Abstract
The detection of gravitational wave modes and polarizations could constitute an extremely important signature to discriminate among different theories of gravity. According to this statement, it is possible to prove that higher-order non-local gravity has formally the same gravitational spectrum of higher-order local gravity. In particular, we consider the cases of f(R,□R,□2R,⋯,□nR)=R+∑i=1nαiR□iR gravity, linear with respect to both R and □iR and f(R,□R)=R+α(□R)2 gravity, quadratic with respect to □R, where it is demonstrated the graviton amplitude changes if compared with General Relativity. We also obtain the gravitational spectrum of higher-order non-local gravity f(R,□−1R,□−2R,⋯,□−nR)=R+∑i=1nαiR□−iR. In this case, we have three state of polarization and n+3 oscillation modes. More in detail, it is possible to derive two transverse tensor (+) and (×) standard polarization modes of frequency ω1, massless and with 2-helicity; n+1 further scalar modes of frequency ω2,…,ωn+2, massive and with 0-helicity, each of which has the same mixed polarization, partly longitudinal and partly transverse.
Highlights
Apart from its remarkable success to interprete today cosmological observations, the Λ-Cold Dark Matter (ΛCDM) model still lacks in according a satisfactory explanation to the issue why the energy density of the cosmological constant is so small if compared to the vacuum energy of the Standard Model (SM) of particle physics
The number of gravitational waves (GWs) polarizations depends on the considered theory of gravity
We have compared oscillation modes of gravitational waves derived from local f R, R, 2R, · · ·, nR models with those derived from non-local f R, −1R, −2R, · · ·, −nR models
Summary
Apart from its remarkable success to interprete today cosmological observations, the Λ-Cold Dark Matter (ΛCDM) model still lacks in according a satisfactory explanation to the issue why the energy density of the cosmological constant is so small if compared to the vacuum energy of the Standard Model (SM) of particle physics. The today observed equivalence, in order of magnitude, of dark matter and dark energy escapes any general explanation but requires the introduction of very strict fine tunings to be addressed Starting from these facts, the cosmological constant cannot be assumed fully responsible for the whole accelerated dynamics, and one has seriously to take into account the incapability, up today, to find final dark matter candidates or a self-consistent quantum theory of gravity. Further scalar fields, having a geometric or a matter origin, could be useful to describe coherently cosmic dynamics at any scale Besides these issue, any self-consistent theory of gravity, in order to be renormalizable and unitary, has to face the problem of non-locality.
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