Tidal effects in gravitational waves from neutron stars in scalar-tensor theories of gravity

List of changes - We corrected the label of citation [64] in line 104. - We added the definition of $g^{LP}$ in eq 17 as the product of metrics with the string of indices corresponding to the values of L and P \begin{equation} g^{L P}=\prod_{n=1}^{\ell} g^{l_n p_n}. \end{equation} - We corrected an overall minus sign in eq. 25a. - At the level of the field equations in section 2.5 we considered both the point particle and tidal contributions to the action. Then we discussed in sec. 3.1 based on the results of arxiv 2302.08480 that the tidal contributions to the near zone fields were of higher PN order and our results then only captured the tidal contribution to the dynamics directly coming from the tidal action in sec. 3.2. However a correction was pointed out to us for arxiv 2302.08480 featuring an improper treatment of the tidal contribution to the near zone fields, recovering that they are vanishing at 1PN which should not be the case. Luckily both in arxiv 2302.08480 and this manuscript we did consider the contribution directly from the tidal action and as is shown in appendix A of arxiv 2310.19679 this yields the same results as letting the tidal corrections enter via the near zone fields at the PN order we are considering. Therefore our results do not change but we removed the consideration of the tidal contributions at the level of the field equations in eq. 18-23 and only considered the tidal corrections at the level of the Lagrangian in sec. 3.2, referring to arxiv 2310.19679 at the beginning of 2.5 to verify that these methods are indeed equivalent. - We added the footnote ‘This type of tidal contribution entering via the relative acceleration due to derivatives to the point particlemultipoles did not contribute in our discussion of the scalar waveform in the previous section 4.1 as they are higher PN order in that case’ in sec. 4.2. - We rewrote the first sentence of sec. 4.5 to ‘Generally, the tidal corrections compared to the GR contributions in the radiation are small. However, during the many GW cycles in the inspiral these corrections accumulate in the phase evolution’. - We added a reference to the expressions of the coefficients below eq (78) and corrected the subscript ‘2’ in eq (80) and eq. B.21 - We changed the labelling of the legend of the bottom plot in Fig.5 to be consistent with the plots above. - Table 1 and 2 were not displayed correctly, usepackage mutirow was added. - We added an additional paragraph to our discussion in sec. 5.5.3 on the hierarchy of the different tidal contributions in the Fourier phase, highlighting this is different than one would expect from purely looking at their relative PN order, see also our response to the referee rapport. - We changed the numbering of the eq. in the appendix to label per section. - We corrected the typo’s as suggested by the referee: * Lines 68-69: "a significant research efforts". Either remove "a" or efforts →effort. * Line 238: charactersitics →characteristics. * Line 364: Greens →Green's. * Line 674: Inverted quotation marks, 'unambiguos BH candidates'.