Cosmic anisotropic hair of nonlocal RT gravity

Abstract

Nonlocal RT gravity has proven effective in explaining the late-time cosmic acceleration while remaining consistent with local gravity tests. However, most previous cosmological studies of this theory have assumed an isotropic background, which may not fully capture the slight anisotropies suggested by current observations, such as those inferred from Type Ia supernovae data. In this paper, we investigate the dynamical evolution of an anisotropic Bianchi type I universe within the framework of nonlocal RT gravity. By introducing six dimensionless variables, we construct the corresponding dynamical system and perform a detailed phase-space analysis. An unexpected finding is that, contrary to many dark energy models and modified gravity theories in which anisotropies decay with time, nonlocal RT gravity predicts a growth of cosmic anisotropy. This behavior poses a challenge to the cosmic no-hair theorem within the nonlocal RT gravity scenario.

Figures (4)

• Figure 1: The trajectories in the three-dimensional phase space are shown, illustrating the evolutions governed by Eq. (\ref{['xd3']}) with initial conditions on the planes $x_{5} = 1$ and $x_{5} = -1.5$. Points $L_1$ to $L_5$ denote critical points, with green points indicating unstable points and red point indicating stable point. The significance of the red-shaded region is discussed in the main text.
• Figure 2: Phase portrait of the dynamical system (\ref{['2w']}). The critical points of the dynamical system are marked by red and green symbols, where the red point is stable and the two green points are unstable. The yellow curve indicates the asymptote: trajectories starting below it converge to the stable point (red), whereas those starting above it diverge. The black arrows show the eigenvector direction at the unstable point, which is tangent to the yellow curve at that location.
• Figure 3: Orange part: The orange dashed curve shows the evolution of $\Omega_{DE}$ as a function of $N$. Here, $N=0$ corresponds to the present epoch. The black point marks the present value of $\Omega_{DE}$ when $\alpha=0.67$, consistent with current observations (Sec. \ref{['sec:03']}). Blue part: The blue curves show the evolution of $x_{5}$ for different values of $x_{5,0}$. The initial conditions are given by $x_{1}=0$, $x_{2}=0$, $x_{3}=0$, $x_{4}=0$, $x_{5}=x_{5,0}$, and $x_{6}=\alpha^{2} H_{0}^{2}/H^{2}$, where $x_{5,0}$ sets the initial values of $x_{5}$. Since $x_{5}$ diverges during the evolution, the plot is truncated for clarity.
• Figure 4: Evolution of $\Sigma$ with different $x_{5,0}$. The initial conditions are given by $x_{1}=0$, $x_{2}=0$, $x_{3}=0$, $x_{4}=0$, $x_{5}=x_{5,0}$, and $x_{6}=\alpha^{2} H_{0}^{2}/H^{2}$, where $x_{5,0}$ sets the initial values of $x_{5}$.