Time dilation, magnitude, and redshift of Type Ia SNe

[mikehelland]

Follow-up to this question by @ExpEarth:

My question is, could this explain the observation that led to the hypothesis of dark energy, that the distant SN were dimmer than expected?

Based on another conversation with @LifeIsStrange, I pointed to this:

https://physics.stackexchange.com/questions/300365/time-dilation-of-distant-cosmic-events-what-is-it

Which contains this image:

Here the broader light curves are more time dilated, but also appear to have brighter magnitudes with redshift. For a standard candle, that's peculiar.

Am I reading that wrong? It looks like magnitudes are brighter with redshift. Similar to quasar magnitudes discussed in #210 .

[ExpEarth]

I don't see how you are getting that the brighter ones are at higher redshift. The figures are from a short popular article by Perlmutter in 2003. I have attached it for convenience. The purpose of the figures is to show how they can weed out "outliers" (the brighter and dimmer ones) to get a true set of standard candles. There is no mention of different redshifts for these SN.

Cosmic acceleration_Perlmutter_PhysicsTodayArticle.pdf

[mikehelland]

I had been interpreting it as the wider light curves were that way because of time dilation, which is the same 1+z as redshift. It looks like the wider ones would be at a higher z and also have the brighter magnitudes. But it seems I'm interpreting it wrong, and this is just natural variation in type Ia SNe.

[RedshiftDrift]

@mikehelland the curves you posted above show that "wider light curves" correspond to "more luminous supernovae", this is just a natural property of SNe observed at very low redshifts. (Not to be confused with time dilation.)

[mikehelland]

Here's a python notebook that downloads the Pantheon+SH0ES data and takes distance modulus, magnitudes, and z:

https://github.com/mikehelland/hubbles-law/blob/master/other/python/snmags.ipynb

Here's mB and m_b_corr:

mB - SALT2 uncorrected brightness
m_b_corr - Tripp1998 corrected/standardized m_b magnitude

https://github.com/PantheonPlusSH0ES/DataRelease/tree/main/Pantheon%2B_Data/4_DISTANCES_AND_COVAR

If you subtract the distance modulus from the (apparent) magnitudes, you should get absolute magnitude:

So from this you can see they just set each SN to -19.25 for absolute magnitude.

[LifeIsStrange]

Layman but SALT2 correct for color reddening with distance and for the stretch factor which are two independent biases that cause scatter and broadening.
Crawford has however shown that there are issues with using SALT2 for time dilation analysis.
Btw thanks a lot for making open source notebooks 🙏

[mikehelland]

Posting this here for completeness:

https://www.youtube.com/watch?v=1vfo-JFc-Io

DES Supernovae - Precisely Measured Time Dilation from Universe's Expansion (White & Davis)

[LifeIsStrange]

I take that to mean SALT2 was not involved in producing those values.

Yes the datasets (B14, pantheon+, DES 5) all provide the raw light curves without SALT2 corrections (they usually provide both).
The SALT2 are usually done during the analysis of cosmic time dilation.

Note that there is no paper testing cosmic time dilation for pantheon+ albeit this dataset has less "high" redshift than DES 5.

They don't appear to change the data very significantly.

This is not true, the SALT3 mention I cited is shown to have significant "hallucinations"
SALT2 has periods (especially the start and the end) of low performance given it is outside of their training datasets as shown too in the ZTF Dr2 paper.
Note that there are alternatives to SALT2 like bayeSN. I believe no curve fitter should be used.
Crawford argue in depth that SALT2 removes all the cosmological information. I interpret this as a pure SALT2 analysis would show no time dilation but I am not sure as Crawford argumentation is more complex and I am bad at maths.

I was not aware of the paper you cite I shall read it.

I think just because someone claims time dilation doesn't exist, doesn't really make the evidence go away.

So what you consider the paper you cite merely a claim?
That is irrelevant, Crawford paper(s) are not made of claims but of empirical analysises, actually until 2024 it was the largest snia time dilation analysis.
https://arxiv.org/abs/1711.11237
Moreover he is the only human on this planet to have exhaustively tested supernovaes, meaning he has tested:

the raw light curves without SALT2 processing.
He shows a falsification of the expandist slope at 63 sigmas for starters.
The raw light curves is the most important thing to test because it bypass SALT2 removal of the cosmological information.
You can see the plot of its figure 2 which completely rules out time dilation.
Crawford also shows that the SALT2 templates are consistent with a static universe
And also, extremely importantly, unlike the DES study, he also test the peak magnitudes (not just the widths) , which are also inconsistent with an expanding universe. (figure 3)

So Crawford analysis is clearly the most complete one in terms of the different things that are tested and made in a model independent way.
On the contrary the des study do circular reasoning and inject time dilation.
Indeed the question being for each Crawford analysis, does he remove the time dilation signal? The same way the des study has to be asked, do they add the time dilation signal?
While the later is explicitly said, the former is unclear and beyond my competence but there is no obvious reason why Crawford asymptotic correction would bias all his different probes, including peak magnitudes.

In either cases correction are made because of dust reddening with distance that mimics a time dilation effect (red is wider than the true blue color) but this correction can be made in a good way? Via spectroscopic alignment of emission lines iirc Cf DES study, or bypassed via sibling golden sample I aforementioned or simply maybe via testing the highest redshift supernovae, which should increase the signal to noise ratio by 290%

[mikehelland]

I still have more to dig into to fully understand what you're saying. This is getting a bit more into the weeds than I've been before.

But, regarding the video I posted, at 29:17 Ryan says they don't use the SALT3 stretch parameter, but simply plot it as a consistency check.

[ExpEarth]

@mikehelland

But it seems Crawford is in a similar boat to this Jensen fellow, intent on making the time dilation go away in order to keep tired light viable.

I noticed that Gupta did a study comparing numerous models on how they predict the SN light curves: https://doi.org/10.3390/universe5050102

He mentions TL models and also Crawford's model, which he considered TL also. He writes:

Generally accepted flux loss phenomena are as follows [14]: (a) Increase in the wavelength causes the flux loss proportional to 1/(1 + z), and (b) In an expanding universe, an increase in detection time between two consecutive photons emitted from a source leads to a reduction of flux, also proportional to 1/(1 + z). Therefore, in an expanding universe the necessary flux correction required is proportional to 1/(1 + z)2, whereas in a non-expanding universe the correction required is proportional only to 1/(1 + z).

He ends up concluding that the LCDM model is the second best fit, an Einstein-deSitter model being the best. He does not mention SALT.

What I am confused about is why Crawford and @LifeIsStrange are so intent on removing the extra (1 + z) time dilation component, when that term is needed to make a good fit. On the other hand, I have read numerous times that TL models do explain the SN light curves adequately. Can you or anyone here shed light on this?

Earlier you advanced a hypothesis where time dilation is just a feature of high redshift. I think this could fit with my shell model, since the Hubble redshift then becomes a gravitational redshift due to the shell. (It's more complicated than this, as new expressions of GR are necessary). The crazy other part is that we naturally tend to think of the gravitational redshift as not being a TL redshift. In my model, it can be. It goes back to the question of whether energy is lost by a photon in the gravitational redshift. Everyone in ACG except for me thought that it is not lost. I think that it is lost, and this lost energy is what gives rise to gravity.

[RedshiftDrift]

Be careful here, Crawford doesn't say that SALT2 should be interpreted as meaning "no time dilation". In his papers Crawford writes that there is an ambiguity in the SALT2 analysis: it can be interpreted as either "there is no time dilation" (consistent with a static model) or "there is time dilation".

Unfortunately, Crawford's own analysis to show there is no time dilation gives incorrect results. A careful examination of his method shows that it is biased toward producing shorter light curve values. (The method is explained in arXiv:1711.11237 on p.112 in this version: Open Astronomy, vol. 26, no. 1, pp. 111–119, Dec. 2017, doi: 10.1515/astro-2017-0013.)

For a completely different method that show there is time dilation, see
K. Boone et al., “The Twins Embedding of Type Ia Supernovae. I. The Diversity of Spectra at Maximum Light,” ApJ, vol. 912, no. 1, p. 70, May 2021, doi: 10.3847/1538-4357/abec3c.
and
K. Boone et al., “The Twins Embedding of Type Ia Supernovae. II. Improving Cosmological Distance Estimates,” ApJ, vol. 912, no. 1, p. 71, May 2021, doi: 10.3847/1538-4357/abec3b.
They use the evolution of the full spectrum to give an "age" for the supernovae, without the ambiguity problems of SALT2.

(Also see my comment on Eric Lerner's papers about citing Crawford...)

[HanDeBruijn]

@ExpEarth.

energy is lost by a photon [ .. ] and this lost energy is what gives rise to gravity.

No. Gravity is not caused explained by electromagnetism.

[mikehelland]

Time dilation isn't a feature of high redshift. Redshifted light is time dilated light. Take light, time dilate it. Its frequency goes down. Walla.

…

On Thu, Jun 27, 2024, 9:26 AM Matt Edwards ***@***.***> wrote: @mikehelland <https://github.com/mikehelland> But it seems Crawford is in a similar boat to this Jensen fellow, intent on making the time dilation go away in order to keep tired light viable. I noticed that Gupta did a study comparing numerous models on how they predict the SN light curves: https://doi.org/10.3390/universe5050102 <http://url> He mentions TL models and also Crawford's model, which he considered TL also. He writes: Generally accepted flux loss phenomena are as follows [14]: (a) Increase in the wavelength causes the flux loss proportional to 1/(1 + z), and (b) In an expanding universe, an increase in detection time between two consecutive photons emitted from a source leads to a reduction of flux, also proportional to 1/(1 + z). Therefore, in an expanding universe the necessary flux correction required is proportional to 1/(1 + z)2, whereas in a non-expanding universe the correction required is proportional only to 1/(1 + z). He ends up concluding that the LCDM model is the second best fit, an Einstein-deSitter model being the best. He does not mention SALT. What I am confused about is why Crawford and @LifeIsStrange <https://github.com/LifeIsStrange> are so intent on removing the extra (1 + z) time dilation component, when that term is needed to make a good fit. On the other hand, I have read numerous times that TL models *do* explain the SN light curves adequately. Can you or anyone here shed light on this? Earlier you advanced a hypothesis where time dilation is just a feature of high redshift. I think this could fit with my shell model, since the Hubble redshift then becomes a gravitational redshift due to the shell. (It's more complicated than this, as new expressions of GR are necessary). The crazy other part is that we naturally tend to think of the gravitational redshift as not being a TL redshift. In my model, it can be. It goes back to the question of whether energy is lost by a photon in the gravitational redshift. Everyone in ACG except for me thought that it is not lost. I think that it is lost, and this lost energy is what gives rise to gravity. — Reply to this email directly, view it on GitHub <#235 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AETKUA45F37TVBEGDV45VG3ZJQOJVAVCNFSM6AAAAABJKUXOACVHI2DSMVQWIX3LMV43SRDJONRXK43TNFXW4Q3PNVWWK3TUHM4TQOJVGEZDQ> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[HanDeBruijn]

@ExpEarth . Do you ever check your links, Matt? How comes that other peoples links work and yours not?

[ExpEarth]

I just use the link icon here. Maybe I should just cut and paste. Anyway, that paper is in the June newsletter.

[mikehelland]

I think you're putting the url where the text goes. Posting a bare url without markdown auto-links.

[RedshiftDrift]

@ExpEarth like every paper by Martin Lopez-Corredoira, this one arXiv:2207.14688 uses data analyzed in the context of LCDM to fit generic static models. That's why the probability of a static model being correct is never as good as that for LCDM.

$\quad$ This also happened for Kepler's elliptical orbits; at first they did not fit observations as well as Ptolemy's epicycles. That's because the epicycles had been adjusted to fit observations with multiple parameters.

$\quad$ Today, LCDM's multiple parameters have been adjusted to fit observations, while static models usually have few (if any) adjustable parameters and don't fit the data so well.

The probabilities assigned by Lopez-Corredoira are meaningless - you can't analyze data with your feet resting in two different paradigms.

[HanDeBruijn]

@RedshiftDrift .

you can't analyze data with your feet resting in two different paradigms.

In thread 225 Mike Helland writes:

using the LCDM best for $H_0$ to the supernovae data is not the best fit for Hubble's constant in a static model.
The best fit (using sum of squared errors) is 70.5 km/s/Mpc.

H = 70.5 km/s/Mpc is deviant from the H = 73.4 km/s/Mpc Riess value that I have been using so far.
Should I use the former or the latter value? What do you think?

[RedshiftDrift]

@HanDeBruijn the analysis done by @mikehelland in thread 225 seems to use the results from the papers from Pantheon+SH0ES, in which the luminosity distance would have been calculated from observations using LCDM. (Is that correct Mike?)

If you want a good value for $H_0$ in the context of VMT, you must re-analyze the raw data taken by Riess et al. using Variable Mass Theory's equations for "luminosity vs redshift", that is, build your own supernovae templates with luminosities obtained from your model and fit that to cepheid-determined distances. Then fit the value of $H_0$.

Since the units [km/s] imply a recession velocity due to space expansion, it would be better to divide by $c$ and express the Hubble constant in terms of a "redshift per unit distance" as $H_z \approx 0.25\mbox{/Gpc}$.

If you don't have enough graduate student (i.e. slaves) working for you, a less accurate method (but much easier) would be to convert "LCDM luminosity distances" to redshift with the cosmological parmeters $H_0$, $\Omega_\Lambda$, $\Omega_m$, etc. used by Riess et al. (effectively rescaling the abcissa on Mike's graph), and then fit $H_z$ to that graph. (You can probably do this easily @mikehelland!?)

It's possible that neither 70.5 nor 73.4 is correct, but my "intuitive guess" is that $H_z$ is close to $(0.244\pm 0.003)\mbox{/Gpc}$.

[ExpEarth]

The CMB measurements would still be important at least with respect to the CMB temperature-redshift relation. I'm not sure how the CMB/BAO would relate to static models. From the Wiki page on BAOs it seems the BAOs are rooted in Big Bang assumptions. I'd say a Hubble tension could still be possible.

[LifeIsStrange]

@RedshiftDrift this is wrong and a popular myth.
See my comment above, BAO doesn't need to be primordial.
The Alcock Paczyinski test is one of the most important cosmological tests and apply for all cosmologies, including static/tired light universes.
The hubble tension exists independently of the CMB as it truly is a tension of cluster measurements with supernovae measurements.

[LifeIsStrange]

You can see for example from this BOSS BAO study conducing the AP test:

Only two of the six models above fit the data of the Alcock & Paczynski test: concordance Lambda-CDM and static universe with tired-light redshift; whereas the rest of them are excluded at a >95% confidence level.
https://arxiv.org/abs/1312.0003

these (BAO) peaks could be
generated with other cosmological assumptions different from the standard interpretation
of acoustic peaks (L´opez-Corredoira & Gabrielli 2013)
https://www.prophy.science/article/711920/

The paper [2] will argue
that a power spectrum with oscillations is a rather normal characteristic ex�pected from any fluid with clouds of overdensities that emit/absorb radiation
or interact gravitationally with the photons, and with a finite range of sizes
and distances for those clouds. It will also show that the angular correlation
function can be fitted by a generic function with a total of ≈ 6 free parame�ters. The standard cosmological interpretation of “acoustic” peaks is just a
particular case; peaks in the power spectrum might be generated in scenarios
that have nothing to do with oscillations due to gravitational compression in
a fluid.

[mikehelland]

The baryonic acoustic oscillations come from some quantumy stuff happening right as inflation kicks in. I'm at a bit of a loss in comprehending what it could possibly refer to outside of that context. The AP test is news to me. Can you explain what's actually being measured and how it relates to non-big bang cosmologies?

Edit: I guess it's not related to inflation. I was thinking that was the cause of the "freeze", but it's just regular expansion.

[LifeIsStrange]

Indeed BAOs stems from quantumy stuff in the standard model and in some possible alternative cosmologies. One has to wonder even in alternative cosmologies, what is the source of variety/diversity in the universe?
Any deterministic law/cellular automata should cyclically reproduce the same pattern over and over, beyond a certain distance. Despite being seemingly isotropic and homogenous, each individual galaxy and their components seems quite unique (even though we can roughly classify them by their shapes)
Of course Chaos theory shows that even with classical physics, a dynamical system can in some cases generate extreme diversity.
Still it is an open question whether there were at the start of the universe (assuming there was a start), primordial sources of randomness that could explain such diversity. Aka quantumy stuff.
Regardless of that point, Cf the paragraph I cited, it appears BAO are a normal phenomena to be expected in any cosmology assuming the universe has periodic large scale variations in matter or radiation densities.

While I have read enough of the literature to know the AP test is fundamental and apply for all cosmologies (and allows to derive record constraints on LCDM parameters), I do not understand precisely how the test is performed in practice.
Like almost all cosmological tests, e.g tolman or distance duality, it seems to leverage the fact that the diverse measures of distances evolve differently in a static versus an expanding universe.
Basically while both cosmologies have roughly the same Redshift distances (hubble diagram), their luminosity distances and angular distances scale differently (e.g. At high distances objects appears larger in an expanding universe because of an optical lens effect)
The issues with both tolman and distance duality tests is that they depend on luminosity uncertainties (can be improved via UV max surface brightness) and they depend on astrophysical evolutions of objects (stars, etc) and properties of dust obscuration.
Because the AP tests is applied on large scale structures such as galactic clusters, it is largely independent of evolution and other sources of uncertainties.

Here are some explanations of the test I could find:

AP is an evaluation of the ratio of observed angular size to radial/redshift size. The main advantage of this test is that it does not depend on the evolution of the galaxies but only on the geometry of the universe. However, the redshift distortions produced by the peculiar velocities of the gravitational infall also have an influence, which should be separated from the cosmological effect.

Or as said by the original inventors:

The test involves the evaluation of the ratio between the differences in the redshifts of an expanding spherically symmetric distribution of radiation-emitting objects and the product of their distance with the angular radius of their distribution on the sky assuming a homogeneous, isotropic cosmology
https://ui.adsabs.harvard.edu/abs/1979Natur.281..358A/abstract
Equations can be found here
https://ned.ipac.caltech.edu/level5/March14/Percival/Percival5.html

So without understanding precisely, it seems the AP test rely on those well known distinct distances evolutions between cosmologies, and more specifically, it is expected that large clusters are on average spherically symmetric, the AP tests seems to shows that if a cosmology gets angular distance and redshift wrong versus empirical observations, it will shows as a distortion (non spherical) in the calculated shape of clusters.

Now the big question to me is how does this relates exactly to BAO?
I don't know but it is a fact BAO datas are what is used for performing the AP test. For some reason I don't understand it appears they extract the redshift and angular size information of clusters from BAOs, or that they disentangle the RSD (redshift spectral distortions noise) via BAOs.
If you want a proper precise answer you could ask Lopez or Fluvio Melia.
The RSD are also interesting and will allow to derive strong cosmological constraints in upcoming sky surveys.

The information is hidden in the DESI DR1 paper but DESI AP test falsify static universes while previous BOSS dataset prefered static universes. Now there are some issues with DR1 so there are still hopes for DR2 but while cosmologists on this forum since to ignore the existence the AP test, it is the viability of our cosmologies that is at play here and this matters even more than the related Hubble tension.
Thankfully we will soon have other large BAO datasets than DESI, especially from Euclid in both optical and infrared but also from radio waves via SKA and others.
Moreover it is often underappreciated that the AP test apply on any spherically symmetric large scale structure, meaning that while most surveys rely on BAO/cluster data, it is becoming possible and competitive to perform the AP test on cosmic voids.
https://arxiv.org/abs/2407.02699

[HanDeBruijn]

Let's recapitulate from thread 216 with this picture.

Again and again, Hubble tensions are observed. Now suppose that people are all wrong and that (my version of) the Variable Mass Theory (VMT) is right (-: just an ambitious assumption). Then, with a piece of that theory, the Hubble parameter is linked to age on one hand and to a characteristic time for Exponential growth on the other hand. Let $\tau=$ so-called orbital time and $t=$ so-called atomic time, then this can be formulated more precisely.

$$ H = \frac{2}{A} \quad \mbox{with} \quad 1 + \tau/A = e^{t/A} $$

This would mean that the value the Hubble parameter depends on the "age" of the phenomenon that people are observing. An extreme example is the Hubble parameter that can be attached to the age of the Earth (in orbital time of course).

$$ H_E = \frac{2}{A_E} \approx 431 \mbox{ (km/s)/Mpc} $$

Calculation:

# Age of the Earth
earth := 4.54*10^9;
# Number of seconds in a year
year := 31556926;
# Hubble parameter (Narlikar)
H := 2/(earth*year);
Mpc := 3.08567758*10^22;
H := H*Mpc/1000;

[RedshiftDrift]

There is only 'one Hubble tension'. The uncertainty on TRGB measurement is too large to conclude it is in tension with the other probes.