Gravitational resonances on f(T)-branes
Qin Tan, Wen-Di Guo, Yu‐Peng Zhang, Yu-Xiao Liu
Abstract
Abstract In this work, we investigate the gravitational resonances in various f ( T )-brane models with the warp factor $$\text {e}^{A(y)}=\tanh \big (k(y+b)\big )-\tanh \big (k(y-b)\big )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mtext>e</mml:mtext> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>(</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mo>tanh</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> </mml:mrow> <mml:mi>k</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>y</mml:mi> <mml:mo>+</mml:mo> <mml:mi>b</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>-</mml:mo> <mml:mo>tanh</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> </mml:mrow> <mml:mi>k</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>y</mml:mi> <mml:mo>-</mml:mo> <mml:mi>b</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , where f ( T ) is an arbitrary function of the torsion scalar T . For three kinds of f ( T ), we give the solutions to the system. Besides, we consider the tensor perturbation of the vielbein and obtain the effective potentials by the Kaluza–Klein (KK) decomposition. Then we analyze what kind of effective potential can produce the gravitational resonances. The effects of different parameters on the gravitational resonances are analyzed. The lifetimes of the resonances could be long enough as regards the age of our universe in some ranges of the parameters. This indicates that the gravitational resonances might be considered as one of the candidates for dark matter. Combining the current experimental observations, we constrain the parameters for these brane models.