International Conference on Research in Natural and Engineering Sciences (ICRNES 2020), Konya, Turkey, 14 - 15 November 2020, pp.175-181
In this study, we aim to examine cylindrically symmetric string cloud with quark matter in unimodular f(R) gravity. f(R) denotes a general function of Ricci scalar in Einstein-Hilbert action. Lagrange multiplier imposes unimodularity in action integral. Determinant of the spacetime metric tensor is set to a constant in unimodular gravitational theories. We use unimodular and static cylindrically symmetric spacetime. Unimodular form of the spacetime is considered an appropriate coordinate transformation. String cloud is a particle connected cosmic string which is one-dimensional topological defect in early universe. Components of the energy momentum tensor are obtained. Field equations are written down. Their solutions for given matter and the spacetime are found. By using an ansatz, arctangential f(R) function is achieved. Graphics of the string tension density and total energy density of string cloud are depicted with respect to radial coordinate (r). It is found that string tension density has a singularity at r = 0. Quark matter density approaches to bag constant (vacuum energy that is surrounding the quark) while radial coordinate goes to infinity. Total energy density becomes zero at r = 0 and r → +∞. Also, it is determined maximum point of total energy density. We get Lagrange multiplier by using the trace of the field equations. Obtained results interpreted by using f(R) models, boundary conditions and matter properties. We show that arctangential f(R) models can be applied in unimodular f(R) gravity. In addition, we concluded that string cloud consisting of quark matter added cosmic string can be exist in unimodular f(R) gravity context.