GW diagnostics

also the interior of compact objects and are much less affected by the astrophysical environment [1532]. Thus, they are best suited to constraining all classes of ECOs.

GW tests based on the ringdown phase The remnant of a binary merger is a highly

distorted object that approaches a stationary configuration by emitting GWs during the “ringdown” phase. If the remnant is a BH in GR, the ringdown can be modeled as a superposition of damped sinusoids described by the quasinormal modes (QNMs) of the BH [1122, 1516, 1517] (see Sec. 3.3). If the remnant is an ECO, the ringdown signal is different:

• For UCOs, the ringdown signal can be qualitatively similar to that of a BH, but the QNMs are different from their Kerr counterpart [1548–1550]. The rates of binary mergers that allow for QNM spectroscopic tests depends on the astrophysical models of BH population [1523]. The estimated rates are lower than 1/yr for current detectors even at design sensitivity. On the other hand, rates are higher for third-generation, Earth-based detectors and range between a few to 100 events per year for LISA, depending on the astrophysical model [1523]. Even if the ringdown frequencies of a single source are hard to measure with current detectors, coherent mode stacking methods using multiple sources may enhance the ability of aLIGO/aVirgo to perform BH spectroscopy [1546]. Such procedure is dependent upon careful control of the dependence of ringdown in alternative theories on the parameters of the system (mass, spin, etc).

• For ClePhOs, the prompt post-merger ringdown signal is identical to that of a BH, because it excited at the light ring [1551, 1553]. However, ClePhOs generically support quasi-bound trapped modes [1758,1759] which produce a modulated train of pulses at late times. The frequency and damping time of this sequence of pulses is described by the QNMs of the ClePhO (which are usually completely different from those of the corresponding BH) [1760, 1761]. These modes were dubbed “GW echoes” and appear after a delay time that, in many models, scales as τecho ∼ M log(1 − 2M/R) [1552]. Such logarithmic dependence is key to allow

for tests of Planckian corrections at the horizon scale [1552, 1553, 1762]. Models of ultracompact stars provide GW echoes with a different scaling [1665, 1763], the latter being a possible smoking gun of exotic state of matter in the merger remnant. • In addition to gravitational modes, matter modes can be excited in ECOs [1506]. So far, this problem has been studied only for boson stars [1193,1196] and it is unclear whether matter QNMs would be highly redshifted for more compact ECOs [1665].

GW tests based on the inspiral phase The nature of the binary components has a

bearing also on the GW inspiral phase, chiefly through three effects:

• Multipolar structure. As a by-product of the BH uniqueness and no-hair theorems [1521], the mass and current multipole moments (M`, S`) of any

stationary, isolated BH can be written only in terms of mass M ≡ M0 and

spin χ ≡ S1/M2. The quadrupole moment of the binary components enters

the GW phase at 2PN relative order, whereas higher multipoles enter at higher PN order [915]. The multipole moments of an ECO are generically different, e.g. MECO

2 = M2Kerr + δq(χ, M/R)M3, and it is therefore possible to constrain

the dimensionless deviation δq by measuring the 2PN coefficient of the inspiral waveform. This was recently used to constrain O(χ2) parametrized deviations in δq [1323]. It should be mentioned that ECOs will generically display higher- order spin corrections in δq and that – at least for the known models of rotating ultracompact objects [1764–1766] – the multipole moments approach those of a Kerr BH in the high-compactness limit. Moreover, the quadrupole PN correction is degenerate with the spin-spin coupling. Such degeneracy can be broken using the I-Love-Q relations [1767, 1768] for ECOs, as computed for instance in the case of gravastars [1764, 1765].

• Tidal heating. In a binary coalescence the inspiral proceeds through energy and angular momentum loss in the form of GWs emitted to infinity. If the binary components are BHs, a fraction of the energy loss is due to absorption at the horizon [1769–1774]. This effect introduces a 2.5PN × log v correction to the GW phase of spinning binaries, where v is the orbital velocity. The sign of this correction depends on the spin [1770–1772], since highly spinning BHs can amplify radiation due to superradiance [1156]. In the absence of a horizon, GWs are not expected to be absorbed significantly, and tidal heating is negligible [1696, 1775]. Highly

spinning supermassive binaries detectable by LISA will provide a golden test of this effect [1775].

• Tidal deformability. The gravitational field of the companion induces tidal deformations, which produce an effect at 5PN relative order, proportional to the so- called tidal Love numbers of the object [918]. Remarkably, the tidal Love numbers of a BH are identically zero for static BHs [1776–1779], and for spinning BHs to first order in the spin [1780–1782], and to second order in the axisymmetric perturbations [1781]. On the other hand, the tidal Love numbers of ECOs are small but finite [1764,1765, 1783, 1784]. Thus, the nature of ECOs can be probed by measuring the tidal deformability, similarly to what is done to infer the nuclear equation of state in NSBs [21, 1785, 1786]. Analysis of the LIGO data shows that interesting bounds on the tidal deformability can be imposed already, to the level that some boson star models (approximated through a polytropic fluid) can be excluded [1787]. The tidal Love numbers of a ClePhO vanish logarithmically in the BH limit [1784], providing a way to probe horizon scales. For Planckian corrections near the horizon, the tidal Love numbers are about 4 orders of magnitude smaller than those of a NS. It is therefore expected that current and future ground-based detectors will not be sensitive enough to detect such small effect, while LISA might be able to measure the tidal deformability of highly-spinning supermassive binaries [1775].

Finally, it is possible that ECOs’ low-frequency modes are excited during the inspiral, leading to resonances in the emitted GW flux [1549,1788,1789]. Low-frequency modes certainly arise in the gravitational sector, as we discussed already. In addition, fluid modes at low frequency can also be excited, although this issue is poorly studied.

Challenges in modeling ECO coalescence waveforms With the notable exception of

boson stars [1678], very little is known about the dynamical formation of isolated ECOs or about their coalescence. While the early inspiral and post-merger phases can be modelled within a PN expansion and perturbation theory, respectively, searches for ECO coalescence require a full inspiral-merger-ringdown waveform. Some combination of numerical and semianalytical techniques – analog to what is done to model precisely the waveform of BH binaries [1101,1111,1297] – is missing.

Concerning the post-merger ringdown part alone, it is important to develop accurate templates of GW echoes. While considerable progress has been recently done [1760, 1790–1796], a complete template which is both accurate and practical is missing. This is crucial to improve current searches for echoes in LIGO/Virgo data [1762,1797–1803]. Model-independent burst searches have recently been reported, and will be instrumental in the absence of compelling models [1804].

5. The dark matter connection

López

The nature and properties of DM and dark energy in the Universe are among the outstanding open issues of modern Cosmology. They seem to be the responsible agents for the formation of large scale structure and the present accelerated phase of the cosmic expansion. Quite surprisingly, there is a concordance model that fits all available set of observations at hand. This model is dubbed ΛCDM because it assumes that the main matter components at late times are in the form of a cosmological constant for the dark energy [1805,1806] and a pressureless component known as cold DM [1807]. These two assumptions, together with the theoretical basis for GR, make up a consistent physical view of the Universe [639].

The nature of the missing mass in the Universe has proven difficult to determine, because it interacts very feebly with ordinary matter. Very little is known about the fundamental nature of DM, and models range from ultralight bosons with masses ∼ 10−22 _{eV to BHs with masses of order 10 M}

. Looking for matter with unknown

properties is extremely challenging, and explains to a good extent why DM has never been directly detected in any experiment so far. However, the equivalence principle upon which GR stands – tested to remarkable accuracy with known matter – offers a solid starting point. All forms of energy gravitate and fall similarly in an external gravitational field. Thus, gravitational physics can help us unlock the mystery of DM: even if blind to other interactions, it should still “see” gravity. The feebleness with which DM interacts with baryonic matter, along with its small density in local astrophysical environments poses the question of how to look for DM signals with GWs.

5.1. BHs as DM

In light of the LIGO discoveries there has been a revival of interest in the possibility that DM could be composed of BHs with masses in the range 1 − 100M

[227,230,286,1808,1809]. To generate enough such BHs to be DM, they would need to be produced from the collapse of large primordial density fluctuations [285,1810,1811]. The distribution of the BH masses that form depends on the model of inflation [1812]. Such BHs can be produced with sufficiently large masses that they would not have evaporated by the current epoch. Alternatively, DM could be composed of ultracompact horizonless objects for which Hawking radiation is suppressed [1813]. Different formation scenarios and constraints on such objects were reviewed in Chapter I, Section6.

If all of the DM is composed of such heavy compact objects a key signature is the frequency of microlensing events [1814]. Microlensing is the amplification, for a short period of time, of the light from a star when a compact object passes close to the line of sight between us and the star. How frequent and how strong these events will be, depends on the distribution of BH masses [1815–1817]. It has been claimed that DM composed entirely of primordial BHs in this mass range is excluded entirely by microlensing [285]; however, such study assumed that the BH mass distribution was a delta function. If the mass distribution is broadened the tension with the microlensing

data weakens [319,320,1818], although whether realistic models can be compatible with the data remains a subject of debate [157]. Further observational signatures include the dynamical heating of dwarf galaxies, through two body interactions between BHs and stars [228, 316], electromagnetic signatures if regions of high BH density also have high gas densities (such as the center of the galaxy) [318, 1819], constraints from the CMB due to energy injection into the plasma in the early universe [312, 314] and from the (absence of) a stochastic background of GWs [1809].

At the very least primordial BHs in the LIGO mass range can be a component of the DM in our universe. Future GW observations determining the mass and spatial distribution of BHs in our galaxy will be key to testing this hypothesis.