If the uncertainty in the age of the Universe is ##\Delta t## then the Uncertainty Principle implies that it has an uncertainty in its energy ##\Delta E## given by

$$\Delta E \ \Delta t \sim h.\tag{1}$$

If this energy fluctuation excites the zero-point electromagnetic field of the vacuum then a photon is created with energy ##\Delta E## and wavelength ##\lambda## given by

$$\Delta E \sim h \frac{c}{\lambda}.\tag{2}$$

Combining Equations ##(1)## and ##(2)## we find that

$$\lambda \sim c\ \Delta t.\tag{3}$$

Now as this characteristic length ##\lambda## is the wavelength of a photon it is a proper length that expands with the Universal scale factor ##a(t)## so that

$$\lambda \sim a(t).\tag{4}$$

Combining Equations ##(3)## and ##(4)##, and taking ##\Delta t \sim t##, we arrive at a unique linear cosmology with the normalized scale factor ##a## given by

$$a(t) = \frac{t}{t_0}.$$

where ##t_0## is the current age of the Universe.

$$\Delta E \ \Delta t \sim h.\tag{1}$$

If this energy fluctuation excites the zero-point electromagnetic field of the vacuum then a photon is created with energy ##\Delta E## and wavelength ##\lambda## given by

$$\Delta E \sim h \frac{c}{\lambda}.\tag{2}$$

Combining Equations ##(1)## and ##(2)## we find that

$$\lambda \sim c\ \Delta t.\tag{3}$$

Now as this characteristic length ##\lambda## is the wavelength of a photon it is a proper length that expands with the Universal scale factor ##a(t)## so that

$$\lambda \sim a(t).\tag{4}$$

Combining Equations ##(3)## and ##(4)##, and taking ##\Delta t \sim t##, we arrive at a unique linear cosmology with the normalized scale factor ##a## given by

$$a(t) = \frac{t}{t_0}.$$

where ##t_0## is the current age of the Universe.

Last edited: