A SGWB atlHz frequencies can in principle be observed in binary pulsars as well as in Earth–Moon-like or Earth–Satellites-like systems. The binary system’s orbits indeed exhibit resonant interactions with the SGWB in some regimes. Current estimates show that such binaries permit to rule out the existence of a SGWB with XGWJ6106at frequenciesf 1lHz, with improvement toXGWJ5109 by late 2030s (Blas and Jenkins2022a,b).
5.2 Generation mechanisms
FOPTs have been done in Caprini et al. (2016), Caprini et al. (2020). Also cosmic defects can generate a cosmological SGWB which crosses the frequency window of the LISA detector. More precisely the GW signal from cosmic defects can be detected if the energy of the phase transition that created the defects is at the right scale (see Sect.7). A recent analysis to probe the ability of LISA to measure this background, considering leading models of the string networks has been done in Auclair et al. (2020). In the most optimistic case, LISA might be able to probe cosmic strings with tensions GlJOð1017Þ. It has been recently pointed out (Boileau et al.2022) that, depending on different assumptions on the astrophysical background and the galactic foreground, LISA will be able to probe cosmic strings with tensionsGlJOð10161015Þ.
The detection of any of these SGWBs from the early universe, would allow us to test high energy scales beyond the reach of particle colliders, like the Large Hadron Collider (LHC).
In Fig. 5 we collect GW cosmological signals expected to peak in the LISA frequency band and we compare them with the sensitivity of present and future GW detectors. To this end we use the PLS curves (Thrane and Romano2013) designed to graphically assess the ability of a given detector to probe SGWBs: a power-law frequency spectrum crossing these curves is detected, provided it is not masked by a greater foreground.
1015 1010 105 1 105
1018 1016 1014 1012 1010 108
f Hz
GW Energy Density vs Detector Sensitivity
Vacuum GW Cosmic Strings Axion Inflation PBH
Phase Transition
LISA
Einstein Telescope LIGO Design NANOGrav SKA DECIGO Planck LITEBird
Fig. 5 SGWB energy densityh2XGWfor different cosmological sources compared to the sensitivity of different GW detectors. As cosmological signals we have the vacuum GW contribution coming from inflation (grey dashed line) withr¼0:044 andnT¼ r=8, the signal expected in axion inflation models (cyan), the signal generated by cosmic string networks withGl¼1010(brown), the signal generated by a FOPT withvw¼0:9,a¼0:1,b=H¼50,g¼100,T¼200GeV (pink) and the signal generated at second-order by the formation mechanism of PBHs withfPBH¼1,r¼0:5,k¼kLISA(orange). For GW detectors we report the sensitivity of Planck (darker green), LITEBird (green), EPTA (blue), SKA (darker blue), LISA (red), DECIGO (purple), LIGO Design (black) and ET (darker black)
5.2.2 Astrophysical
The astrophysical SGWB results from the incoherent superposition of signals emitted by numerous unresolved astrophysical sources from the onset of stellar activity until today. As any other background of radiation, the astrophysical SGWB is quantifiable through its isotropic energy density level and through the spatial angular power spectrum encoding its anisotropy. Many different astrophysical sources contribute to the astrophysical SGWB, including SOBBHs and BNSs (Abbott et al. 2016a;
Regimbau et al. 2017; Mandic et al. 2016; Dvorkin et al. 2016a; Nakazato et al.
2016; Dvorkin et al.2016b; Evangelista and Araujo2014), merging MBBHs (Kelley et al.2017), rotating neutron stars (Surace et al.2016; Talukder et al.2014; Lasky et al. 2013), stellar core collapse (Crocker et al. 2017, 2015) and population III binaries (Kowalska et al.2012). The astrophysical information that can be extracted from the intensity and polarisation maps of the astrophysical SGWB, are the collective properties of a given population of astrophysical sources (redshift and mass distribution, local properties of galactic environment,...).
The astrophysical SGWB from BBHs is expected to be dominant in the LISA band (Dvorkin et al.2016a) and below, and may become a source of confusion noise for other sources and cosmological background emissions. Observations with LISA will allow for the study of some aspects of BBH populations that are difficult to observe with ground-based interferometers. For example, at the mHz frequencies accessible to LISA, some of the binaries may not be fully circularised, and their residual eccentricities may provide an indication to their formation channel. In particular, binaries formed through dynamical processes in dense stellar clusters can have measurable eccentricities. These can be constrained for the subset of resolved merger, and in addition the distribution of eccentricities of the entire population may also affect the resulting astrophysical SGWB.
The detection of the BNS merger by the LIGO/Virgo network (Abbott et al.
2017d, e, 2020a) and the estimated rate of mergers in the local universe of R¼ 131900 Gpc3yr1(Abbott et al.2023) led to the conclusion that in the Hz band these sources may have a comparable contribution to the astrophysical SGWB relative to BBHs (Abbott et al.2018b,2021g). We may therefore expect that their contribution to the anisotropies of the astrophysical SGWB will also be important also for LISA. While it will be difficult to disentangle the relative contributions of BBHs and BNSs to the overall astrophysical SGWB, especially in view of the large modelling uncertainty in the BNS merger rates (Chruslinska et al.2018; Giacobbo and Mapelli2019), it is interesting to note that their host galaxies are expected to have different properties. In the isolated BH formation scenario discussed e.g. in Cusin et al. (2019b), BH masses are heavily influenced by the metallicity of their progenitor stars. Specifically, metal-poor stars retain most of their mass throughout their evolution and collapse to form heavier BHs. As a consequence, these BHs form preferentially in high-redshift and/or low-mass galaxies (Lamberts et al.2016; Cao et al.2018; Mapelli et al.2018; Artale et al.2019). In contrast, NSs can also form in metal-rich environments. In view of the different clustering properties of the host galaxy populations, BBHs and BNSs can in principle give rise to very different
anisotropic components of the astrophysical SGWB (Cusin et al.2019b). Note that, to put this into practice, we need to understand better the time delays between formation and merger, which can change the host galaxy property if delays are long.
Finally, LISA will also allow one to study the astrophysical SGWB from other types of sources such as close white dwarf binaries (see e.g. Vecchio2002), which may also produce anisotropies in the galactic plane (Ungarelli and Vecchio 2001;
Kudoh and Taruya2005). We refer the reader to Amaro-Seoane et al. (2023) for an in-depth discussion on the astrophysical populations leading to this and the aforementioned astrophysical SGWBs.
5.3 Characteristics of the stochastic gravitational-wave background