New test on general relativity and $f(T)$ torsional gravity from galaxy-galaxy weak lensing surveys. (arXiv:1907.12225v3 [astro-ph.CO] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Chen_Z/0/1/0/all/0/1">Zhaoting Chen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Luo_W/0/1/0/all/0/1">Wentao Luo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Cai_Y/0/1/0/all/0/1">Yi-Fu Cai</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Saridakis_E/0/1/0/all/0/1">Emmanuel N. Saridakis</a>

We use galaxy-galaxy weak lensing data to perform a novel test on general

relativity (GR) and $f(T)$ torsional gravity. In particular, we impose strong

constraints using the torsional (teleparallel) formulation of gravity in which

the deviation from GR is quantified by a single parameter $alpha$, an

approximation which is always valid at low-redshift Universe and weak

gravitational fields. We calculate the difference in the deflection angle and

eventually derive the modified excess surface density profile, which is mainly

affected at small scales. Confronting the predictions with weak lensing data

from the Sloan Digital Sky Survey Data Release 7, we obtain the upper bound on

the deviation parameter, which, expressed via the dimensionless percentage in

the Universe energy content, reads as ${rm{log_{10}}}Omega_alphale

-18.52_{-0.42}^{+0.80}$(stat)$_{-0.37}^{+1.50}$(sys)$ [R_c/0.015R_{200}]$ with

systematics mainly arising from the modelling of astrophysics, upon a

reasonable choice of cut-off radius for $f(T)$ gravity in form of $T + alpha

T^2$. To our knowledge, this is the first time that GR is verified at such an

accuracy at the corresponding scales.

We use galaxy-galaxy weak lensing data to perform a novel test on general

relativity (GR) and $f(T)$ torsional gravity. In particular, we impose strong

constraints using the torsional (teleparallel) formulation of gravity in which

the deviation from GR is quantified by a single parameter $alpha$, an

approximation which is always valid at low-redshift Universe and weak

gravitational fields. We calculate the difference in the deflection angle and

eventually derive the modified excess surface density profile, which is mainly

affected at small scales. Confronting the predictions with weak lensing data

from the Sloan Digital Sky Survey Data Release 7, we obtain the upper bound on

the deviation parameter, which, expressed via the dimensionless percentage in

the Universe energy content, reads as ${rm{log_{10}}}Omega_alphale

-18.52_{-0.42}^{+0.80}$(stat)$_{-0.37}^{+1.50}$(sys)$ [R_c/0.015R_{200}]$ with

systematics mainly arising from the modelling of astrophysics, upon a

reasonable choice of cut-off radius for $f(T)$ gravity in form of $T + alpha

T^2$. To our knowledge, this is the first time that GR is verified at such an

accuracy at the corresponding scales.

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