Observational constraints on generic models of non-minimal curvature-matter coupling

Abstract We investigate two classes of non-minimally coupled curvature-matter models in the FLRW Universe with a perfect fluid and analyze their cosmological implications using Supernova Ia, observed Hubble data, and baryon acoustic oscillation measurements. Non-minimal coupling is introduced via an additional term <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>∫</mml:mo> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>x</mml:mi> <mml:msqrt> <mml:mo>−</mml:mo> <mml:mi>g</mml:mi> </mml:msqrt> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">G</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>R</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> in the Einstein–Hilbert action. To obtain observational constraints, we use an exponential-type fluid-pressure profile <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mi>a</mml:mi> <mml:mi>k</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> characterized by the dimensionless parameter k and parameterize <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>R</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> as R n with another dimensionless parameter n . Two additional parameters, α and β in the functional form of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">G</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> determine the coupling strength. We identify significant regions in the ( n , k )-parameter space for fixed coupling strength values where non-minimally coupled models align with observed late-time cosmic evolution. Additionally, we explore and discuss features of energy transfer between the curvature and matter sectors using observational data.