Summary of what I think your introduction is about:

There is a model, LCDM, for the density profile of the location of
dark matter in a galaxy.  This model predicts that you should see a
cusp, if there aren't baryonic effects.  You have a galaxy without
baryonic effects, and you want to see if galactic observations are
consistent with this density profile.  You hope to do this using ABC,
which is some form of likelihood free inference.

General Comments:

Overall I think this section motivates the work you are doing really
well, but I felt like I needed to do a bit of work while reading
the introduction to put the pieces together.  All of the sentences are
a good length, and I never get lost in them, but I think reordering
some of the information could help focus on the work you are doing and get the
reader more excited.  I think all of the information for a non-astro
person to understand the paper is present, and I think defining a few
things a little more explicitly would help.

Specific Comments:

Use of "dark matter profile":

You use the term phrase "dark matter profile" and
sometimes "dark matter density profile" a lot, but you never give a
specific definition.  I think the dark matter density profile is some
function that represents the density of the dark matter throughout the
3D space of a galaxy, but it took me a while to figure this out, and
I'm still not 100% sure that I'm right.

I think early in the paper giving a good technical definition and
saying you will refer to it as the "dark matter profile" for the rest
of the paper would help a lot.  This helps with the defining before
using problem, and also won't distract people with wondering if dark
matter profile and dark matter density profile are the same thing.

These issues are all related to Bem's idea of using consistent
language and defining technical terms.


Putting ABC up front:

The idea behind the paper seems to be using ABC to solve some problem
in astrophyics, but you do not mention the method until halfway
through the last paragraph.

I wonder if you could use a form suggested by Bem where the
information is "hour-glass shaped" in the sense that it starts at a
very high-level, and slowly goes further into the details.

To accomplish this, you might be able to have a new first paragraph
that says what you are going to do in a less specific way. Perhaps:

1) The standard model for cosmic evolution is LCDM
2) This model makes predictions about the density profile of dark
matter in galaxies (Maybe you can define this here)
3) These predictions have implications about the parameters governing
galactic observations
4) The relationship between these parameters and those observations is
complex (maybe you can say why this relationship is complex?)
5) ABC methods are well suited for inferring parameters when the
relationship between parameters and observations is complex.
6) In this paper we use ABC to make inferences about parameters to see
if observations are consistent with LCDM.

Some of the ideas might need a couple of sentences, but I got
the impression that this chain of ideas is the real motivation of this
paper.  It points out the cool new method you are using, and also
brings up the idea that you can use that method to check, or
contradict, implications of the standard model, which seems really
exciting to me.

After an introductory paragraph like this, I think all of the other
paragraphs work pretty well without too much modification.  I think
the background information doesn't seem too long, but presents most of
the astrophyrics information needed to understand what you are doing.


Baryonic Effects:

I couldn't really tell what these were in the section.  I got the
point that the predictions you are talking about only make sense in
the absences of baryonic effects.  If it's important that I understand
what those are, maybe you should define it up front, but if I don't
need it later, it's probably fine the way it is.