Metric-Affine Version of Myrzakulov <em>F</em>(<em>R</em>,<em>T</em>,<em>Q</em>,<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">T</mi></semantics></math></inline-formula>) Gravity and Cosmological Applications

• Main Authors: Damianos Iosifidis, Nurgissa Myrzakulov, Ratbay Myrzakulov
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Universe
• Subjects: cosmology; torsion
• Online Access: https://www.mdpi.com/2218-1997/7/8/262

We derive the full set of field equations for the metric-affine version of the Myrzakulov gravity model and also extend this family of theories to a broader one. More specifically, we consider theories whose gravitational Lagrangian is given by <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><mi>Q</mi><mo>,</mo><mi mathvariant="script">T</mi><mo>,</mo><mi mathvariant="script">D</mi><mo>)</mo></mrow></semantics></math></inline-formula> where <i>T</i>, <i>Q</i> are the torsion and non-metricity scalars, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">T</mi></semantics></math></inline-formula> is the trace of the energy-momentum tensor and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">D</mi></semantics></math></inline-formula> the divergence of the dilation current. We then consider the linear case of the aforementioned theory and, assuming a cosmological setup, we obtain the modified Friedmann equations. In addition, focusing on the vanishing non-metricity sector and considering matter coupled to torsion, we obtain the complete set of equations describing the cosmological behavior of this model along with solutions.