Non-interacting holographic dark energy with Torsion via Hubble Radius

TL;DR

This work addresses holographic dark energy with a Hubble radius infrared cut-off in a cosmology that includes torsion, within Einstein–Cartan theory, while assuming no interaction with dark matter. It derives the modified Friedmann equations with a time-dependent torsion scalar $\phi(t)$ and sets the IR cut-off to $L = H^{-1}$, leading to $\rho_X = 3 d^{2} M_p^{2} H^{2}$ and a corresponding expression for $\rho_m$, combined into a dynamic equation of state $\omega_X$ that depends on $\phi/H$, $\dot{\phi}$, and the deceleration parameter $q$. By analyzing three torsion regimes (steady-state, constant, time-dependent), the paper shows that the Hubble radius can serve as a viable IR cut-off in a non-interacting setting, with explicit minima for $\omega_X^0$ in the time-dependent case and a near-Lambda behavior for $d$ close to unity. This provides a non-interacting holographic DE framework with torsion that can reproduce cosmic acceleration while avoiding causality and circular logic issues associated with future horizons, suggesting a closer alignment with ΛCDM for $d\approx1$ but with a dynamical equation of state.

Abstract

We reconstruct a holographic dark energy model within a Friedmann cosmology incorporating torsion scalar, assuming no interaction between dark energy and dark matter. Setting the Hubble radius as an infrared (IR) cut-off, we focus on a system dominated by contribution of a time-dependent torsion scalar induced by the spin of matter. In this regime, our results show that even very weak torsion causes cosmic acceleration. Specifically, we find that minima of the current equation of state for holographic dark energy, $(ω_X^{0})_{min}$, lies in the range $-1 < (ω_X^{0})_{min} < -0.778$ as a free parameter $d$ varies from $1$ to $0.654$. Focusing on the free parameter $d \approx 1$, we find that $(ω_X^{0})_{min}$ exhibits slightly different behavior from the cosmological constant. Introducing torsion allows the Hubble radius to serve as a viable IR cut-off even without assuming the interaction between them. Moreover, this approach provides a non-interacting limit not found in earlier interacting models that use the Hubble radius as the IR cut-off.

Figures (3)

• Figure 1: The current equation of state $\omega_{X}^{0}$ with the constant torsion scalar for various values of the free parameter $d = 0.5$ (red), $d = 0.886$ (blue), $d = 0.95$ (green), and $d = 1$ (purple).
• Figure 2: Possible solutions of $\omega_{X}^{0}$ with the time-dependent torsion scalar \ref{['ansatz 2']} for various values of the free parameter $d = 0.5$ (red), $d = 0.886$ (blue), $d = 0.95$ (green), and $d = 1$ (purple).
• Figure 3: Close-up view of Fig. \ref{['fig.2']} for $\phi_{0}/H_{0} \geq 0$, highlighting the minima of $\omega_{X}^{0}$ (black dots) located at $(\phi_{0}/H_{0})_{min}$. For $d = 1$, the red dot represents $\omega_X^{0} = -1$ at $\phi_{0}/H_{0} = 0$, which is not a minimum. The inset illustrates the dependence of $(\phi_{0}/H_{0})_{min}$ on $d$, where the pink solid line indicates valid solutions within the weak torsion range for $0.654 < d < 1$.