling scalar field triplet \(\phi ^{a}\) ${\varphi }^a$ was responsible for the creation of global monopoles, which are massive objects that arise during these phase transitions. The initial global symmetry of O(3) undergoes a process of spontaneous breaking, resulting in U(1) symmetry. In this paper we describe a model of global monopole consisting of the Higgs triplet of scalar fields with Tachyonic fluid described by the relativistic Lagrangian \(\mathscr {L}_{Tach}=-V(\phi ^{a})\sqrt{1+g^{\mu \nu }\partial _{\mu }\phi ^{a}\partial _{\nu }\phi ^{a}}\) ${\mathcal{L}}_{\mathit{Tach}}=-V({\varphi }^a)\sqrt{1+g^{\mu \nu }{\partial }_{\mu }{\varphi }^a{\partial }_{\nu }{\varphi }^a}$ . In the weak field approximation, we were able to discover the solution for the scalar field and space-time produced by the global monopole and the Einstein equation that emerges from these scenario exhibits a high degree of non-linearity. Our investigation focused on determining whether the global monopole produces gravitational pull on a test particle that is in motion within its spacetime. Finally, we have calculated the bending of light due to gravitational field of this global monopole.