Dynamical system analysis in modified Galileon cosmology

Abstract In this paper, we have investigated the phase space analysis in modified Galileon cosmology, where the Galileon term is considered a coupled scalar field, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϕ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> . We focus on the exponential type function of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϕ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> and the three well-motivated potential functions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mi>V</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ϕ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> . We obtain the critical points of the autonomous system, along with their stability conditions and cosmological properties. The critical points of the autonomous system describe different phases of the Universe. The scaling solution for critical points was found in our analysis to determine the matter-dark energy and radiation-dark energy-dominated eras of the Universe. In these scaling solutions, dark energy is typically introduced alongside another component, such as radiation or matter, and helps explain the transition between cosmological eras. The dark energy dominated critical points show stable behavior and indicate the late-time cosmic acceleration phase of the Universe. Further, the results are examined with the Hubble rate H ( z ) and the Supernovae Ia cosmological data sets.