Dynamical analysis of bouncing cosmology in the Capozziello–De Laurentis model of f(R) gravity

Abstract In this study, we analyze f ( R ) gravity employing the $$ f(R) = R+ \alpha _1 R^p - \alpha _2 R^{-q} $$ <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>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>α</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>α</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msup> <mml:mi>R</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> model within the Friedmann–Lemaître–Robertson–Walker (FLRW) background. We derive the Friedmann equations via modified gravity action and subsequently reexpress them in terms of the standard Friedmann equations. Our investigation explores the behavior of a bouncing cosmological model within this modified gravity context, offering a potential solution to the singularity problem encountered in the standard Big Bang cosmology. We represent cosmological parameters as functions of cosmic time and scrutinize the conditions for a cosmic bounce. Additionally, we reconstruct the f ( R ) gravity model using the redshift parameter and graphically present cosmological parameters as functions of redshift. These plots reveal an accelerated nature of Universe expansion. Furthermore, we reconstruct f ( R ) gravity models for scale factors, $$a(t) = e^{e^{\lambda t}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>e</mml:mi> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msup> </mml:msup> </mml:mrow> </mml:math> which exhibits the bouncing behavior. Finally, we investigated the stability scenario by examining the sound speed. The resulting graph of sound speed plotted against redshift confirms late-time stability.