Using the Newman−Penrose formalism, we obtain the explicit expressions for the polarization modes of weak, plane gravitational waves with a massive graviton. Our analysis is restricted for a specific bimetric theory whose term of mass, for the graviton, appears as an effective extra contribution to the stress-energy tensor. We obtain for such kind of theory that the extra states of polarization have amplitude several orders of magnitude smaller than the polarizations purely general relativity (GR), h + and h × , in the VIRGO−LIGO frequency band. This result appears using the best limit to the graviton mass inferred from solar system observations and if we consider that all the components of the metric perturbation have the same amplitude h. However, if we consider low frequency gravitational waves (e.g., f GW ∼ 10 −7 Hz), the extra polarization states produce similar Newman−Penrose amplitudes that the polarization states purely GR. This particular characteristic of the bimetric theory studied here could be used, for example, to directly impose limits on the mass of the graviton from future experiments that study the cosmic microwave background (CMB).

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In this work, we consider the stochastic background of gravitational waves (SBGWs) produced by pre‐galactic stars, which form black holes in scenarios of structure formation. The calculation is performed in the framework of hierarchical structure formation using a Press–Schechter‐like formalism. Our model reproduces the observed star formation rate at redshifts z≲ 6.5. The signal predicted in this work is below the sensitivity of the first generation of detectors but could be detectable by the next generation of ground‐based interferometers. Specifically, correlating two coincident advanced Laser Interferometer Gravitational‐Wave Observatory (LIGO) detectors (LIGO III interferometers), the expected signal‐to‐noise ratio (S/N) could be as high as 90 (10) for stars forming at redshift z≃ 20 with a Salpeter initial mass function with slope x= 0.35 (1.35), and if the efficiency of generation of gravitational waves, namely, εGW is close to the maximum value ∼7 × 10−4. However, the sensitivity of the future third generation of detectors as, for example, the European antenna EGO could be high enough to produce S/N > 3 same with εGW∼ 2 × 10−5. We also discuss what astrophysical information could be derived from a positive (or even negative) detection of the SBGWs investigated here.

A continuous stochastic background of gravitational waves (GWs) for burst sources is produced if the mean time interval between the occurrence of bursts is smaller than the average time duration of a single burst at the emission, i.e., the so called duty cycle must be greater than one. To evaluate the background of GWs produced by an ensemble of sources, during their formation, for example, one needs to know the average energy flux emitted during the formation of a single object and the formation rate of such objects as well. In many cases the energy flux emitted during an event of production of GWs is not known in detail, only characteristic values for the dimensionless amplitude and frequencies are known. Here we present a shortcut to calculate stochastic backgrounds of GWs produced from cosmological sources. For this approach it is not necessary to know in detail the energy flux emitted at each frequency. Knowing the characteristic values for the "lumped" dimensionless amplitude and frequency we show that it is possible to calculate the stochastic background of GWs produced by an ensemble of sources. 04.30.Db, 02.50.Ey, 98.70.Vc

Cosmological Gravitational Waves (GWs) are usually associated with the transverse-traceless part of the metric perturbations in the context of the theory of cosmological perturbations. These modes are just the usual polarizations '+' and '×' which appear in the general relativity theory. However, in the majority of the alternative theories of gravity, GWs can present more than these two polarization states. In this context, the Newman-Penrose formalism is particularly suitable for evaluating the number of non-null GW modes. In the present work we intend to take into account these extra polarization states for cosmological GWs in alternative theories of gravity. As an application, we derive the dynamical equations for cosmological GWs for two specific theories, namely, a general scalar-tensor theory which presents four polarization states and a massive bimetric theory which is in the most general case with six polarization states for GWs. However, the mathematical tool presented here is quite general, so it can be used to study cosmological perturbations in all metric theories of gravity.