Nonsingular Phantom Cosmology in Five-Dimensional <i>f</i>(<i>R</i>, <i>T</i>) Gravity

We obtain exact solutions to the field equations for five-dimensional locally rotationally symmetric (LRS) Bianchi type-I spacetime in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> theory of gravity, where specifically, the following three cases are considered: (i) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>μ</mi><mo>(</mo><mi>R</mi><mo>+</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula>, (ii) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>=</mo><mi>R</mi><mi>μ</mi><mo>+</mo><mi>R</mi><mi>T</mi><msup><mi>μ</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, and (iii) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>=</mo><mi>R</mi><mo>+</mo><mi>μ</mi><msup><mi>R</mi><mn>2</mn></msup><mo>+</mo><mi>μ</mi><mi>T</mi></mrow></semantics></math></inline-formula>, where <i>R</i> and <i>T</i>, respectively, are the Ricci scalar and trace of the energy–momentum tensor. It is found that the equation of state (EOS) parameter <i>w</i> is governed by the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> involved in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> expressions. We fine-tune the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> to obtain the effect of phantom energy in the model. However, we also restrict this parameter to obtain a stable model of the universe.