We thank the referee for making useful comments and suggestions.
We have incorporated them and have marked the corresponding changes
in the text in blue fonts.

> My main impression is that the manuscript is written in a very
> confusing way, and that the authors should elaborate the text in order
> to make much more clear the physics they are studying, and frame it
> better in a cosmological context.

We have now added additional pieces of information in the manuscript,
especially in the introduction, in Sec. IV, and in the  conclusions.
We have also added an Appendix A now.

> I recommend the authors to give a careful reading to the text,
> especially the Introduction and the Conclusions. I believe those
> sections deserve to be rewritten, extending the explanations on the
> origin of the so-called 'imposed' field, the problems of magnetic
> helicity evolution in the presence of background fields and commenting
> on the concrete observational features of the system they study. Some
> points that in my view must also be cleared are

We have now added additional comments about the significance of an
imposed magnetic field and the differences compared with an initially
statistically homogeneous field, but we also emphasize the cosmological
significance of the former.

> 1) what does it mean, in a cosmological context an "imposed field"?

In an unbounded domain, a homogeneous magnetic field is really the same
as an imposed one. To clarify this, we have, on the first occurrence in
the abstract, replaced imposed by homogeneous, and have then said later
that such a field can never change and it acts therefore as an imposed
magnetic field.

> 2) why a primordial magnetic field would be homogeneous, and not
> statistically homogeneous? Does it correspond to a special
> cosmological model? which are the physical reasons for this?
> considering e.g. that a galactic scale is is very much larger than the
> horizon at the end of inflation, and as the universe evolves initially
> causally disconnected regions enter in contact, on which scales the
> field would be homogeneous?

We now address this point in the third paragraph and the beginning of
the fourth paragraph of the introduction, where we discuss the special
model under consideration and emphasize the difference to earlier work.

> 3) which processes would produce a homogeneous field in the Early
> Universe? which would be its coherent scale? In some paragraphs the
> authors refer to the magnetic field studied in their reference [16],
> is this the only one mechanism? If so, then it should be better
> explained in the text, especially in the Introduction, that the
> manuscript deals with a very specific cosmological model.

We have done this now; see the third paragraph and the beginning
of the fourth paragraph of the introduction.

> 4) The authors will study the different evolution of homogeneous and
> statistically homogeneous fields? or the evolution of a turbulent
> field superimposed on those fields? Because if the second case is what
> is studied, then there is no need to resort to cosmology, as it is a
> general problem that can be treated e.g. What would be the
> observational imprints of that evolution?

Yes, we have studied the difference between a statistically homogeneous
and a truly homogeneous field (a field with infinite correlation length),
and we have found a very relevant difference in the evolution of a helical
perturbation on top of such a field: the truly homogeneous field allows for
the non-conservation of helicity of the perturbation, which is not the case
in a statistically homogeneous field, where a helical magnetic field added
on top of the initial field decays very slowly via inverse cascade. Even if
this behavior is more general than the cosmological case which we study here,
it is of interest for cosmology. A magnetic field with a coherence scale much
larger than the Hubble horizon can play the role of a homogeneous magnetic
field in cosmology. To emphasize these points more strongly, we have added
additional sentences in Sec. IV.B; see the blue pieces of text. We also recall
that observational imprints were already mentioned in the third paragraph
of the conclusions, especially with regard to E and B polarization patterns.

> 5) To which 'periodic domain' do the authors refer, in a cosmological
> context, where magnetic helicity is not conserved?

The use of a periodic domain is a computational convenience or a tool
to compute averages over an infinitely extended domain. This point is now
made in Appendix A.

> 6) In principle, a zero-flux scale-invariant magnetic field (as
> introduced in section B) is not a homogeneous field. The authors
> consider scales shorter than the coherence length of this field, where
> it could be considered as homogeneous, and over it study the evolution
> of a fluctuating field. Which is the difference between this field and
> an 'imposed field'? what would be the physical meaning of an 'imposed
> field' in cosmology? (again the first question I raised).

The difference between the two cases is tremendous, which is not sufficiently
appreciated in the cosmology community. To emphasize this point more strongly
we have made various additions in Sec. IV.B.

> I know the works of Berger & Field on conservation of magnetic
> helicity, but for the benefit of readers unaware of them, I believe
> that a better discussion on the conservation of mh in the presence of
> homogeneous fields should be provided.

In paragraph 2 of Sect. III.B, we now refer to Appendix A, where we
recall the basic derivation of magnetic helicity evolution in the presence
of an imposed magnetic field. Starting with da/dt = uxb + uxB0 - eta*j, we
have d<a.b>/dt = 2<b.(uxb)> + 2<b.(uxB0)> - 2*eta*<j.b>, so, unlike the
first term, which vanishes, the second one doesn't. This is the basic point.