How do you find that the mass must increase with a expansion? To me it should be the other way, the more distance between masses, the lesser the overall gravity (possibly definable as being of one set magnitude, relative the mass existing, getting 'stretched out' by a expansion). Only if you can prove that there is more mass coming into existence can you define the mass per volume as growing, and if that was true then gravity between masses should? I don't know there what would be right, stay constant possibly?

As it is the 'mass versus gravity' we can measure, inside a galaxy or solar system, should be more or less constant, as the expansion is defined to be to 'weak' to oppose the suns etc gravity, holding together that galaxy, solar system etc. It's between galaxies the (accelerating) expansion is presumed to exist as I've seen it.

There are three 'shapes' suggested depending on matter density, 'positively curved' as a ball, 'negatively curved' as a saddle, or 'flat'. The one that seems to fit best, so far, is the 'flat' model in where a universe can be defined as 'stretching out' forever in all directions, That is the shape of our universe, accelerating its expansion, as far as I get the mainstream definition.

"The CMB holds clues to the nature and distribution of structure in the Universe, and the average density of this matter plays a key role in determining the geometry of the Universe. The geometry of the Universe can take on one of three shapes: it can be curved like the surface of a ball and finite in extent (positively curved); curved like a saddle and infinite in extent (negatively curved), or it can be flat and infinite. The geometry and density of the Universe are related in such a way that, if the average density of matter in the Universe is found to be less than the so-called critical density (roughly equal to 6 hydrogen atoms per cubic metre) the Universe is open and infinite. If the density is greater than the critical density the Universe is closed and finite. If the density just equals the critical density, the Universe is flat.

Cosmologists study the relative sizes of the oscillations of the fluid of matter and radiation at the time the CMB was released to learn more about the shape of the Universe. The oscillations translate into regions of higher and lower temperature on the CMB map, and contain information about the amount of particles present. More specifically, the shape of the Universe can be determined by looking at where the first of these oscillations appears in the power spectrum.

The location of the first oscillation corresponds to a specific size in the early Universe called the sound horizon – the maximum distance that a sound wave could have crossed from the Big Bang until the time of the CMB release. To cosmologists, the sound horizon works like a standard measure of known length. By measuring its length in the temperature fluctuations of the CMB, it is possible to determine if the Universe is flat or curved. This is expressed in terms of the parameter 'Omega_K' and is equal to zero for exactly flat space."

http://www.esa.int/Our_Activities/Space_Science/Planck/History_of_cosmic_structure_formation And.

"At large look-back times and distances the linearity of Hubble?s law breaks down and the distances depend on the energy density of the universe. The various constituents, typically matter and radiation are considered, contribute in different ways to the energy density. Radiation ceased to be gravitationally important at a redshift of about z=1000, a time from which we can only measure the cosmic microwave background radiation. Another component is the famous cosmological constant introduced by Albert Einstein to reconcile the solutions of his equations with a static universe. He later abandoned this term, when Edwin Hubble discovered the general expansion of the universe. For many decades the cosmological constant was not considered in the world models as there was no obvious reason to include it and as it was not possible to connect it to any particle theory. In modern terms, it represents the contribution of the vacuum energy (Carroll et al. 1992). "

http://www.eso.org/~bleibund/papers/EPN/epn.html Now, that last statement about a proved 'vacuum energy' is worthy of a thread of its own, but the rest seems coherent enough to me

" The WMAP spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were flat, the brightest microwave background fluctuations (or "spots") would be about one degree across. If the universe were open, the spots would be less than one degree across. If the universe were closed, the brightest spots would be greater than one degree across.

Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."

http://map.gsfc.nasa.gov/universe/uni_shape.html