# Understanding the expansion of the universe

The universe is not only thought to be expanding but the rate at which it is expanding is said to be accelerating. Which of these models (if any) is a correct way of looking at this?

Model A: Let’s pretend the universe is 100 units across and expanding by 1% per year. So each year, each of the 100 units grows to become 1.01 units and at the end of the first year, the universe is 101 units across. In the next year, if each unit grows again to become 1.01 units, then the universe will be 102.01 units across. It grew 1 unit in year 1 and 1.01 units in year two and so on -the absolute size of the universe is expanding and the expansion is accelerating.

Model B: Similar to the above except the universe is expanding by 1% in the first year, 1.1% in the second, 1.2% in the third. The universe is expanding, the expansion is accelerating and the same applies to every unit length within the universe.

• I don't believe the acceleration is completely accepted: Inhomogenous cosmologies, perhaps advocated most vigorously by Laura Mersini-Houghton (who predicted a void and other phenomena subsequently verified by the WMAP project), can relate local differences in the expansion rate as simulating (or exaggerating) an acceleration. Jun 22, 2021 at 19:15

According to mainstream cosmology even case $$A$$ can be an accelerating universe.
If there is exponential growth of the scale factor $$a$$ as in case $$A$$, $$a=a_0e^{Ht}$$ where $$H$$ is the Hubble parameter, assumed constant here.
the decelaration parameter $$q$$
works out negative even for a constant $$H$$. Negative $$q$$ means acceleration, as explained in the link, so the universe can be 'accelerating' even if the Hubble parameter is constant.