Cosmological applications of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity with dynamical curvature and torsion

We investigate the cosmological applications of Myrzakulov $F(R,T)$ gravity. In this theory ones uses a specific but nonspecial connection, and thus both curvature and torsion are dynamical fields related to gravity. We introduce a parametrization that quantifies the deviation of curvature and torsion scalars form their corresponding values obtained using the special Levi-Civita and Weitzenb\"ock connections, and we extract the cosmological field equations following the minisuperspace procedure. Even for the simple case where the action of the theory is linear in $R$ and $T$, we find that the Friedmann equations contain new terms of geometrical origin, reflecting the nonspecial connection. Applying the theory at late times we find that we can acquire the thermal history of the universe, where dark energy can be quintessencelike or phantomlike, or behave exactly as a cosmological constant and thus reproducing $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology. Furthermore, we show that these features are obtained for other Lagrangian choices, too. Finally, early-time application leads to the de Sitter solution, as well as to an inflationary realization with the desired scale-factor evolution.

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