Consider the energy of a quantum system(adsbygoogle = window.adsbygoogle || []).push({});

[itex] E_t = h f [/itex]

[itex] E_t = \frac{h}{\Delta t} [/itex]

where [itex]\Delta t[/itex] is the period of the quantum system in cosmological time [itex]t[/itex].

What is the energy of the system in co-moving co-ordinates?

In co-moving co-ordinates time is measured in conformal time [itex]\tau[/itex] given by

[itex] \Delta \tau = \frac{\Delta t}{a(t)} [/itex]

Thus the energy of the co-moving quantum system is given by

[itex] E_\tau = \frac{h}{\Delta \tau} [/itex]

[itex] E_\tau = a(t) \frac{h}{\Delta t} [/itex]

[itex] E_\tau = a(t) E_t [/itex]

Is this correct?

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# Energy in co-moving co-ordinates?

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