Matter Creation Cosmologies and Accelerated Expansion

TL;DR

This work demonstrates that matter-creation cosmologies within General Relativity, featuring a DM component with particle creation and a secondary fluid with constant w, can reproduce a wide range of cosmic histories. By performing a thorough dynamical-systems analysis across multiple phenomenological Γ prescriptions, it identifies decelerating DM-dominated phases and diverse accelerating attractors, including DM- and DE-dominated de Sitter, quintessence, and phantom regimes, as well as accelerating scaling solutions. The results show that many Γ choices yield late-time acceleration without invoking dark energy, with some models producing ΛCDM-like behavior at low redshift but distinctive signatures at higher redshift, offering observational tests and potential solutions to the coincidence problem in certain regimes. Overall, the paper establishes matter creation as a phenomenologically rich and viable alternative to ΛCDM, DE, and modified gravity, capable of producing a variety of acceleration histories and cosmological evolutions.

Abstract

Non-conservation of dark matter can lead to late-time cosmic acceleration. This mechanism is known as the matter creation theory and this replaces the need of dark energy and modified gravity theories. We consider a two-fluid system consisting of a cold dark matter and a second fluid with constant barotropic equation of state. We performed detailed investigations of such cosmologies using the powerful techniques of qualitative analysis of dynamical systems. Considering a wide variety of the creation rates, we examine the phase space analysis of the individual scenario. According to our analyses, these scenarios predict decelerating unstable dark matter (or second fluid) dominated critical points, accelerating attractors dominated either by dark matter or the second fluid, accelerating scaling attractors in which dark matter and the second fluid co-exist. The regime of late-time accelerating expansion can be classified as either quintessence, phantom or driven by a cosmological constant. This huge variety of critical points makes these scenarios phenomenologically rich, and naturally suggests that such scenarios can be viewed as viable and potential alternatives to the mainstream cosmological models.

Figures (21)

• Figure 1: Description of the phase space of the matter creation scenarios in which the matter creation rate is constant, i.e. $\Gamma = \Gamma_0$. Upper Left Plot: The phase plot of the system (\ref{['RG-DS-1']}) when we have assumed $w=0.1$ and $\alpha=2$. For other values of $w>0$ and $\alpha>0$, we can also obtain similar phase space structure. Upper Middle Plot: The phase space of the system (\ref{['RG-DS-1']}) when the EoS $w$ takes the value $0$. Here we use $\alpha =2$ but any positive value of $\alpha$ gives same type of phase portrait. Upper Right Plot: The phase plot of the system (\ref{['RG-DS-1']}) considering $w=-0.8$ and $\alpha=3$. Also, we can get similar type of graphics for any positive value of $\alpha$ and negative value of $w$ in the interval $(-1,0)$. Lower Left Plot: The phase space of the system (\ref{['RG-DS-1']}) when the EoS $w$ takes the value $-1$. Here we use $\alpha =3$ but any positive value of $\alpha$ gives similar type of phase portrait. Lower Right Plot: The phase plot of the system (\ref{['RG-DS-1']}) when we assume $w=-1.5$ and $\alpha=3$. For other values of $w<-1$ and $\alpha>0$, we can also obtain similar graphics. In all five two-dimensional plots, green region corresponds to the decelerating phase ($q >0$), cyan region represents the accelerating phase with $-1<q<0$ and the yellow region corresponds to the super accelerating phase (i.e. $q <-1$). The black dotted curve separating the cyan and yellow regions (in the left plot, this separating curve is not visible because of the line of critical points) corresponds to $q= -1$.
• Figure 2: We provide the evolution plots for the dynamical system (\ref{['RG-DS-1']}), showing the behavior of the DM density parameter $\Omega_{\rm dm}^{\rm eff}$, the second fluid density parameter $\Omega_f$, the deceleration parameter $q$, and the effective equation of state of DM $w_{\rm dm}^{\rm eff}$ under the constant particle creation rate $\Gamma=\Gamma_0$. Upper Left Plot: This figure is drawn with the model parameters $w=0.1$, $\alpha=1$, and it shows that the final fate of the universe is late time accelerated evolution in cosmological constant era dominated by DM. Upper Right Plot: This figure is produced for the parameters values $w=0$ and $\alpha=1$. Here also, the final fate of the universe is late time accelerated evolution in cosmological constant era dominated by DM. Lower Left Plot: We have used $w=-1$ and $\alpha=1$. This plot depicts that the ultimate fate of the universe is found to be late time accelerated evolution in cosmological constant epoch which is achieved after the occurrence of a decelerated DM dominated phase. Lower Right Plot: We have taken $w=-1.3$ and $\alpha=1$. This plot highlights that the ultimate fate of the universe is found to be late time DE dominated accelerated evolution in phantom epoch which is achieved after the occurrence of a decelerated DM dominated phase.
• Figure 3: The redshift evolution of $H/H_0$ for the matter creation model $\Gamma= \Gamma_0$ and the $\Lambda$CDM model (upper panel) and the fractional difference $\Delta H/H = (H_{\rm Model} - H_{\Lambda {\rm CDM}})/H_{\Lambda {\rm CDM}}$ (lower panel) have been shown. For the matter creation model we have taken $w= 0$, $\alpha~(= \Gamma/H_0) = 0.1$, $\Omega_{f0} =0.04$, while for the $\Lambda$CDM model we set the matter density parameter at present $\Omega_{m0} =0.3$.
• Figure 4: Description of the phase space of the two-fluid system for the matter creation rate $\Gamma = \Gamma_0 H$. Upper Left Plot: The phase plot of the system (\ref{['DS-2']}) assuming $w=0.1$ and $\Gamma_0=2$. If we take any value of $w$ from $w>-1$ and $\Gamma_0$ in the region $0<\Gamma_0<3$, satisfying $3w+\Gamma_0>0$, we can get similar plot. Upper Right Plot: The phase plot of the system (\ref{['DS-2']}) for $-1 <w <0$ satisfying $3w+\Gamma_0=0$. Here when we have assumed $w=-0.8$ and $\Gamma_0=2.4$, however, any value of $w$ lying in $(-1, 0)$ and any positive value of $\Gamma_0$ satisfying the above condition will give similar plot. Lower Left Plot: The phase plot of the system (\ref{['DS-2']}) when the EoS of the second fluid $w$ adopts the value $w=-1$. In this context, we choose $\Gamma_0=0.2$ but any positive value of $\Gamma_0$ satisfying $3w+\Gamma_0<0$ produces similar type of phase space diagram. Lower Right Plot: This is the phase plot of the system (\ref{['DS-2']}) for $w <-1$ satisfying $3w+\Gamma_0<0$. Here we use $w=-1.8$ and $\Gamma_0=0.1$ for drawing the graphics, however, any typical value of $w < -1$ and any positive value of $\Gamma_0$$(\Gamma_0\neq 3)$ will give similar plot. Here the green region corresponds to the decelerating phase ($q >0$), cyan region represents the accelerating phase with $-1<q<0$ and the yellow region corresponds to the super accelerating phase ($q <-1$). In the lower right graph, the vertical black dotted line corresponds to $q =-1$.
• Figure 5: We display the evolution plots of the DM density parameter $\Omega_{\rm dm}^{\rm eff}$, the second fluid density parameter $\Omega_f$, the deceleration parameter $q$, and the effective equation of state of DM $w_{\rm dm}^{\rm eff}$ corresponding to the dynamical system (\ref{['DS-2']}), with the matter creation rate $\Gamma=\Gamma_0 H$. Left Plot: We have drawn this plot using the model parameters $w=0.1$ and $\Gamma_0=2$. Here, the trajectories end in DM dominated accelerated quintessence era. In this case, the past DM-dominated era can not be realized since no decelerating DM-dominated saddle point appears (see the upper left plot of Fig. \ref{['fig2B']}). Middle Plot: This plot is produced adopting the values of the model parameters $w=-1$ and $\Gamma_0=0.2$ where the late time evolution of the universe is attracted by DE dominated cosmological constant era connecting through DM dominated decelerated era. Right Plot: For this plot, we take $w=-1.2$ and $\Gamma_0=0.1$ where one can see that trajectories are attracted by DE dominated phantom era at late-times joining through a DM dominated decelerated phase.