# Is the Big Bang inflation caused by Dark Energy

The rate of expansion of the universe after the Big Bang is described as Inflation. It is stated as being initially very fast then slowed. But the expansion is still continuing. Some say expansion is currently powered by Dark Energy. The equations unlike gravity say that the rate appears to be linearly proportional to distance, like Hooke's Law for springs. Initially the universe was very small, so if the spring constant is dependent on the size of the universe, could this explain the inflation? What experiment could be devised to test this?

The expansion caused by a cosmological constant (a particularly simple version of dark energy) is not exactly Hooke's law, it is an expansion that maintains a fixed Hubble constant. So this means $\mathrm{d}a/\mathrm{d}t = Ha$, for scale parameter $a$ and constant $H$. The solution is exponentially growing in time. Hooke's law (without the minus sign) would have the acceleration $\mathrm{d}^2 a/\mathrm{d}t^2$ being proportional to $a$, which permits more complicated solutions, but you're right it certainly has similarities if one picks out the exponentially growing solution.