Evolutionary behaviour of cosmological parameters with dynamical system analysis in f(Q, T) gravity

Abstract We have investigated the accelerating behaviour of the Universe in f ( Q , T ) gravity in an isotropic and homogeneous space-time. We have initially derive the dynamical parameters in the general form of $$f(Q,T)=\alpha Q^m+\beta T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> <mml:msup> <mml:mi>Q</mml:mi> <mml:mi>m</mml:mi> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>β</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> (Xu et al. in Eur Phys J C 79:708, 2019) and then split it into two cases (i) one with $$m=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and the (ii) other with $$\beta =0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . In the first case, it reduces to the linear form of the functional f ( Q , T ) and second case leads to the higher power of the nonmetricity Q . In an assumed form of the hyperbolic scale factor, the models are constructed and its evolutionary behaviours are studied. The geometrical parameters as well the equation of state parameter are obtained and found to be in the preferred range of the cosmological observations. Marginal variation has been noticed in the behaviour of $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> and $$\omega _{eff}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mi>eff</mml:mi> </mml:mrow> </mml:msub> </mml:math> at present time. The violation of strong energy conditions in both the cases are shown. The dynamical system analysis for the models has been performed.

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