Momentum and energy of photon

Question

Does the momentum and energy of photon change when it travels from distant galaxies through the Space?

Answer 1

A photon traveling through intergalactic distances in space does lose energy and momentum, due to spacetime expansion (universal expansion). This is termed cosmological redshift where the wavelength at which the light is originally emitted becomes lengthened as it travels through an expanding universe, meaning the photon loses energy.

The energy of a photon is given by $$E = \frac{hc}{\lambda}$$ where $h$ is Planck’s constant, $c$ is the speed of light, and $\lambda$ is the photon’s wavelength. So if $\lambda$ increases, energy decreases.

The momentum of photon is $$p=\frac{E}{c}=\frac{h}{\lambda}$$ which means it also loses momentum due to universal expansion.

Here we assume the photon moves through empty space and does not interact (and redshift) with gravitational fields of massive objects. That is, energy loss is due to universal expansion only (the photon "interacts" with the expanding universe only).