Unexplored regions in teleparallel $f(T)$ gravity: Sign-changing dark energy density

TL;DR

The paper investigates unexplored regions of teleparallel $f(T)$ gravity using the exponential infrared model $f(T)=T e^{\beta T_0/T}$, revealing a dual-branch structure in the parameter $\beta$ that yields qualitatively different cosmic histories for a fixed present matter density $\Omega_{\rm m0}$. By treating the torsional corrections as an effective dark energy component, the authors show that the negative branch $\beta_-$ can produce a sign-changing DE density with a zero-crossing at $z_\dagger\approx1.5$ while remaining ghost-free via $f_T>0$, and the positive branch $\beta_+$ yields phantom-like behavior consistent with late-time acceleration and SH0ES data. They also explore the inclusion of a cosmological constant $\Lambda$, which broadens the viable cosmologies and permits combinations where phantom or sign-changing DE coexists with $\Lambda$, offering enhanced flexibility to fit CMB, BAO, and local $H_0$ measurements, including recent DESI indications of evolving acceleration. Overall, the work highlights that relaxing the usual positivity constraint on the effective DE density in $f(T)$ gravity opens new avenues for addressing cosmological tensions and invites a reexamination of both $f(T)$ and $f(Q)$ models in light of these dynamics and screening mechanisms.

Abstract

While $f(T)$ gravity has shown considerable potential in addressing cosmological tensions, we explore previously overlooked solution spaces that hold further promise. We examine the case where the customary assumption of a strictly positive effective DE density may not apply, offering new possibilities. Focusing on $f(T) = T e^{T_*/T}$, we investigate cosmological solutions parametrized by the parameter $β= T_*/T_0$. This parameter uniquely determines $Ω_{\rm m0}$, and its sign plays a crucial role in characterizing deviations from the $Λ$CDM. We elaborate on the structural asymmetry between the positive- and negative-$β$ branches: while the $β_{+}$ leads to dynamics with modest departures from $Λ$CDM, the $β_{-}$ yields more pronounced and nontrivial deviations. Despite these deviations, the negative-$β$ branch can remain consistent with local gravity constraints through an effective chameleon-like mechanism. We also examine the model in the context of dynamical DE. Ensuring consistency with CMB data, the widely studied $β_{+}$ exhibits phantom behavior, while the previously overlooked $β_{-}$ features a sign-changing DE density that transitions smoothly from negative to positive values at $z_{\dagger} \sim 1.5$. Though the sign-changing DE leads to a larger-than-expected enhancement, we extend the analysis by incorporating $Λ$. This extension broadens the solution space consistent with the SH0ES measurement while maintaining consistency with CMB. Additionally, it introduces richer phenomenological possibilities, including the potential moderation or cessation of cosmic acceleration at very low redshifts, aligning with recent observational analyses, such as those from DESI BAO data. Our findings suggest that existing $f(T)$ models, as well as $f(Q)$ models, should be revisited in light of the novel theoretical insights presented here.

Figures (8)

• Figure 1: $\Omega_{\rm m0}$ vs $\beta$ plotted by using Eq. \ref{['eq:constraint']}. The curve is separated into four regions as described in Sec. \ref{['fig:SolutionRegions']}: the dotted orange part (Region I) is the new region that covers negative values of the present-day density parameter of matter, i.e., $\Omega_{\rm m0}<0$. The solid orange part (Region II) is the widely studied region Awad:2017yodHashim:2020sezHashim:2021pkq, which corresponds to $0<\Omega_{\rm m0}< 1$, because reasonable $\Omega_{\rm m0}$ values from the observational point of view shown by the wheat-colored band lie in this region. The dot-dashed blue curve (Region III) is another new region leading to $\Omega_{\rm m0}$ values larger than unity. The solid blue curve (Region IV) is an overlooked region in the literature even though the observationally reasonable $\Omega_{\rm m0}$ values can be obtained in this region as well. Some special points are $(\beta=-1/2,\,\Omega_{\rm m0}=2/\sqrt{e}=1.21306)$ represented by black diamond, $(\beta \to -\infty, \,\Omega_{\rm m0} \to 0)$ by blue triangle, $(\beta=1/2, \,\Omega_{\rm m0}=0)$ by green circle and $(\beta=0, \,\Omega_{\rm m0}=1)$ by purple square.
• Figure 2: Evolution of the normalized Hubble parameter scaled by $(1+z)$, i.e., $E(z)/(1+z)$, as a function of redshift $z$, for the standard $\Lambda$CDM model (red) and for the present teleparallel gravity model with $\Omega_{\rm m0}=0.3$. The two branches of the model correspond to $\beta = 0.399$ (orange, positive branch) and $\beta = -3.207$ (blue, negative branch). All three curves converge to the Einstein--de Sitter behavior at high redshift in the matter-dominated era. While the positive branch shows only mild deviations from $\Lambda$CDM, the negative branch exhibits substantial departures in the post-matter-dominated regime.
• Figure 4: Top panel:$f_T$ with respect to $H/H_0$. Bottom panel:$\dot{\mathcal{G}}_{\rm eff}/\mathcal{G}_{\rm eff}$ scaled by $H_0$ with respect to $H/H_0$ for some chosen $\beta$ values representing regions presented in Fig \ref{['fig:evo_beta_2']}.
• Figure 5: Top left panel:$\rho_{\rm T}(z)/\rho_{\rm cr0}$ (energy density of torsional DE scaled by present-day critical density). Top right panel: $p_{\rm T}(z)/\rho_{\rm cr0}$ (pressure of torsional DE scaled by present-day critical density). Bottom left panel: $w_{\rm T}(z)$ (EoS parameter of torsional DE). Bottom right panel: $\Omega(z)$ (density parameters) of matter (dashed curves) and torsional DE (solid curves). To ensure the consistency with the CMB data, we use $H_0=67.70 \,{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ for the $\Lambda$CDM model shown by the red curve, $H_0=72.36 \,{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ for the phantom DE model ($\beta_{+}$) shown by the orange curve, and $H_0=84.54 \,{\rm km\,s}^{-1}{\rm Mpc}^{-1}$ for the sign-changing DE model ($\beta_{-}$) shown by the blue curve.
• Figure 6: Top panel:$\dot{a}=H(z)/(1+z)$ (comoving Hubble parameter). Bottom panel:$q(z)$ (deceleration parameter). The green bars corresponds to SH0ES collaboration measurement Riess:2021jrx and clustering measurements for the BAO samples in Ref. eBOSS:2020yzd; BOSS DR12 consensus Galaxy (from $z_{\rm{eff}} = 0.38, 0.51$), eBOSS DR16 LRG (from $z_{\rm{eff}}= 0.70$), eBOSS DR16 Quasar (from $z_{\rm{eff}}= 1.48$), eBOSS DR16 Lyman$\alpha$ (Ly$\alpha$)-Ly$\alpha$ (from $z_{\rm{eff}} = 2.33$) and eBOSS DR16 Ly$\alpha$-quasar (from $z_{\rm{eff}} = 2.33$ but shifted to $z_{\rm{eff}} = 2.35$ in the figures for visual clarity) measurements.