F(R) gravity dark energy model of an interaction between dark radiation and dark matter
Yannan Qi, Weiqiang Yang, Yi‐Tao Wang, Tianyi Han, Yabo Wu
Abstract
Abstract In this work, we will study the late-time dynamic evolution of the F ( R ) gravity dark energy model of an interaction between dark radiation and dark matter. We explore the possibility of the apparent extra dark radiation being linked directly to the physics of cold dark matter (CDM). In particular, we consider a generic scenario where dark radiation, as a result of an interaction, is produced directly by a fraction of the dark matter density effectively decaying into dark radiation. The decay process is controlled by its rate $$Q=\alpha H\rho _{dm}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> <mml:mi>H</mml:mi> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>dm</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , where $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> is the (constant) dimensionless parameter quantifying the strength of the decay mechanism, for the weak coupling between dark matter and dark radiation $$\alpha \ll 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . We will solve the field equations numerically by using the statefinder function $$y_{H}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>y</mml:mi> <mml:mi>H</mml:mi> </mml:msub> </mml:math> to appropriately represent the field equation. The F ( R ) gravity model we consider is described by a nearly $$R^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -model at early epochs and at late-time the model mimic the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> -Cold-Dark-Matter model ( $$\Lambda CDM$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mi>C</mml:mi> <mml:mi>D</mml:mi> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> ), and we fine tune the parameters to achieve viability and compatibility with the latest Planck constraints at late-time. Furthermore, we consider the behavior of several well-known statefinder quantities, we find that statefinder diagnostic and Om diagnostic can not only break the degeneracy of different parameter values in the F ( R ) gravity dark energy model, but also effectively distinguish the difference between the F ( R ) gravity model and the $$\Lambda CDM$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mi>C</mml:mi> <mml:mi>D</mml:mi> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> model. At last, we compared the theoretical results with the SNIa data.