Constraining Modified Theories of Gravity with Gravitational-Wave Stochastic Backgrounds

The direct discovery of gravitational waves has finally opened a new observational window on our Universe, suggesting that the population of coalescing binary black holes is larger than previously expected. These sources produce an unresolved background of gravitational waves, potentially observable by ground-based interferometers. In this Letter we investigate how modified theories of gravity, modeled using the parametrized post-Einsteinian formalism, affect the expected signal, and analyze the detectability of the resulting stochastic background by current and future ground-based interferometers. We find the constraints that Advanced LIGO would be able to set on modified theories, showing that they may significantly improve the current bounds obtained from astrophysical observations of binary pulsars.

Figure 1

The spectral energy density ${\mathrm{\Omega }}_{\mathrm{GW}}(f)$ is plotted as a function of frequency. ${\mathrm{\Omega }}_{\mathrm{GW}}(f)$ is computed in GR and in modified theories with PPE parameter $\beta =2$, and $\beta =1$, and different values of $\alpha$. The power-law integrated sensitivity curve for 1 year of integration with AdLIGO is also shown.

Figure 2

(Left) Same as Fig. 1, for values of negative $\alpha$ and different values of $\beta$, compared to the ET sensitivity curve for 1 year of observation. (Right) The SNR with which AdLIGO would detect a PPE background is plotted for some of the gravity theories considered in Sec. IV versus the integration time.

Figure 3

Contour lines corresponding to different SNR, for gravity theories with PPE parameters $\alpha >0$ and $\beta \in [0.2,2]$ assuming 1 and 3 years of integration with AdLIGO. The shaded region identifies the parameter space where the PPE parameters satisfy the bound $|\alpha u^{\beta }|<1$, while the long-dashed curves correspond to the pulsar constraint [23]. The allowed parameter space is the colored region on the right side of the pulsar constraint.

Figure 4

(Top) Values of $\alpha$ and $\beta$ yielding ${\mathcal{R}}_{\mathrm{PL}}=1$ and ${\mathcal{R}}_{\mathrm{PPE}}=1$, computed for AdLIGO with 1 and 3 years of integration. The long-dashed line and the shaded region correspond to the pulsar constraints and the parameter space where $|\alpha u^{\beta }|<1$, respectively. The green curves represent the contour line for the GWB detectable with $\mathrm{SNR}=3$ and 5. (Bottom) Likelihood ratios ${\mathcal{R}}_{\mathrm{PPE}}$ and ${\mathcal{R}}_{\mathrm{PL}}$, computed for ET as a function of the integration time, for PPE models with $\alpha =0.1$ and $\beta =(2,1.5)$.