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Astrophysicists believe that dark energy exists and makes up ~70% of the universe's energy content. What is the evidence that dark energy exists? Wikipedia gives five lines of evidence:

  1. Supernovae. A specific type of supernovae (type 1A) are supposed to be standard candles - that is, their luminosity is known. In turn this lets us measure distance to faraway galaxies, check how fast those galaxies are receding from us, and check if that recession speed is increasing over time.

  2. CMB. Data from the Cosmic Microwave Background indicates the universe is approximately flat. Visible matter + dark matter can account for ~30% of the energy content required to make the universe flat, leaving ~70% for something else - dark energy.

  3. BAO. Baryon acoustic oscillations act as a "standard ruler" that lets us measure how the Hubble constant varies with redshift (i.e. time), and see if the recession speed is increasing with time.

  4. Late-time ISW. ISW stands for integrated Sachs-Wolfe effect. The idea is that, usually, a photon that enters a potential well gains energy as it falls in and loses energy as it emerges, and gain/loss exactly cancel. If a universe is expanding in accelerated fashion, then this is untrue; the potential wells / hills are smoothed out and there is a permanent shift in the photon's energy and therefore temperature. If we see a correlation between hot and cold spots on the CMB and the locations of superclusters and voids, then it's a sign of accelerated expansion.

  5. Galaxy evolution. This uses (known) evolution of early-type galaxies as a standard clock. Once we know how long it takes for a galaxy to evolve from one state to another, as well as their redshifts, we can reconstruct how the Hubble constant varies over time, and see if the recession speed is increasing with time.

Two questions:

  1. Did I understand any of these five methods wrong?
  2. Are there any other lines of evidence for the existence of dark energy?
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    $\begingroup$ All this evidence is model dependent. One cannot justify the existence of dark energy to support the Friedmann model by using the Friedmann model to support the existence of the dark energy. This is a circular logic. $\endgroup$ – safesphere Feb 12 at 6:27
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    $\begingroup$ Actual evidence for Dark Energy and Dark Matter? Zero. $\endgroup$ – White Prime Feb 12 at 8:23
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    $\begingroup$ @safesphere your logic is circular. When one uses energy and momentum conservation to define the existence of the neutrino, one is using special relativity algebra but one is not supporting special relativity. One makes a model in the context of special relativity, and if the model is validated, the results stand. neutrinos are now in the elementary particle table. Consistency is not "support" in the way you used it. $\endgroup$ – anna v Feb 12 at 9:50
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    $\begingroup$ @WhitePrime This is a mainstream physics site, and for main stream physics there is ample evidence for the need of dark matter and recently dark energy in order to fit the observations. What they actually are, is a different problem under research presently both experimental and theoretical. $\endgroup$ – anna v Feb 12 at 9:53
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    $\begingroup$ @annav There is no dark energy or the need dark energy outside of the Friedmann model. The concept of dark energy doesn’t come from observations. It comes from a dramatic failure of the Friedmann model to explain them. This model mismatches the observed matter content of the new inverse by 95% and is invalidated with the confidence of 4.4 sigma by the Hubble tension (physics.stackexchange.com/questions/530143/…). It is hard to imagine a more spectacular scientific failure. $\endgroup$ – safesphere Feb 12 at 12:02
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One should note that the evidence #1–5 of OP first and foremost counts as evidence of accelerated cosmological expansion. While one could also view these observations as evidence of dark energy, it is worth noting that there are other possible explanations for accelerated expansion that could not be classified as dark energy models.

A general name for such models is “modified gravity”. The distinction between dark energy and modified gravity comes from the way Einstein field equations are modified. Dark energy enters EFEs as a source term (either cosmological constant or slowly evolving field) and interacts with other matter gravitationally. Modified gravity, as the name suggests, introduces new dynamic in the gravitational sector, possibly introducing new particles mediating “fifth force”. Examples of theories of modified gravity are massive gravity, brane world models, certain scalar-tensor theories. Note, there are also modifications of gravity that attempt to eliminate the need for dark matter, rather than dark energy, but we will not discuss these.

For more on the distinction between dark energy and modified gravity see review:

From the text:

… we draw a distinction between Dark Energy and Modified Gravity by means of the strong equivalence principle (SEP). We classify any theory which obeys the SEP as Dark Energy, and any theory which violates it as Modified Gravity (see Sec. 2.3). Heuristically, the strong equivalence principle forbids the presence of fifth forces.

The following image from this review illustrates the distinction:

image from Joyce et al.

At the level of Friedmann equations and even for the description of large-scale structure evolution the distinction between dark energy and modified gravity might appear nonexistent (and some authors do not make it), but such distinction offers a new class of evidence in support of dark energy: observations , not directly related to cosmic acceleration, but favoring dark energy over modified gravity models. So, if some astronomical observation or experiment eliminates (or constraints) modification of gravity that offers explanation for cosmic acceleration, we could consider this an evidence for the dark matter.

For example, gravitational wave event GW170817 and corresponding gamma-ray burst GRB 170817A establishes with great precision that gravitational waves travel at the speed of light. This eliminates (or seriously constrain) many modifications of gravity and so could be seen as evidence of dark energy models (paper 1, paper 2, paper 3).

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