In the present article we analyze the matter-geometry coupled f(Q, T) theory of gravity. We offer the fully covariant formulation of the theory, with which we construct the correct energy balance equation and employ it to conduct a dynamical system analysis in a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. We consider three different functional forms of the f(Q, T) function, specifically, $$f(Q,T)=\alpha Q+ \beta T$$ , $$f(Q,T)=\alpha Q+ \beta T^2$$ , and $$f(Q,T)=Q+ \alpha Q^2+ \beta T$$ . We attempt to investigate the physical capabilities of these models to describe various cosmological epochs. We calculate Friedmann-like equations in each case and introduce some phase space variables to simplify the equations in more concise forms. We observe that the linear model $$f(Q,T)=\alpha Q+ \beta T$$ with $$\beta =0$$ is completely equivalent to the GR case without cosmological constant $$\Lambda $$ . Further, we find that the model $$f(Q,T)=\alpha Q+ \beta T^2$$ with $$\beta \ne 0$$ successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model $$f(Q,T)= Q+ \alpha Q^2+ \beta T$$ with $$\alpha \ne 0$$ represents an accelerated de-Sitter epoch for the constraints $$\beta < -1$$ or $$ \beta \ge 0$$ .
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"surname": "De",
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"value": "In the present article we analyze the matter-geometry coupled f(Q, T) theory of gravity. We offer the fully covariant formulation of the theory, with which we construct the correct energy balance equation and employ it to conduct a dynamical system analysis in a spatially flat Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker spacetime. We consider three different functional forms of the f(Q, T) function, specifically, $$f(Q,T)=\\alpha Q+ \\beta T$$ <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> <mo>=</mo> <mi>\u03b1</mi> <mi>Q</mi> <mo>+</mo> <mi>\u03b2</mi> <mi>T</mi> </mrow> </math> , $$f(Q,T)=\\alpha Q+ \\beta T^2$$ <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>\u03b1</mi> <mi>Q</mi> <mo>+</mo> <mi>\u03b2</mi> <msup> <mi>T</mi> <mn>2</mn> </msup> </mrow> </math> , and $$f(Q,T)=Q+ \\alpha Q^2+ \\beta T$$ <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>Q</mi> <mo>+</mo> <mi>\u03b1</mi> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>+</mo> <mi>\u03b2</mi> <mi>T</mi> </mrow> </math> . We attempt to investigate the physical capabilities of these models to describe various cosmological epochs. We calculate Friedmann-like equations in each case and introduce some phase space variables to simplify the equations in more concise forms. We observe that the linear model $$f(Q,T)=\\alpha Q+ \\beta T$$ <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> <mo>=</mo> <mi>\u03b1</mi> <mi>Q</mi> <mo>+</mo> <mi>\u03b2</mi> <mi>T</mi> </mrow> </math> with $$\\beta =0$$ <math> <mrow> <mi>\u03b2</mi> <mo>=</mo> <mn>0</mn> </mrow> </math> is completely equivalent to the GR case without cosmological constant $$\\Lambda $$ <math> <mi>\u039b</mi> </math> . Further, we find that the model $$f(Q,T)=\\alpha Q+ \\beta T^2$$ <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>\u03b1</mi> <mi>Q</mi> <mo>+</mo> <mi>\u03b2</mi> <msup> <mi>T</mi> <mn>2</mn> </msup> </mrow> </math> with $$\\beta \\ne 0$$ <math> <mrow> <mi>\u03b2</mi> <mo>\u2260</mo> <mn>0</mn> </mrow> </math> successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model $$f(Q,T)= Q+ \\alpha Q^2+ \\beta T$$ <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>Q</mi> <mo>+</mo> <mi>\u03b1</mi> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>+</mo> <mi>\u03b2</mi> <mi>T</mi> </mrow> </math> with $$\\alpha \\ne 0$$ <math> <mrow> <mi>\u03b1</mi> <mo>\u2260</mo> <mn>0</mn> </mrow> </math> represents an accelerated de-Sitter epoch for the constraints $$\\beta < -1$$ <math> <mrow> <mi>\u03b2</mi> <mo><</mo> <mo>-</mo> <mn>1</mn> </mrow> </math> or $$ \\beta \\ge 0$$ <math> <mrow> <mi>\u03b2</mi> <mo>\u2265</mo> <mn>0</mn> </mrow> </math> ."
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