Fingerprints of freeze-in dark matter in an early matter-dominated era

Dear Editor,

We thank the Referee for making valuable comments and suggestions. In the revised manuscript we address the issues raised by the Referee by adding clarifications to the text in appropriate places and updating the figures and references.

The detailed response to the Referee’s comments and the corresponding revisions made in the manuscript are itemized below:

1. In the first paragraph of the Introduction (page 2) we rephrase the sentence "Such a tiny interaction strength renders freeze-in dark matter invisible to the experiments" to "Such a tiny interaction strength makes freeze-in dark matter models challenging to detect at the experiments compared to the usual WIMP scenarios. For recent attempts to detect FIMP, see for example [30–33]." We have also added the relevant references including 1904.07915 and 1807.01730.

2. We have included 1807.01730 in the list of references (Ref [31]) in contexts of detection of freeze-in scenarios (Introduction, page 2, end of 1st pargraph) and the dark photon portal models (Introduction, page 3, 2nd paragraph).

3. In accordance with the Referee's suggestion we have updated Table 1 with an additional column detailing the origin of the dissipation rates with appropriate references.

4. We have cited 2007.04328 in appropriate places and explicitly mention where we have reproduced their results (page 5, after Eq.2.4) and where we differ from their parametrizations (footnote 3, page 4).

5. The discussion on page 7 (page 8 in the updated manuscript) is clarified as per the Referee's suggestion. In the updated manuscript we choose benchmark parameters such that the dark matter yield approximately saturates the observed relic abundance in the radiation dominated universe. In contrast the DM remains under-abundant in a matter dominated universe for the same set of parameters. We have introduced a new Eq.3.7 to estimate the dilution of the DM relic density in the EMD scenario. This clearly indicates that a larger coupling strength between the DM and the SM particles would be required to reproduce the correct freeze-in relic density for this case. We have modified Fig.1 and Fig.2 with new set of parameters to clarify this point.

6. As commented by the Referee, we have indeed checked that additional processes do not spoil the existing freeze-in condition. In particluar, we ensure that the dark photon does not achieve thermal equilibrium via the inverse decay processes. As a consequence, number changing processes within the dark sector can be safely neglected. In the manuscript we elucidate this point in two different places for two scenarios, (i) M_A'> 2m_\chi (page 9, paragraph starting with "In this range of parameters...") and (ii) M_A'< 2m_\chi (page 10, last paragraph of section 4).

7. We thank the Referee for pointing out the references on supernova bounds. We indeed found out that the constraints given in the 1st reference (1901.08596) are relevant for our parameter space. We have included it in the right panel of Fig.3. On the other hand we observe that the limits given in the 2nd reference (1905.09284) do not provide any additional constraint than the existing bound on the parameter space relevant for our paper.

We hope that the modified manuscript will be considered for publication.

Sincerely, Avik Banerjee (On behalf of all authors)

Point by point list of changes in the revised manuscript:

1. The last sentence of the first paragraph of the Introduction (page 2) is rephrased in accordance with the Refree's comment.

2. We have included 1509.01598 (Ref[30]), 1807.01730(Ref [31]), and 1904.07915 (Ref[32]) in the list of references.

3. As per the Referee's suggestion we have updated Table 1 (page 4) with an additional column detailing the origin of the dissipation rates with appropriate references.

4. We have cited 2007.04328 in appropriate places and explicitly mention where we have reproduced their results (page 5, after Eq.2.4) and where we differ from their parametrizations (footnote 3, page 4).

5. The discussion on page 8 is expanded with a new equation (Eq.3.7) for clarification as per the Referee's suggestion. In the same context, Fig.1 and Fig.2 are also modified with new set of parameters for the ease of discussion. The figure captions are updated accordingly.

6. Text added in page 9, paragraph starting with "In this range of parameters..." and page 10, last paragraph of section 4 in context of the point 6 raised by the Referee.

7. The right panel of Fig.3 is updated with a new constraint (purple region) given in 1901.08596 (Ref[106]), as suggested by the Referee.