Exact cosmological models in metric-affine F(R, T) gravity

Abstract

Abstract A flat Friedmann–Lematre–Robertson–Walker (FLRW) spacetime metric was used to investigate some exact cosmological models in metric-affine F ( R , T ) gravity in this paper. The considered modified Lagrangian function is $$F(R,T)=R+\lambda T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>R</mml:mi><mml:mo>+</mml:mo><mml:mi>λ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math> , where R is the Ricci curvature scalar, T is the torsion scalar for the non-special connection, and $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>λ</mml:mi></mml:math> is a model parameter. We also wrote $$R=R^{(LC)}+u$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>L</mml:mi><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>u</mml:mi></mml:mrow></mml:math> and $$T=T^{(W)}+v$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>W</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>v</mml:mi></mml:mrow></mml:math> , where $$R^{(LC)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>L</mml:mi><mml:mi>C</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:math> is the Ricci scalar curvature with respect to the Levi–Civita connection and $$T^{(W)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>T</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>W</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:math> is the torsion scalar with respect to the Weitzenbock connection, and u and v are the functions of scale factor a ( t ), connection and its derivatives. For the scale factor a ( t ), we have obtained two exact solutions of modified field equations in two different situations of u and v . Using this scale factor, we have obtained various geometrical parameters to investigate the universe’s cosmological properties. We used Markov chain Monte Carlo (MCMC) simulation to analyze two types of latest datasets: cosmic chronometer (CC) data (Hubble data) points and Pantheon SNe Ia samples, and found the model parameters that fit the observations best at $$1-\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>σ</mml:mi></mml:mrow></mml:math> , and $$2-\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:mo>-</mml:mo><mml:mi>σ</mml:mi></mml:mrow></mml:math> regions. We have performed a comparative and relativistic study of geometrical and cosmological parameters. In model-I, we have found that the effective equation of state (EoS) parameter $$\omega _{eff}$$ <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> varies in the range $$-1\le \omega _{eff}\le 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mi>ω</mml:mi><mml:mrow><mml:mi>eff</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> , while in model-II, it varies as $$-1.0345\le \omega _{eff}\le 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.0345</mml:mn><mml:mo>≤</mml:mo><mml:msub><mml:mi>ω</mml:mi><mml:mrow><mml:mi>eff</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> . We found that both models are transit phase (moving from slowing down to speeding up) universes with a transition redshift $$z_{t}=0.5874_{-0.0197}^{+0.2130}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:msubsup><mml:mn>5874</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.0197</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.2130</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math> and $$z_{t}=0.6865_{-0.0303}^{+0.1719}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:msubsup><mml:mn>6865</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.0303</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.1719</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math> .

Topics & Concepts