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When light is red shifted from distant galaxies, the photons have lost energy. When dark energy pushes objects apart, those objects have gained energy from a larger gravitational potential. Is the amount of energy that dark energy applies to push objects apart equal to the amount of energy lost because light from distant galaxies is red shifted?

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    $\begingroup$ When it comes to cosmological scale beware that an intuitive balance of energy (conservation) might not be the case. I am still in doubt even by taking into account dark energy, that by the way is of unknown origin and might violate conservation anyway. Perhaps better suited for Physics SE. $\endgroup$ – Alchimista Aug 13 at 9:21
  • $\begingroup$ Remember that "dark energy" doesn't necessarily mean it's energy subject to our currently known four forces (EM, grav, strong & weak nuclear). As such we can't speculate on how it might affect photons -- other than that we don't seem to observe any untoward effects. $\endgroup$ – Carl Witthoft Aug 13 at 15:29
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Is the amount of energy that dark energy applies to push objects apart equal to the amount of energy lost because light from distant galaxies is red shifted?

No, dark energy existed prior to the expansion and the shift towards blue or red is based on the direction of movement of the emitter relative to the observer, so the amount isn't equal.

Sources:

  • Wikipedia: Dark Energy - "Change in expansion over time":

    "Recent results from the Hubble Space Telescope Higher-Z Team indicate that dark energy has been present for at least 9 billion years and during the period preceding cosmic acceleration.".

  • Wikipedia: "Integrated Sachs–Wolfe effect":

    "The integrated Sachs–Wolfe (ISW) effect is also caused by gravitational redshift, but it occurs between the surface of last scattering and the Earth, so it is not part of the primordial CMB. It occurs when the Universe is dominated in its energy density by something other than matter. If the Universe is dominated by matter, then large-scale gravitational potential energy wells and hills do not evolve significantly. If the Universe is dominated by radiation, or by dark energy, though, those potentials do evolve, subtly changing the energy of photons passing through them.

    There are two contributions to the ISW effect. The "early-time" ISW occurs immediately after the (non-integrated) Sachs–Wolfe effect produces the primordial CMB, as photons course through density fluctuations while there is still enough radiation around to affect the Universe's expansion. Although it is physically the same as the late-time ISW, for observational purposes it is usually lumped in with the primordial CMB, since the matter fluctuations that cause it are in practice undetectable.".

  • Wikipedia: "Theories of Dark Energy":

    The Equation of State (EoS) of Dark Energy for 4 common models by Redshift:

    Dark Energy EoS Models
                A: CPL Model   B: Jassal Model   C: Barboza & Alcaniz Model   D: Wetterich Model

This question was closed on our Physics.SE site: "Could some Red and Blue shifts be the result of light passing through “dark matter”? [closed]", while this: "Redshifted Photon Energy" was not.

See also:

  • "New Aspects of Photon Propagation in Expanding Universes" (Oct 6 2016), by H.-J. Fahr and M. Heyl.

  • Wikipedia: "Friedmann equations":

    "The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity.".

  • Wikipedia: "Cosmic Expansion History":

    Since the densities of various species scale as different powers of $a$, e.g. $a^{-3}$ for matter etc., the Friedmann equation can be conveniently rewritten in terms of the various density parameters as

    $$H(a)\equiv {\frac {\dot {a}}{a}}=H_{0}{\sqrt {(\Omega _{c}+\Omega _{b})a^{-3}+\Omega _{\text{rad}}a^{-4}+\Omega _{k}a^{-2}+\Omega _{DE}a^{-3(1+w)}}}$$

    where $w$ is the equation of state of dark energy, and assuming negligible neutrino mass (significant neutrino mass requires a more complex equation). The various $\Omega$ parameters add up to 1 by construction.

As you can see the contribution to shift (either way) is very small compared to the amount of dark energy present. The dark matter particles interact with each other and other particles only through gravity and possibly the weak force.

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