On gravitational waves in spacetimes with a nonvanishing cosmological constant

Abstract

We study the effect of a cosmological constant Λ on the propagation and detection of gravitational waves. To this purpose we investigate the linearised Einstein's equations with terms up to linear order in Λ in a de Sitter and an anti-de Sitter background spacetime. In this framework the cosmological term does not induce changes in the polarization states of the waves, whereas the amplitude gets modified with terms depending on Λ. Moreover, if a source emits a periodic waveform, its periodicity as measured by a distant observer gets modified. These effects are, however, extremely tiny and thus well below the detectability by some twenty orders of magnitude within present gravitational wave detectors such as LIGO or future planned ones such as LISA.

Gravitational waves inf(R,T)andf(R,TAlves1, Moraes2, Araújo3 et al. 2016Phys. Rev. D1210530View full textAdd to dashboardCite

“…As it is well known, Λ does not introduce any additional polarization states for GWs [40]. Therefore, we can conclude that GWs in the f (R, T φ ) = −R/4 + 2λT φ theory have only the two usual polarizations of GR, i.e., + and ×.…”

“…However, it has already been shown that a CC does not introduce any additional polarization states for GWs (see Ref. [40]). …”

f(R) gravity with torsion and the Immirzi field: Signature for gravitational wave detection

“…we compare the trace of (29) with (30), it turns out that the scalar perturbation δφ has to vanish identically. Therefore, as it can be seen by (37) and (38), this condition compels the breathing mode to disappear as well and allows us to rescue the traceless condition oñ h µν . Thus, the two standard polarizations are restored, in agreement with the Palatini formulation of gravitational waves [36,37].…”

“…Therefore, as it can be seen by (37) and (38), this condition compels the breathing mode to disappear as well and allows us to rescue the traceless condition oñ h µν . Thus, the two standard polarizations are restored, in agreement with the Palatini formulation of gravitational waves [36,37]. Furthermore, since the geometrical scalar perturbation δφ is forced to vanish in linearized theory, the contorsion tensor simply reduces to a completely antisymmetric tensor, that is:…”

Gravitational wave polarization modes inf(R)theories

“…If f (R) = αR 2 , it can be shown that the associated theory actually corresponds to GR with a cosmological constant [26], which yields the two usual tensorial polarization modes + and × [27].…”