No constraints for $f(T)$ gravity from gravitational waves induced from primordial black hole fluctuations. (arXiv:2205.06094v1 [gr-qc])

<a href="http://arxiv.org/find/gr-qc/1/au:+Papanikolaou_T/0/1/0/all/0/1">Theodoros Papanikolaou</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Tzerefos_C/0/1/0/all/0/1">Charalampos Tzerefos</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Basilakos_S/0/1/0/all/0/1">Spyros Basilakos</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Saridakis_E/0/1/0/all/0/1">Emmanuel N. Saridakis</a>

Primordial black hole (PBH) fluctuations can induce a stochastic

gravitational wave background at second order, and since this procedure is

sensitive to the underlying gravitational theory it can be used as a novel tool

to test general relativity and extract constraints on possible modified gravity

deviations. We apply this formalism in the framework of $f(T)$ gravity,

considering three viable mono-parametric models. In particular, we investigate

the induced modifications at the level of the gravitational-wave source, which

is encoded in terms of the power spectrum of the PBH gravitational potential,

as well as at the level of their propagation, described in terms of the Green

function which quantifies the propagator of the tensor perturbations. We find

that, within the observationally allowed range of the $f(T)$ model-parameters,

the obtained deviations from general relativity, both at the levels of source

and propagation, are practically negligible. Hence, we conclude that realistic

and viable $f(T)$ theories can safely pass the primordial black hole

constraints, which may offer an additional argument in their favor.

Primordial black hole (PBH) fluctuations can induce a stochastic

gravitational wave background at second order, and since this procedure is

sensitive to the underlying gravitational theory it can be used as a novel tool

to test general relativity and extract constraints on possible modified gravity

deviations. We apply this formalism in the framework of $f(T)$ gravity,

considering three viable mono-parametric models. In particular, we investigate

the induced modifications at the level of the gravitational-wave source, which

is encoded in terms of the power spectrum of the PBH gravitational potential,

as well as at the level of their propagation, described in terms of the Green

function which quantifies the propagator of the tensor perturbations. We find

that, within the observationally allowed range of the $f(T)$ model-parameters,

the obtained deviations from general relativity, both at the levels of source

and propagation, are practically negligible. Hence, we conclude that realistic

and viable $f(T)$ theories can safely pass the primordial black hole

constraints, which may offer an additional argument in their favor.

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