Can <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity resolve the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>H</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> tension?
Deng Wang, David F. Mota
Abstract
Motivated by the discrepancy in measurements of ${H}_{0}$ between local and global probes, we investigate whether teleparallel gravities could be a better model to describe the present-day observations or at least to alleviate the ${H}_{0}$ tension. Specifically, in this work we study and place constraints on three popular $f(T)$ models in light of the Planck-2018 cosmic microwave background data release. We find that the $f(T)$ power-law model can alleviate the ${H}_{0}$ tension from $4.4\ensuremath{\sigma}$ to $1.9\ensuremath{\sigma}$ level, while the $f(T)$ model of two exponentials fails to resolve this inconsistency. Moreover, for the first time, we obtain constraints on the effective number of relativistic species ${N}_{\mathrm{eff}}$ and on the sum of the neutrino masses $\mathrm{\ensuremath{\Sigma}}{m}_{\ensuremath{\nu}}$ in $f(T)$ gravity. We find that the constraints obtained are looser than in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. However, the introduction of massive neutrinos into the cosmological model alleviates the ${H}_{0}$ tension for the power-law model. Finally, we find that whether a viable $f(T)$ theory can mitigate the ${H}_{0}$ tension depends on the mathematical structure of the distortion factor $y(z,b)$. These results could provide a clue for theoreticians to write a more physical-motivated expression of $f(T)$ function.