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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, 2019 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. $\endgroup$ Aug 13, 2019 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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  • $\begingroup$ I think you're misunderstanding the quote from Wikipedia: Dark energy existed prior to accelerated expansion (because other forms of energy dominated); they don't claim to know whether dark energy existed before expansion (which allegedly started already some 1e-36 seconds after the ig Bang). $\endgroup$
    – pela
    May 28 at 10:20
  • $\begingroup$ @Pela I've made no such claim, that it affects the correctness of the answer, but you can see it here: hub.jhu.edu/2019/08/08/dark-matter-existed-before-big-bang/…. en.wikipedia.org/wiki/Dark_energy or more simply: wired.com/story/… - your comment isn't helpful, and is irrelevant. $\endgroup$
    – Rob
    May 28 at 18:19
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Yes, the loss in energy between the redshifting photons and the gain in energy by the expansion of the universe (as the energy density per unit volume of space is maintained with the expansion) appears to be exactly conserved according to this astronomer:

Is Energy Conserved When Photons Redshift In Our Expanding Universe?

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  • $\begingroup$ Undoubtedly there's some published theoretical backing to the view he posited. Did you bother to check for such before posting your baseless criticism? It is a layman's article for more information on the topic and I think the OP would find it useful, as will many other laypeople who visit the site. $\endgroup$
    – djayjp
    May 29 at 14:51
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    $\begingroup$ It is true I may have been too dismissive. But this article (a) doesn't cite any peer reviewed work or research, (b) admits that energy conservation in GR isn't required and (c) avoids any discussion of dark energy at all, which is the subject of this question. $\endgroup$
    – ProfRob
    May 29 at 15:20
  • $\begingroup$ In fact, here is a far more balanced piece by the same author! forbes.com/sites/startswithabang/2018/07/28/… which would be far more relevant. $\endgroup$
    – ProfRob
    May 29 at 15:35
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The energy is emitted and received in two different reference frames. Energy is not a frame-independent invariant, even in Special Relativity and different observers routinely measure different values for photon energy. This is true even for the basic Doppler effect.

There is a further problem that in General Relativity it is not even clear that you can have energy conservation even in a global sense and the highly upvoted answers to this question on physics stack exchange should be studied. See also this discussion piece by Sean Carroll, which I think represents the more mainstream view of (lack of) energy conservation in GR when applied to the universe as a whole.

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