Utility of observational Hubble parameter data on DE

[Garth]

Another paper in Friday's physics arXiv on using the H(z) v z plot to investigate any possible evolution of DE: Utility of observational Hubble parameter data on dark energy evolution.

From that eprint:

As discussed in the Marginal evidence for cosmic acceleration from Type Ia SNe, this paper includes two further high z plots, all three are binned in the fourth (purple) bin in their Figure 1 below.

As Chalnoth said in #41 of that thread:

So the smart money here is on there being something wrong with the z=2.34 measurement from the Lyman-alpha forest. This suggests the need for more independent high-redshift data to resolve the issue.

Here are two more measurements at z ~ 2.3 and they agree!

Also of course that fourth bin is consistent with linear expansion (h_o = 0. 67) but not with the $\Lambda CDM$ model. Just a thought...

Garth

 

[Chalnoth]

Those aren't three independent measurements. They're three different estimates from the Lyman-alpha forest using data from the BOSS survey:
http://arxiv.org/abs/1211.2616
http://arxiv.org/abs/1311.1767
http://arxiv.org/abs/1404.1801

By independent high-redshift data, I meant preferably data using different observational instruments and different observables. These are just different analyses of different data from the same survey.

 

[Garth]

Okay, three observations from the same survey.

Then as they conclude:

Finally, we note that it is necessary to place our main emphasis of research on BAO observation. Using BAO peak position as a standard ruler in the radial direction or combining measurements of BAO peak and Alcock-Paczynski distortion, we can limit the precision of H(z) data better than 7% (Gazta˜naga et al. 2009; Blake et al. 2012). As putting into operation of future space and ground-based telescopes (James Webb Space Telescope, Wide-Field Infrared Survey Telescope, planned adaptive optics systems with Keck, Large Synoptic Survey Telescope, and Thirty Meter Telescope et al.), more high-redshift, high-accuracy H(z) determinations from BAO observations will undoubtedly perform a very useful role in the future study of the DE.

We wait for the next generation of space and ground telescopes...

Garth

 

[Chalnoth]

Okay, three observations from the same survey.

Then as they conclude:

We wait for the next generation of space and ground telescopes...

Garth

Better would be a measurement using different observable parameters.

 

[Garth]

Better would be a measurement using different observable parameters.

Such as the ages of passively evolving galaxies as in The Age-Redshift Relationship of Old Passive Galaxies?

But though galaxy age estimates currently tend to slightly favour Rh = ct over CDM, the known sample of such measurements is still too small for us to completely rule out either model. We have therefore considered two synthetic samples with characteristics similar to those of the 32 known age measurements, one based on a CDM background cosmology, the other on Rh = ct. From the analysis of these simulated ages, we have estimated that a sample of about 45 − 55 galaxy ages would be needed to rule out Rh = ct at a ∼ 99.7% confidence level if the real cosmology were in fact CDM, while a sample of 350 − 500 ages would be needed to similarly rule out CDM if the background cosmology were instead Rh = ct. These ranges allow for the possible contribution of an uncertainty into the variance of the observed age of the Universe at each redshift. The difference in required sample size is due to CDM’s greater flexibility in fitting the data, since it has a larger number of free parameters.

(emphasis mine)

At least with less flexibility the linearly expanding model is easier to falsify - strange then (in the matter dominated era) that it hasn't been...

Just a thought.

Garth

 

[Chalnoth]

Such as the ages of passively evolving galaxies as in The Age-Redshift Relationship of Old Passive Galaxies?

That seems like an extremely tricky measurement that is going to be difficult to do precisely.

And the parameter estimates from that paper are weird. Their best-fit $\Lambda$CDM model has $H_0 = 94$, $\Omega_m = 0.12$. Both are pretty far away from other measurements of the same parameters. The $H_0$ measurement isn't too ridiculous, because the error bars are very large and encompass the much more precise values measured by other experiments. The estimate for $\Omega_m$, however, seems to indicate some unaccounted systematic errors.

This measure clearly still has errors that are too big for use in determining cosmological parameters.

At least with less flexibility the linearly expanding model is easier to falsify - strange then (in the matter dominated era) that it hasn't been...

It's very easy to falsify. Just include CMB data. Or notice that there is matter in the universe.

 

[Garth]

At least with less flexibility the linearly expanding model is easier to falsify - strange then (in the matter dominated era) that it hasn't been...

It's very easy to falsify. Just include CMB data. Or notice that there is matter in the universe.

Well as I said the model would be linearly expanding in the matter epoch, as CMB is transmitted at about the transition stage it gives information about the radiation dominated epoch.

The linearly expanding model's EoS would have to be $\omega = - \frac{1}{3}$ in that matter epoch.

Garth

 

[Chalnoth]

The matter dominated epoch started quite a while before the emission of the CMB.

 

[Garth]

The matter dominated epoch started quite a while before the emission of the CMB.

True, but as the EoS would have to change from $\omega = +\frac{1}{3}$ in the radiation dominated epoch to $\omega = - \frac{1}{3}$, in a linearly expanding matter dominated epoch then I would envisage this being a gradual transition process and some time passing before true linear expansion sets in.

If, for example, the linearly expanding EoS is delivered by some sort of scalar field coupled to matter, its influence would gradually kick in as $\rho_m$ begins to dominate $\rho_r$.

So much for speculation, but here the question is, "What is the data (BAO, galaxy ages etc.) actually telling us?

If $\Lambda$CDM then well and good, but for the sake of having models to test it against I suggest the linear model to be one good candidate - and others seem to have taken the same view.

Garth

 

[Chalnoth]

True, but as the EoS would have to change from $\omega = +\frac{1}{3}$ in the radiation dominated epoch to $\omega = - \frac{1}{3}$, in a linearly expanding matter dominated epoch then I would envisage this being a gradual transition process and some time passing before true linear expansion sets in.

Except you have no theory at all for why the we should have $w = -1/3$ in the first place. "There's probably some gradual transition" is just a cop-out. Why would there be a gradual transition? What causes the transition? Precisely how gradual is that transition?

Furthermore, as I pointed out, the universe was matter-dominated for quite some time before the CMB was emitted. The main reason why I say the CMB will completely destroy these theories is not because of the dynamics prior to the CMB, but because of the redshift/distance relation that the CMB itself represents (comoving distance of 14.2 Gpc at z = 1088). What would your R=ct model predict for that?

 

[Garth]

Except you have no theory at all for why the we should have $w = -1/3$ in the first place. "There's probably some gradual transition" is just a cop-out. Why would there be a gradual transition? What causes the transition? Precisely how gradual is that transition?

That's a work in progress. Actually there is a theory that delivers $\omega = -\frac{1}{3}$ (A New Self Creation Cosmology) but I am in the process of rewriting that paper. Here in this thread I am looking at observational evidence that might support a linear expansion, whether there is a valid theory at present or not.

If linear expansion keeps cropping up from observational evidence and such a valid theory does not at present exist then the community should look for one.

All I was saying above was that if we start with the BBN and CMB evidence and accept the standard model is correct up to radiation-mattter equality but also find by observation that there has been a linear expansion later on, then there has been a DE evolution with a (gradual) change from $\omega = +\frac{1}{3}$ to $\omega = -\frac{1}{3}$ at some stage.

Furthermore, as I pointed out, the universe was matter-dominated for quite some time before the CMB was emitted. The main reason why I say the CMB will completely destroy these theories is not because of the dynamics prior to the CMB, but because of the redshift/distance relation that the CMB itself represents (comoving distance of 14.2 Gpc at z = 1088). What would your R=ct model predict for that?

In a flat, R = ct, $\omega = -\frac{1}{3}$ $\rho_m = 0.33, \rho_\Lambda = 0.77$ universe the co-moving distance at z = 1088 is 13.6 Gpc.

I do accept there is work to be done on interpreting the CMB data - as I said it is a 'work in progress'.

Garth

 

[Garth]

Just to reiterate about the "observational evidence that might support a linear expansion," I have re-posted Figure 1 from the OP link Utility of observational Hubble parameter data on dark energy evolution eprint but I have added the R = ct plot for comparison with the observed data points and the yellow $\Lambda$CDM plot.

There is a problem for R =ct around z = 0.5 but otherwise a good fit, especially at high z ~ 2.3.

Bin 2 fits $\Lambda$CDM but not R=ct, (Edit: actually it doesn't, it lies below both plots but nearer the $\Lambda$CDM one,) whereas Bin 4 fits R=ct but not $\Lambda$CDM.

However it is more difficult to determine $\omega$ at low redshift; from the OP eprint:

It is worth noticing that high accuracy Observational Hubble parameter Data is especially necessary in w(z) reconstruction at low redshift.

Garth

 

[Chalnoth]

In a flat, R = ct, $\omega = -\frac{1}{3}$ $\rho_m = 0.33, \rho_\Lambda = 0.77$ universe the co-moving distance at z = 1088 is 13.6 Gpc.

...which is about 5 standard deviations away from the WMAP 9-year result, and getting close to 30 standard deviations away from the Planck 2015 results.

I do accept there is work to be done on interpreting the CMB data - as I said it is a 'work in progress'.

Should get cracking on that, then. Because the CMB is the most precise data set we have, especially as it has the lowest chance for systematic errors.

 

[Garth]

In a flat, R = ct, $\omega = -\frac{1}{3}$ $\rho_m = 0.33, \rho_\Lambda = 0.77$ universe the co-moving distance at z = 1088 is 13.6 Gpc.

...which is about 5 standard deviations away from the WMAP 9-year result, and getting close to 30 standard deviations away from the Planck 2015 results.

And in a flat, R = ct, $\omega = -\frac{1}{3}, \Omega_m = 0.3166, \Omega_\Lambda = 0.6834$ universe the co-moving distance at z = 1088 is 13.8 Gpc.

Garth

 

[Chalnoth]

And in a flat, R = ct, $\omega = -\frac{1}{3}, \Omega_m = 0.3166, \Omega_\Lambda = 0.6834$ universe the co-moving distance at z = 1088 is 13.8 Gpc.

Garth

I don't quite see what your point is here. That's still very far away from the observations.

 

[Garth]

I don't quite see what your point is here.

I was simply answering your question with the best values of $\Omega_m$ and $\Omega_\Lambda$ available.

That's still very far away from the observations.

What you mean is: 'from interpretations of the observations' - they depend on the priors you assume...

Garth

 

[Chalnoth]

What you mean is: 'from interpretations of the observations' - they depend on the priors you assume...

Garth

While there is some model dependence on the parameter estimates, I sincerely doubt it will be enough to close a 20+ sigma gap.

 

[Garth]

While there is some model dependence on the parameter estimates, I sincerely doubt it will be enough to close a 20+ sigma gap.

One prior I would question that would significantly alter observation interpretation is the assumption that SNe 1a are standard candles out to cosmological distances.

As I said in jim mcnamara's thread Standard candle - in question - affects distance estimates, there are at least three types of SN 1a now known, which was not realized in 1998:

Single Degenerate (SD) systems, (Chandrasekhar SNe), - A white dwarf accretes matter from a companion red giant that has expanded into its Roche limit until it approaches the Chandrasekhar limit of about 1.44 M☉ when it detonates. As they all detonate at ~ 1.4 M☉ all SNe 1a are meant to have the same intinsic luminosity with a Mv peak between -14.2 and -18.9.

Double Degenerate (DD) systems, (Super-Chandrasekhar SNe) - where a a binary WD or WD/neutron star system spiral into each other through the emission of gravity waves and detonate - but these would seem to have a mass of double or more of the SD SNe 1a system, and hence perhaps twice the luminosity, with a Mv peak brighter than -19.3.

And about half of all SNe 1a are
Contaminated White Dwarf (CWD) systems, (Sub-Chandrasekhar SNe) - with detonation at around 0.85 - 1.2 M☉ depending on the amount of hydrogen contamination. As only a tiny amount of hydrogen (concentrations from 10⁻¹⁶ to 10⁻²¹) is required they would still be classified as SNe 1a from their spectra. With less than Chandrasekhar mass they would be less luminous than the SD's with a Mv peak less bright than -14.2.

The problem over cosmological time scales is that the ratio of the three types of detonation (SD : DD : CWD) within any particular set of observations is likely to change because of the different lifetimes the three systems require.

(With added luminosity information provided by |Glitch| in the post following that one - thank you |Glitch|.)

What has not been resolved is the evolution of the ratio of these three (possibly more) types over cosmological time scales.

Garth

 

[Chalnoth]

One prior I would question that would significantly alter observation interpretation is the assumption that SNe 1a are standard candles out to cosmological distances.

Uhh, what? That has nothing to do with the CMB observations.

 

[Garth]

Uhh, what? That has nothing to do with the CMB observations.

Really? I would have thought $\Omega_\Lambda$ would have quite a lot to do with the interpretation of CMB observations.

The whole $\Lambda$CDM model interpreting the CMB data is a compilation of the questionable theory of Inflation, with its requirement that $\Omega = 0$ or very nearly so, and the independent SNe 1a observation that apparently indicates that $\Omega_\Lambda$ is positive such that $\Omega_m$ + $\Omega_\Lambda$ = 0.

Even under the assumption that they are standard candles SNe 1a only give marginal evidence (<3$\sigma$) that the universe is accelerating.

If an improved analysis of SNe 1a observations, taking into account the evolution of the ratio of the three or more types, should reveal $\Omega_\Lambda \neq 0.68$ or nowhere near that value, then the standard schema of interpretation would begin to crumble.

There are a number of degeneracies between the cosmological parameters that can be extracted from the CMB power spectrum which can only be lifted by combining CMB data with other data sets such as the SNe 1a observations or large scale structure formation surveys. (Which BTW is why the presence of over-massive evolved objects at high z might also be pertinent.)

So I would say the assumption of SNe 1A being standard candles out to cosmological distances (z = 1 and beyond) has everything to do with the interpretation of CMB observations.

Garth

 

[Chalnoth]

Really? I would have thought $\Omega_\Lambda$ would have quite a lot to do with the interpretation of CMB observations.

You do need some nearby data to make the error bars on the CMB data reasonable, but it doesn't have to be supernova data. Even just a measurement of H_0 from nearby galaxies is sufficient to disentangle most of the degeneracies. Using BAO data is usually quite a bit better at constraining the final result than supernova data.

The whole $\Lambda$CDM model interpreting the CMB data is a compilation of the questionable theory of Inflation, with its requirement that $\Omega = 0$ or very nearly so, and the independent SNe 1a observation that apparently indicates that $\Omega_\Lambda$ is positive such that $\Omega_m$ + $\Omega_\Lambda$ = 0.

Presumably you meant $\Omega_k = 0$?

But lots and lots of theorists have proposed alternatives to $\Omega_\Lambda$. Nobody has yet found a model that is simpler than this one and also fits the data. It's conceivable that we don't have a cosmological constant, but nobody has found a reason why the cosmological constant should be zero either.

So I would say the assumption of SNe 1A being standard candles out to cosmological distances (z = 1 and beyond) has everything to do with the interpretation of CMB observations.

You'd be wrong.

 

[Garth]

Presumably you meant $\Omega_k = 0$?

Of course.

But lots and lots of theorists have proposed alternatives to $\Omega_\Lambda$. Nobody has yet found a model that is simpler than this one and also fits the data. It's conceivable that we don't have a cosmological constant, but nobody has found a reason why the cosmological constant should be zero either.

Well that depends on the data - one recent paper that attempts to alleviate the tension between the data discussed in the OP plotted on the diagram:

is this one: Consistency of non-flat ΛCDM model with the new result from BOSS
The author tries a model with positive curvature.

Following [8], we noticed that the lower values of H(z) at higher redshifts can be achieved in phenomenological models of interacting dark sector as discussed in Subsection 2.1. Therefore, the new result from BOSS could be an indication of interaction in the dark sector as pointed out in [8]. The lower values of H(z) at higher redshifts can also be accommodated in modified CDM model via screening mechanism as illustrated in Subsection 2.2, following [9]. Motivated by the screening idea, we have considered the non-$\Lambda$CDM model with positive curvature. We have found that this model successfully accommodates the lower value of H(z) at higher z suggested by BOSS

(emphasis mine)

Garth

 

[Garth]

There are several papers about this tension between the data and the standard $\Lambda$CDM model:

There's the original publication of the data plotted above: Baryon Acoustic Oscillations in the Lyα forest of BOSS DR11 quasars

We report a detection of the baryon acoustic oscillation (BAO) feature in the flux-correlation function of the Ly-$\alpha$ forest of high-redshift quasars with a statistical significance of five standard deviations. The study uses 137,562 quasars in the redshift range 2:1 < z < 3:5 from the Data Release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of SDSS-III. This sample contains three times the number of quasars used in previous studies.

For the value r_d = 147:4 Mpc, consistent with the cosmic microwave background power spectrum measured by Planck, we find D_A(z = 2:34) = 1662 ±96(1$\sigma$) Mpc and H(z = 2:34) = 222±7(1$\sigma$) km s^-1Mpc^-1. Tests with mock catalogs and variations of our analysis procedure have revealed no systematic uncertainties comparable to our statistical errors. Our results agree with the previously reported BAO measurement at the same redshift using the quasar-Ly$\alpha$ forest cross correlation.

Then discussing the tension are:

Evolving DE?
[/PLAIN]
Model independent evidence for dark energy evolution from Baryon Acoustic Oscillations which suggests evolving DE.

In the absence of systematics in the CMB & SDSS data sets, our results suggest a strong tension between concordance cosmology and observational data....
Evolving dark energy models which might accommodate the SDSS data better than ΛCDM include those in which the cosmological constant was screened in the past.

or

Interacting DE?
[/PLAIN]
New Evidence for Interacting Dark Energy from BOSS

In this Letter we show that an interaction between dark matter and dark energy is favored by the most recent large scale structure observations. The result presented by the BOSS-SDSS collaboration measuring the baryon acoustic oscillations of the Ly-α forest from high redshift quasars indicates a 2.5σ departure from the standard ΛCDM model. ... We show here that a simple phenomenological interaction in the dark sector provides a good explanation for this deviation, naturally accommodating the Hubble parameter obtained by BOSS, H(z=2.34)=222±7kms⁻¹Mpc⁻¹, for two of the proposed models with a positive coupling constant and rejecting the null interaction at more than 2σ. For this we used the adjusted values of the cosmological parameters for the interacting models from the current observational data sets. This small and positive value of the coupling constant also helps alleviate the coincidence problem.

and a review with comparison with the other cosmological data sets

Cosmological implications of baryon acoustic oscillation (BAO) measurements

The application of the BAO technique to large cosmological surveys has enabled the first percent-level measurements of absolute distances beyond the Milky Way.In combination with CMB and SN data, these measurements yield impressively tight constraints on the cosmic expansion history and correspondingly stringent tests of dark energy theories. Over the next year, the strength of these tests will advance significantly with the final results from BOSS and with CMB polarization and improved temperature maps from Planck. In the longer term, BAO measurements will gain in precision and redshift range through a multitude of ongoing or planned spectroscopic surveys, including SDSS-IV eBOSS, HET-DEX, SuMIRE, DESI, WEAVE, Euclid, and WFIRST. These data sets also enable precise measurements of matter clustering through redshift-space distortion analyses, the shape of the 3-dimensional power spectrum, and other clustering statistics. In combination with the expansion history constraints, these measurements can test modified gravity explanations of cosmic acceleration and probe the physics of inflation, the masses of neutrinos, and the properties of dark matter. In parallel with these large spectroscopic surveys, supernova measurements of expansion history are gaining in precision, data quality, and redshift range, and weak lensing constraints on matter clustering are advancing to the percent and sub-percent level as imaging surveys grow from millions of galaxy shape measurements to many tens or hundreds of millions. From the mid-1990s through the early 21st century, improving cosmological data sets transformed our picture of the universe. The next decade - of time and of precision - could bring equally surprising changes to our understanding of the cosmos.

We live in exciting times, we wait and see!

Garth

 

[ruarimac]

Bin 2 fits $\Lambda$CDM but not R=ct, (Edit: actually it doesn't, it lies below both plots but nearer the $\Lambda$CDM one,) whereas Bin 4 fits R=ct but not $\Lambda$CDM.

However it is more difficult to determine $\omega$ at low redshift; from the OP eprint:

H(z)

You really need a lesson in statistics. Those are 1 sigma errors, only 2/3 of points should sit on the model within error bars, just because it's outside an error bar doesn't mean it isn't consistent. What you ignore is that you have removed the 2 sigma tension at high redshift and replaced with with much greater significance deviation at z~0.5 where the constraints are much tighter and your "fit" is much worse. Even rejected at high significance. This plot does not appear support your claim.

They aren't measuring w(z) there, that's a plot of H(z) which is there high accuracy H(z) measurement. They do not say it is more difficult. The errors in the plot reflect the uncertainty, they tell you everything you need to know other than correlation, the low redshift results are far more precise and so the model not fitting there is a much greater problem.

Lastly hand drawn fits are not statistically rigorous, chi by eye is useless. Do the statistics properly.

 

[Garth]

H(z)

You really need a lesson in statistics. Those are 1 sigma errors, only 2/3 of points should sit on the model within error bars, just because it's outside an error bar doesn't mean it isn't consistent. What you ignore is that you have removed the 2 sigma tension at high redshift and replaced with with much greater significance deviation at z~0.5 where the constraints are much tighter and your "fit" is much worse. Even rejected at high significance. This plot does not appear support your claim.

They aren't measuring w(z) there, that's a plot of H(z) which is there high accuracy H(z) measurement. They do not say it is more difficult. The errors in the plot reflect the uncertainty, they tell you everything you need to know other than correlation, the low redshift results are far more precise and so the model not fitting there is a much greater problem.

Lastly hand drawn fits are not statistically rigorous, chi by eye is useless. Do the statistics properly.

Of course, just a view of the data - ignore my comments.

However the tension is intriguing and may be indicative of DE evolution, as several authors have commented.

Garth

 

[Chalnoth]

Of course, just a view of the data - ignore my comments.

However the tension is intriguing and may be indicative of DE evolution, as several authors have commented.

Garth

Not very likely. Dark energy is a much, much smaller component of the energy density at $z=2.3$ than it is today.

 

[ruarimac]

However the tension is intriguing and may be indicative of DE evolution, as several authors have commented.

For the moment it is a 2 σ result, we should not get carried away with that on the promise of exciting physics. We should also not ignore other results, analyses like this don't take place in a vacuum. To convince anyone that this is real evidence of w_a=/=0 they should calculate probability distributions for the DE equation of state and show that their constraints on w are tighter than other results which don't see this. If they are then you could claim this could be evidence for that, if not then it is systematic.

After taking the time to look at the paper a bit better I can see one quite major issue, their use of Gaussian statistics to bin the values of H(z). The variance of each data point is purely the combination of the variances of the binned points, it does not reflect disagreement between these different measurements (with different systematics). Even if the individual data points going into each bin disagreed by 1000 σ this would not be reflected in the error and the binned data point would have a smaller error bar than the points being binned. I don't trust this, I don't think it's appropriate and I think their error bars are underestimated.