Weak field limit and gravitational waves in higher-order gravity

Abstract

We derive the weak field limit for a gravitational Lagrangian density $L_g=(R+a_0{R}^2+{\sum }_{k=1}^p{a}_{k}R{\square }^{k}R)\sqrt{-g}$ 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 $R{\square }^{k}R$ 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 $\square$ operator appearing in the gravitational Lagrangian. More specifically: the mode ${\omega }_1$, with $k^2=0$, has transverse polarizations ${\epsilon }_{\mu \nu }^{\left(+\right)}$ and ${\epsilon }_{\mu \nu }^{\left(\times \right)}$ with helicity 2; the $(p+1)$ modes ${\omega }_m$, with $k^2\ne 0$, have transverse polarizations ${\epsilon }_{\mu \nu }^{\left(1\right)}$ and non-transverse ones ${\epsilon }_{\mu \nu }^{\left(\text{TT}\right)}$, ${\epsilon }_{\mu \nu }^{\left(\text{TS}\right)}$, ${\epsilon }_{\mu \nu }^{\left(L\right)}$ with helicity 0.

arXiv comment21 pages, to appear in Int.J.Geom.Meth.Mod.Phys

References in corpus (35)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Confrontation between General Relativity and Experiment
• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The Confrontation between General Relativity and Experiment
• f(T) teleparallel gravity and cosmology
• Lecture Notes on General Relativity
• On the theory and applications of modern cosmography
• Fourth order gravity: equations, history, and applications to cosmology
• Speeding up the universe using dust with pressure
• Massive, massless and ghost modes of gravitational waves from higher-order gravity
• Second Order Scalar Invariants of the Riemann Tensor: Applications to Black Hole Spacetimes
• Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817
• Constraints on scalar-tensor theory of gravity by the recent observational results on gravitational waves
• Testing f(R)-theories using the first time derivative of the orbital period of the binary pulsars
• Newtonian, Post Newtonian and Parameterized Post Newtonian limits of f(R, G) gravity
• Test-particle dynamics in general spherically symmetric black hole spacetimes
• The Newtonian limit of fourth and higher order gravity
• Quadrupolar gravitational radiation as a test-bed for f(R)-gravity
• Gravitational waves in modified teleparallel theories of gravity
• Dark Energy and Dark Matter from an additional adiabatic fluid
• The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity
• Gravitational waves and the polarizations in Hořava gravity after GW170817
• Holographic dark matter and dark energy with second order invariants
• Gravitational waves in Einstein-Æther theory and generalized TeVeS theory after GW170817
• The gravitational energy-momentum pseudo-tensor of Higher-Order Theories of Gravity
• Cosmological dark energy effects from entanglement
• Information entropy and dark energy evolution
• The post-Minkowskian limit of f(R)-gravity
• Entangled states in quantum cosmology and the interpretation of Lambda
• Light bending in $F\left[g(\square )R\right]$ extended gravity theories
• Dark energy from Geometrothermodynamics
• Dark energy from entanglement entropy
• Entanglement inside the cosmological apparent horizon

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