Weak field limit and gravitational waves in higher-order gravity. (arXiv:1812.11557v1 [gr-qc])

Weak field limit and gravitational waves in higher-order gravity. (arXiv:1812.11557v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Capozziello_S/0/1/0/all/0/1">Salvatore Capozziello</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Capriolo_M/0/1/0/all/0/1">Maurizio Capriolo</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Caso_L/0/1/0/all/0/1">Loredana Caso</a>

We derive the weak field limit for a gravitational Lagrangian density
$L_{g}=(R+a_{0}R^{2}+sum_{k=1}^{p} a_{k}RBox^{k}R)sqrt{-g}$ where
higher-order derivative terms in the Ricci scalar $R$ are taken into account.
The interest for this kind of effective theories comes out from the
consideration of the infrared and ultraviolet behaviors of gravitational field
and, in general, from the formulation of quantum field theory in curved
spacetimes. Here, we obtain solutions in weak field regime both in vacuum and
in the presence of matter and derive gravitational waves considering the
contribution of $RBox^{k}R$ terms. By using a suitable set of coefficients
$a_{k}$, it is possible to find up to $(p+2)$ normal modes of oscillation with
six polarization states with helicity 0 or 2. Here $p$ is the higher order term
in the $Box$ operator appearing in the gravitational Lagrangian. More
specifically: the mode $omega_{1}$, with $k^{2}=0$, has transverse
polarizations $epsilon_{munu}^{left(+right)}$ and
$epsilon_{munu}^{left(timesright)}$ with helicity 2; the $(p+1)$ modes
$omega_{m}$, with $k^{2}neq0$, have transverse polarizations
$epsilon_{munu}^{left(1right)}$ and non-transverse ones
$epsilon_{munu}^{left(text{TT}right)}$,
$epsilon_{munu}^{left(text{TS}right)}$,
$epsilon_{munu}^{left(Lright)}$ with helicity 0.

We derive the weak field limit for a gravitational Lagrangian density
$L_{g}=(R+a_{0}R^{2}+sum_{k=1}^{p} a_{k}RBox^{k}R)sqrt{-g}$ where
higher-order derivative terms in the Ricci scalar $R$ are taken into account.
The interest for this kind of effective theories comes out from the
consideration of the infrared and ultraviolet behaviors of gravitational field
and, in general, from the formulation of quantum field theory in curved
spacetimes. Here, we obtain solutions in weak field regime both in vacuum and
in the presence of matter and derive gravitational waves considering the
contribution of $RBox^{k}R$ terms. By using a suitable set of coefficients
$a_{k}$, it is possible to find up to $(p+2)$ normal modes of oscillation with
six polarization states with helicity 0 or 2. Here $p$ is the higher order term
in the $Box$ operator appearing in the gravitational Lagrangian. More
specifically: the mode $omega_{1}$, with $k^{2}=0$, has transverse
polarizations $epsilon_{munu}^{left(+right)}$ and
$epsilon_{munu}^{left(timesright)}$ with helicity 2; the $(p+1)$ modes
$omega_{m}$, with $k^{2}neq0$, have transverse polarizations
$epsilon_{munu}^{left(1right)}$ and non-transverse ones
$epsilon_{munu}^{left(text{TT}right)}$,
$epsilon_{munu}^{left(text{TS}right)}$,
$epsilon_{munu}^{left(Lright)}$ with helicity 0.

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