  Observations of gravitational wave (GW) signals produced by coalescing binary
neutron stars (NS), like the GW event GW170817, can be exploited to constrain
the equation of state (EoS) of matter in the stars' inner core. The information
on the internal structure and composition of the stars is encoded in their
tidal Love numbers, which leave an imprint in the waveform of the GW signal
emitted from the binary during the late inspiral phase. We extended the theory
of tidal deformations of compact objects by computing the spin-tidal
corrections that affect the dynamics and the GW emission of a binary system at
the leading post-Newtonian (PN) order and to linear order in the spin. These
corrections are divided into two classes: terms due to the coupling between the
standard tidal Love numbers and the spins of the objects, and terms depending
on the rotational tidal Love numbers. Both enter the GW phase at 6.5PN order.
We analysed the impact of the spin-tidal couplings by estimating the parameter
bias induced on GW170817-like events, assuming second- and third-generation
ground based interferometers. If relatively high spinning ($\chi \gtrsim 0.1$)
NS binaries exist in nature, these effects might be observed by the next
generation of detectors. Lastly, we proved the feasibility of solving the
so-called inverse stellar problem using GW detections, i.e., reconstructing the
EoS from the measurement of NS masses and tidal Love numbers. Our results show
that few observations of coalescing binary NS by a network of advanced
detectors would allow us to put interesting constraints on the phenomenological
parameters of a piecewise polytropic representation of the EoS, and to perform
a model selection among the realistic EoS proposed in the literature.

General Relativity and Quantum Cosmology;High Energy Astrophysical Phenomena