A possible new cosmological redshift effect due to $\Lambda$ on traveling gravitational waves in Friedmann universes

In this paper we continue the investigation concerning the propagation of gravitational waves in a cosmological background using Laplace transform \cite{A}. We analyze the possible physical consequences of the result present in \cite{A} where it is argued that a non-vanishing positive abscissa of convergence caused by the de Sitter expansion factor $a(t)=e^{Ht}$ implies a shift in the frequencies domain of a traveling gravitational waves as measured by a comoving observer. In particular, we show that in a generic asymptotically de Sitter cosmological universe this redshift effect does also arise. Conversely, in a universe expanding with, for example, a power law expansion, this phenomenon does not happen. This physically possible new redshift effect, although negligible for the actual very low value of $\Lambda$, can have interesting physical consequences concerning for example its relation with Bose-Einstein condensation or more speculatively with the nature of the cosmological constant in terms of gravitons, as recently suggested in \cite{B} near a Bose-Einstein condensation phase.