Vavryčuk's conformal FLRW metric as an alternative to dark energy and dark matter

Václav Vavryčuk has written two articles on replacing the standard FLRW metric in cosmology with what he calls a "conformal FLRW metric", which he claims explains astrophysical and cosmological phenomena traditionally attributed to dark energy and dark matter/MOND, such as the dimming of type 1a supernovae, the baryonic Tully-Fisher relation, and the radial acceleration relation in galaxies:

Cosmological Redshift and Cosmic Time Dilation in the FLRW Metric​

Gravitational orbits in the expanding Universe revisited​

Madeleine Birchfield said:

Václav Vavryčuk has written two articles [...]

Cosmological Redshift and Cosmic Time Dilation in the FLRW Metric​

Gravitational orbits in the expanding Universe revisited​

As you have posted these references here, is it correct that you have studied these papers first, and think they're ok? I.e., not crackpot, and of reasonable scientific merit?

I was wrong in calling the metric "Vavryčuk's conformal FLRW metric" in the title; the concept of the conformal FLRW metric was first been developed by Leopold Infred and Alfred Schild in 1945 in

A New Approach to Kinematic Cosmology​

Various others have studied the conformal FLRW metric in cosmology as well long before Vavryčuk, such as

• FRW Universe Models in Conformally Flat Spacetime Coordinates
  I: General Formalism by Øyvind Grøn, Steinar Johannesen
  
• Redshift and the Hubble Constant in Conformally Flat Spacetime by Geoffrey Endean
  
• Conformally Friedmann–Lemaître–Robertson–Walker cosmologies by Matt Visser

That the conformal FLRW metric could replace dark energy seems to have first been studied by Behnke et al in 2002:

Description of supernova data in conformal cosmology without cosmological constant​

Lucas Lombriser wrote an article published last month about using metric transformations to cast and reinterpret Lambda-CDM into static Minkowski spacetime, resulting in a theory using the conformal FLRW metric physically equivalent to Lambda-CDM, but where the interpretations of the phenomena are different:

Cosmology in Minkowski space​

This implies that when properly done, there should not be any differences in predictions for observable quantities between cosmologies using the standard FLRW metric and a conformal FLRW metric.

However, Lombriser also said in the article that

It is worthwhile noting that if not performing the analogous transformations in the metric
sector, or only performing them in the metric but not in the matter sector, one does modify
physics. For instance, if not applying the conformal transformation for the matter sector in
Eq. (16), one recovers a scalar-tensor modification of gravity.

Vavryčuk's model seems to only do a transformation in the metric sector but not in the matter sector when compared to Lambda-CDM, so it should be equivalent to a modified gravity theory. This explains his second article where he was able to derive MOND-like effects in galaxies.

There aren't all that many modified gravity theories that explain both dark matter phenomena and dark energy phenomena (kudos to conformal gravity for doing both), even though there are maybe a dozen of those that are meaningfully different from each other.

But there are a very great many more gravity theories that can at least explain dark energy phenomena without dark energy. So the result isn't that surprising.

This is possible because locally dark energy phenomena are extremely weak effects (even relative to dark matter phenomena). So, a lot of minutia that don't perfectly cancel out, which distinguish slight variations on GR from plain vanilla GR, that would be routinely neglected in other contexts and can't be measured directly, are still big enough to be relevant to determining the source of dark energy phenomena.

ohwilleke said:

There aren't all that many modified gravity theories that explain both dark matter phenomena and dark energy phenomena [...]

Alas, Madeleine continues to ignore the question I asked her in post #2. Instead, she doubles down in her post #4, where she asserts:

Madeleine Birchfield said:

[...] explains [Vavrychuk's] second article where he was able to derive MOND-like effects in galaxies.

So do you (@ohwilleke) think that Vavrychuk's paper "Gravitational orbits in the expanding universe revisited" (2nd link in post #1 above) actually does what Vavrychuk claims? I.e.,

Vavrychuk said:

... The theory predicts flat rotation curves without an assumption of dark matter surrounding the galaxy...

Does Vavrychuk indeed do this in section 2.4 of this paper? If "yes", are you sure? If "no", then where?

Full disclosure: I'm wondering whether anyone besides me has actually checked this.

There is at least one error in Vavryčuk's paper. In equation 23, the term ##\alpha c^2##, which equals ##- \frac{G M}{r}## by equation 22, has units of ##\frac{L^2}{T^2}##; however, the rest of the terms in equation 23 has units of ##\frac{L}{T^2}## by dimensional analysis. Furthermore, when one takes the limit of equation 23 as ##\alpha## goes to ##0## and ##c^2## goes to ##\infty##, one gets
$$\frac{\dot{a}}{a} \dot{r} + \ddot{r} + \frac{G M}{r} - r \dot{\phi}^2 = 0$$
When evaluating equation 25, which Vavryčuk claims to be derivable from equation 23 at the above limits, one gets
$$\frac{1}{a} \frac{d}{d t} \left(a \dot{r}\right) = \frac{\dot{a}}{a} \dot{r} + \frac{1}{a} a \ddot{r} = - \frac{G M}{r^2} + \frac{(r \dot{\phi})^2}{r}$$
$$\frac{\dot{a}}{a} \dot{r} + \ddot{r} + \frac{G M}{r^2} - r \dot{\phi}^2 = 0$$
It is possible that Vavryčuk left out a factor of ##\frac{1}{r}## in the term ##\alpha c^2## in equation 23.

I've been waiting to see whether @ohwilleke will venture an opinion. Apparently not.

OK, well,... (Madeleine), the error you mentioned is relatively minor compared to the main error that I noticed. Which is: Vavrychuk's formulas, e.g., (25) do not yield asymptotically flat rotation curves for low acceleration. For circular orbits, his ##v_\phi## is proportional to ##r^{-1/2}##, exactly as in Newtonian gravitation. He seems not to understand that his formula (26) gives a constant of the motion, meaning something which is constant along the orbits (since it comes from the EoM). It doesn't mean that ##v_\phi## is constant for different orbits. This invalidates his core assertion in his abstract, i.e., that his theory "predicts flat rotation curves".

strangerep said:

I've been waiting to see whether @ohwilleke will venture an opinion. Apparently not.

Sorry, too busy fighting the forces of evil and defending widows and orphans in the real world this month.