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Marginal evidence for cosmic acceleration from Type Ia supernovae

Scientific Reports volume 6, Article number: 35596 (2016) Cite this article

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Abstract

The ‘standard’ model of cosmology is founded on the basis that the expansion rate of the universe is accelerating at present — as was inferred originally from the Hubble diagram of Type Ia supernovae. There exists now a much bigger database of supernovae so we can perform rigorous statistical tests to check whether these ‘standardisable candles’ indeed indicate cosmic acceleration. Taking account of the empirical procedure by which corrections are made to their absolute magnitudes to allow for the varying shape of the light curve and extinction by dust, we find, rather surprisingly, that the data are still quite consistent with a constant rate of expansion.

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Introduction

In the late 1990’s, studies of Type Ia supernovae (SN Ia) showed that the expansion rate of the universe appears to be accelerating as if dominated by a cosmological constant1,2,3 . Since then supernova cosmology has developed rapidly as an important probe of ‘dark energy’. Empirical corrections are made to reduce the scatter in the observed magnitudes by exploiting the observed (anti) correlation between the peak luminosity and the light curve width and the colour4,5 . Other such correlations have since been found e.g. with the host galaxy mass6 and metallicity7 . Cosmological parameters are then fitted, along with the parameters determining the light curves, by simple χ2 minimisation1,8,9,10,11 . This method has a number of pitfalls as has been emphasised earlier12,13 .

With ever increasing precision and size of SN Ia datasets, it is important to also improve the statistical analysis of the data. To accomodate model comparison, previous work14,15,16 has introduced likelihood maximisation. In this work we present an improved maximum likelihood analysis, finding rather different results.

Supernova Cosmology

There are several approaches to making SN Ia ‘standardiseable candles’. The different philosophies lead to mildly different results but the overall picture seems consistent17 . In this paper we adopt the widely used approach of ‘Spectral Adaptive Lightcurve Template 2′ (SALT2)18,19 wherein the SN Ia are standardised by fitting their light curve to an empirical template, and the parameters of this fit are used in the cosmological analysis. (A more comprehensive statistical model of light curves spanning optical through near-infrared data has subsequently been constructed in a hierarchical Bayesian framework20 ). Every SN Ia is assigned three parameters, one being , the apparent magnitude at maximum (in the rest frame ‘B-band’), while the other two describe the light curve shape and colour corrections: x1 and c. The distance modulus is then taken to be:

where M is the absolute magnitude, and α and β are assumed to be constants for all SN Ia. These global constants are fitted along with the cosmological parameters. The physical mechanism(s) which give rise to the correlations that underlie these corrections remain uncertain21,22 . The SN Ia distance modulus is then compared to the expectation in the standard ΛCDM cosmological model:

where dL, dH, H are the luminosity distance, Hubble distance and Hubble parameter respectively, and Ωm, ΩΛ, Ωk are the matter, cosmological constant and curvature density in units of the critical density3 . There is a degeneracy between H0 and M0 so we fix the value of the Hubble parameter today to h = 0.7 which is consistent with independent measurements.

Maximum Likelihood Estimators

To find the maximum likelihood estimator (MLE) from the data, we must define the appropriate likelihood:

i.e. we have to first specify our model of the data. For a given SN Ia, the true data are drawn from some global distribution. These values are contaminated by various sources of noise, yielding the observed values . Assuming the SALT2 model is correct, only the true values obey equation (1). However when the experimental uncertainty is of the same order as the intrinsic variance as in the present case, the observed value is not a good estimate of the true value. Parameterising the cosmological model by θ, the likelihood function can be written as13 :

which shows explicitly where the experimental uncertainties enter (first factor) and where the variances of the intrinsic distributions enter (second factor).

Having a theoretically well-motivated distribution for the light curve parameters would be helpful, however this is not available. For simplicity we adopt global, independent gaussian distributions for all parameters, M, x1 and c (see Fig. 1), i.e. model their probability density as:

Figure 1

Distribution of the SALT2 stretch and colour correction parameters for the JLA sample11 of SN Ia, with our gaussian models superimposed.

All 6 free parameters are fitted along with the cosmological parameters and we include them in θ. Introducing the vectors Y = {M1, x11, c1, ... MN, x1N, cN}, the zero-points Y0, and the matrix , the probability density of the true parameters writes:

where |...| denotes the determinant of a matrix. What remains is to specify the model of uncertainties on the data. Introducing another set of vectors , the observed , and the estimated experimental covariance matrix Σd (including both statistical and systematic errors), the probability density of the data given some set of true parameters is:

To combine the exponentials we introduce the vector and the block diagonal matrix

With these, we have and so . The likelihood is then

which can be integrated analytically to obtain:

This is the likelihood (equation (3)) for the simple model of equation (4), and the quantity which we maximise in order to derive confidence limits. The 10 parameters we fit are . We stress that it is necessary to consider all of these together and Ωm and ΩΛ have no special status in this regard. The advantage of our method is that we get a goodness-of-fit statistic in the likelihood which can be used to compare models or judge whether a particular model is a good fit. Note that the model is not just the cosmology, but includes modelling the distributions of x1 and c.

With this MLE, we can construct a confidence region in the 10-dimensional parameter space by defining its boundary as one of constant . So long as we do not cross a boundary in parameter space, this volume will asymptotically have the coverage probability

where is the pdf of a chi-squared random variable with ν degrees of freedom, and is the maximum likelihood.

To eliminate the so-called ‘nuisance parameters’, we set similar bounds on the profile likelihood. Writing the interesting parameters as θ and nuisance parameters as φ, the profile likelihood is defined as

We substitute by in equation (10) in order to construct confidence regions in this lower dimensional space; ν is now the dimension of the remaining parameter space. Looking at the Ωm − ΩΛ plane, we have for {0.68 ("1σ"), 0.95 ("2σ"), 0.997 ("3σ")}, the values respectively.

Comparison to other methods

It is illuminating to relate our work to previously used methods in SN Ia analyses. One method14 maximises a likelihood, which is written in the case of uncorrelated magnitudes as

so it integrates over μSN to unity and can be used for model comparison. From Equation (3) we see that this corresponds to assuming flat distributions for x1 and c. However the actual distributions of and are close to gaussian, as seen in Fig. 1. Moreover although this likelihood apparently integrates to unity, it accounts for only the data. Integration over the x1, c data demands compact support for the flat distributions so the normalisation of the likelihood becomes arbitrary, making model comparison tricky.

More commonly used1,8 is the ‘constrained χ2’

but this cannot be used to compare models, since it is tuned to be 1 per degree of freedom for the ΛCDM model by adjusting an arbitrary error σint added to each data point. This has been criticised12,13 , nevertheless the method continues to be widely used and the results presented without emphasising that it is intended only for parameter estimation for the assumed (ΛCDM) model, rather than determining if this is indeed the best model.

Analysis of JLA catalogue

We focus on the Joint Lightcurve Analysis (JLA) catalogue11 . (All data used are available on http://supernovae.in2p3.fr/sdss_snls_jla/ReadMe.html — we use the covmat_v6.) As shown already in Fig. 1, the distributions of the light curve fit parameters and are well modelled as gaussians. Maximisation of the likelihood under specific constraints is summarised in Table 1 and the profile likelihood contours in the Ωm − ΩΛ plane are shown in Fig. 2. In Fig. 3 we compare the measured distance modulus, with its expected value in two models: ‘ΛCDM’ is the best fit (Table 1) accelerating universe, while ‘Milne’ is an universe expanding with constant velocity. The error bars are the square root of the diagonal elements of Σl + AT−1ΣdA−1 so include both experimental uncertainties and intrinsic dispersion. We show also the residuals with respect to the Milne model (which has been raised to take into account the change in M0).

Table 1 Maximum likelihood parameters under specific (boldface) constraints ().
Figure 2

Contour plot of the profile likelihood in the Ωm − ΩΛ plane.

We show 1, 2 and 3σ contours, regarding all other parameters as nuisance parameters.

Figure 3

Comparison of the measured distance modulus with its expected value for the best fit accelerating universe (ΛCDM) and a universe expanding at constant velocity (Milne).

The error bars include both experimental uncertainties and intrinsic dispersion. The bottom panel shows the residuals relative to the Milne model.

To assess how well our Gaussian model for the latent variables describes the data, we show the ‘pull’ distribution in Fig. 4. These are defined as the normalised, decorrelated residuals of the data,

Figure 4

Distribution of pulls (14) for the best-fit model compared to a normal distribution.

where U is the upper triangular Cholesky factor of the covariance matrix Σd + ATΣlA. Performing a K-S test, comparing the pull distribution to a unit variance gaussian gives a p-value of 0.1389.

To check the validity of our method and approximations, we do a Monte Carlo simulation of experimental outcomes from a model with parameters matching our best fit (see Table 1). Figure 5 shows the distribution of , which is just as is expected.

Figure 5

The distribution of the likelihood ratio from Monte Carlo, with a χ2 distribution with 10 d.o.f. superimposed.

Discussion

That the SN Ia Hubble diagram appears consistent with an uniform rate of expansion has been noted earlier16,23,24,25 . We have confirmed this by a statistically principled analysis, using the JLA catalogue of 740 SN Ia processed by the SALT2 method. We find marginal (i.e. ) evidence for the widely accepted claim that the expansion of the universe is presently accelerating3 .

The Bayesian equivalent of this method (a "Bayesian Hierarchical Model") has been presented elsewhere13 and has recently been applied to the same dataset, finding results consistent with ours26 . We note that a Bayesian consistency test27 has been applied (albeit using the flawed ‘likelihood’ (equation 12) and ‘constrained χ2’ (equation 13) methods) to determine the consistency between the SN Ia data sets acquired with different telescopes28 . These authors do find inconsistencies in the UNION2 catalogue but none in JLA. This test had been applied earlier to the UNION2.1 compilation finding no contamination, but those authors29 fixed the light curve fit ‘nuisance’ parameters, so their result is inconclusive. Including a ‘mass step’ correction for the host galaxies of SN Ia11 has little effect.

While our gaussian model (4) is not perfect, it appears to be an adequate first step towards understanding SN Ia standardisation. One might be concerned that various selection effects (e.g. Malmquist bias) affect the data. Such effects may not be amenable to our approximate method and are better addressed in a Bayesian approach26 . We are concerned here solely with performing the analysis in a statistically sound manner to highlight the different conclusion from previous analyses11 of the same data.

Whether the expansion rate is accelerating or not is a kinematic test and it is only for ease of comparison with previous results that we have chosen to show the impact of doing the correct statistical analysis in the ΛCDM framework. In particular the ‘Milne model’ refers here to an equation of state p = −ρ/3 and should not be taken to mean an empty universe. For example the deceleration due to gravity may be countered by bulk viscosity associated with the formation of structure, resulting in expansion at approximately constant velocity even in an universe containing matter but no dark energy30 . Such a cosmology is not prima facie in conflict with observations of the angular scale of fluctuations in the cosmic microwave background or of baryonic acoustic oscillations, although this does require further investigation. In any case, both of these are geometric rather than dynamical measures and do not provide compelling direct evidence for a cosmological constant — rather its value is inferred from the assumed ‘cosmic sum rule’: ΩΛ = 1 − Ωm + Ωk. This would be altered if e.g. an additional term due to the ‘back reaction’ of inhomogeneities is included in the Friedmann equations31 .

The CODEX experiment on the European Extremely Large Telescope will aim to measure the ‘redshift drift’ over a 10–15 year period to determine whether the expansion rate is really accelerating32 .

Methods: Confidence ellipsoids

The confidence ellipsoid is the collection of points , which obey

where is a symmetric matrix and xMLE is the MLE. The enclosed volume is a confidence region with coverage probability corresponding with high precision to the value obtained from Equation (10). The eigenvectors of are then the principal axes of the ellipsoid, and the eigenvalues are the inverse squares of the lengths of the principal axes. We approximate this matrix with the sample covariance from the MC of section 3 as .

To make reading the matrix of eigenvectors easier, we round all numbers to 0.1. Thus, we get the following approximate eigenvectors of , in columns

with respective lengths of semi-axes

We also list the rounded correlation matrix,

We see that the only pronounced correlations are between Ωm, ΩΛ and M0. This is also apparent from Table 1.

Code Availability

The code and data used in the analysis are available at: http://dx.doi.org/10.5281/zenodo.34487

Additional Information

How to cite this article: Nielsen, J. T. et al. Marginal evidence for cosmic acceleration from Type Ia supernovae. Sci. Rep. 6, 35596; doi: 10.1038/srep35596 (2016).

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Acknowledgements

We thank the JLA collaboration for making their data and software public and M. Betoule for making the corrections we suggested to the catalogue. This work was supported by the Danish National Research Foundation through the Discovery Center at the Niels Bohr Institute and the award of a Niels Bohr Professorship to S.S.

Author information

Authors and Affiliations

  1. Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, 2100, Denmark

    J. T. Nielsen & S. Sarkar

  2. Dipartimento di Fisica, Università degli Studi di Torino, via P. Giuria 1, Torino, I-10125, Italy

    A. Guffanti

  3. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK

    S. Sarkar

Authors
  1. J. T. Nielsen
  2. A. Guffanti
  3. S. Sarkar

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All authors participated in the analysis and in the writing of the paper.

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The authors declare no competing financial interests.

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Nielsen, J., Guffanti, A. & Sarkar, S. Marginal evidence for cosmic acceleration from Type Ia supernovae. Sci Rep 6, 35596 (2016). https://doi.org/10.1038/srep35596

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Comments

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  1. Rodney Bartlett

    While the expansion of space appeared to be confirmed by Edwin Hubble's 1929 observations, Hubble always disagreed with the expanding-universe interpretation of the data:

    "... if redshift are not primarily due to velocity shift ... there is no evidence of expansion, no trace of curvature ... and we find ourselves in the presence of one of the principles of nature that is still unknown to us today ... whereas, if redshifts are velocity shifts which measure the rate of expansion, the expanding models are definitely inconsistent with the observations that have been made ... expanding models are a forced interpretation of the observational results." ("Effects of Red Shifts on the Distribution of Nebulae" by E. Hubble, Ap. J., 84, 517, 1936)

    It seems to me that the universe is not physically expanding from a Big Bang at all. It appears to be undergoing topological extension in a Steady State. Computers' binary digits could be encoded by the quantum fluctuations / energy pulses called Virtual Particles which fill space-time. This is possible because the motions of virtual particles may not be random but may obey Chaos theory's principle of "order within apparent disorder" (chaos theory is sometimes called the third most important discovery of recent science, after Relativity and quantum mechanics). The digits are coded into the form of two-dimensional programs shaped as Mobius strips which are joined as four-dimensional figure-8 Klein bottles* (this process accounts for General Relativity's curvature of space-time). The bottles are extended from math form to structures in space-time that the energy of gravitational-electromagnetic interaction gives tangible form to. The above would only necessitate a God if
    time was exclusively a straight line. Since Einstein showed that space and time are curved, it's within the potential of future humanity to be responsible for the universe's creation.

    * Joining two Mobius strips (or Mobius bands) forms a four-dimensional Klein bottle [Polthier K, "Imaging maths - Inside the Klein bottle" http://plus.maths.org/conte...]

    Is it possible that the extension by mathematical topology's figure-8 Klein bottles is, in Edwin Hubble's words, "one of the principles of nature that is still unknown to us today"? It would replace the expanding-universe model which Hubble always disagreed with and be the cause of measurements of redshift and the Hubble constant. This constant would, in reality, measure topological extension rather than physical expansion. Regarding photons (e.g. microwave photons) alleged to be leftover from the Big Bang - they could be weakened by collisions with dust, gas and stars etc; and wavelengths would be redshifted by (perceived) distance to microwave wavelength from a higher, possibly gamma-ray, wavelength).

    A diagram of many figure-8 Klein bottles would show that their positive curvature (on the spherical parts) fits together with their negative curvature (on saddle-shaped parts) to cancel and produce the flatness of space-time's infinity/eternity (Hubble's "no trace of curvature"). Referring to mathematics' Complex Number Plane - like the pommel protruding from the front of a saddle, negative curvature can cause an "imaginary" space – and thanks to the indissoluble union of spatial plus temporal phenomena – the well established science concept of imaginary time; to extend 90 degrees from the "surface" of real, flat space-time. In this way, imaginary time gains reality and is no longer a mere mathematical trick. Itzhak Bars of the University of Southern California in Los Angeles says, "one whole dimension of time and another of space have until now gone entirely unnoticed by us". ("A Two-Time Universe? Physicist Explores How Second Dimension of Time Could Unify Physics Laws" - May 15, 2007 By Tom Siegfried - Read more at: http://phys.org/news/2007-0...

    For the note below on the figure-8 Klein bottle, I refer to – (11), (12), (13), (14), (15).
    (11) Bourbaki, Nicolas (2005). "Lie Groups and Lie Algebras". Springer
    (12) Conway, John (1986). "Functions of One Complex Variable I". Springer
    (13) Gamelin, Theodore (January 2001). "Complex Analysis". Springer
    (14) Joshi, Kapli (August 1983). "Introduction to
    General Topology". New Age Publishers
    (15) Spanier, Edwin (December 1994). "Algebraic Topology". Springer

    Informally - if an object in space consists of one piece and does not have any "holes" that pass all the way through it, it is called simply-connected. A doughnut (and the figure-8 Klein bottle it resembles) is "holey" and not simply connected (it’s multiply connected). "Some scientists believe that large warm and cool spots in the Cosmic Microwave Background could actually be evidence for this kind of ... (doughnut/figure-8 Klein bottle) ... topology" ("What Shape is the Universe?" by Vanessa Janek: (May 11, 2015) http://www.universetoday.co... - see later (in next paragraph) where figure-8 Klein bottles can be made into plausible subunits of a flat and infinite universe.

    A flat universe that is also simply connected implies an infinite universe. (Luminet, Jean-Pierre; Lachi`eze-Rey, Marc - "Cosmic Topology" - Physics Reports 254 (3): 135–214 (1995) arXiv:gr-qc/9605010) So it seems the infinite universe cannot be composed of subunits called figure-8 Klein bottles. But positive and negative curvatures can complement each other's shape, and digitised images can morph to perfect the complementarity if necessary (perhaps by binary digits filling in gaps and irregularities in the same way that computer drawings can extrapolate a small patch of blue sky to make a sky that's blue from horizon to horizon). This makes space-time relatively smooth and continuous - and gets rid of holes, making these types of Klein subunits feasible.

    On the subject of feasibility:

    "If the universe was nonorientable ie if it contained orientation-reversing curves such as the Möbius and Klein, there would be strange physical consequences that have not yet been observed. While they could be happening outside of our field of vision, it is unlikely that our universe is nonorientable." ("The Shape of the Universe" by Stacy Hoehn, formerly of Vanderbilt University's Mathematics Department: https://my.vanderbilt.edu/s... -
    October 13, 2009)

    [My comment: It can indeed be nonorientable if these strange physical consequences are happening outside of our field of vision i.e. if the universe is infinite*. What I regard as the strangest physical consequence would be that of the universe violating the Copernican ideal – this ideal makes man's view as typical and ordinary throughout the course of time as it is throughout the extent of space. Violating that ideal means our little corner of space-time really is different, in non-fundamental ways, from particular portions of the rest of spacetime (those different parts would still have binary digits / Mobius strips / figure-8 Klein bottles as their basis). Another strange consequence is the extra dimensions of Professor Itzhak Bars.

    * "The evidence keeps flooding in. It now truly appears that the universe is infinite" and "Many separate areas of investigation – like baryon acoustic oscillations (sound waves propagating through the denser early universe), the way type 1a supernovae compare with redshift, the Hubble constant, studies of cosmic largescale structure, and the flat topology of space – all point the same way."("Infinite Universe" by Bob Berman: "Astronomy" – Nov. 2012)

    The Klein bottle is a closed surface with no distinction between inside and outside. There cannot be other universes outside our infinite and eternal universe – there’s only one cosmos. To be fair, it could be called a multiverse since it's composed of multiple - even infinite - figure 8 Klein bottles.

    The above paragraphs seem to explain astronomer Alex Filippenko's statement, "there's something important missing in our physical understanding of the universe." ("Universe expanding faster than expected" by Korey Haynes - Astronomy Magazine's October 2016 issue, p.11)

  2. Damien Replied to Rodney Bartlett

    Facepalm... you realize this is saying that the expansion is not ACCELERATING... not that its not expanding... its CERTAINLY expanding, the question here is what is the rate of that expansion.

    All that nonsense and you cannot even understand the basic premise of what you are commenting on... Please stop being an imbecile.

  3. Abdul Malek

    The whole edifice of modern official cosmology is unfortunately
    built on the axiomatic mathematical idealism and the assumed "continuous
    spacetime field" of Einstein’s GR. The derived notions (like Ptolemic
    epicycles) of Big Bang, Inflation, black holes, dark matter, dark energy etc.
    of modern cosmology are all infected with the limitation of GR.

    "Matter in Motion", the primary premise of materialism has
    no role in GR; and neither it has any philosophical, ontological and logical basis. "The Philosophy of Space-Time: Whence Cometh Matter and Motion?" : https://www.amazon.co.uk/Ph...

    Ironically, it was the genius of Einstein himself who expressed doubt on the validly of such a premise in a letter to his friend Besso, "I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structure. In that case, nothing remains of my entire castle in the air, gravitation theory included, (and of) the rest of modern physics" A. Pais, Subtleis the Lord ..." The Science and the Life of Albert Einstein", Oxford University Press, (1982) 467,

  4. Emmette Davidson

    These guys are on the right track. Hopefully, the scientific community will take heed. There is no accelerated expansion (and by the same token, no inflation nor consequent many worlds, and therefore no need of "anything goes" string theory). There’s nothing wrong with Einstein’s theory of gravity, only that it is incomplete in not having unified all the forces of nature; with that completion, everything falls into place quite nicely.

  5. Damien Replied to Emmette Davidson

    Clearly you didnt read or understand the paper... it still very very much supports the idea that the universe is accelerating.

  6. Michael Replied to Damien

    Clearly, neither did you. The paper supports the idea that the universe is EXPANDING, but purports that the expansion is constant, not accelerating.

  7. Damien Replied to Michael

    No.... it doesnt. Figure 2 shows exactly what it asserts. Note how much of the probability contour is above the line no acceleration and how much of it is on or below it... It asserts that the data supports instead of the single extremely likely hypothesis that the expansion is accelerating, the data rather supports the very very likely hypothesis that the expansion is accelerating and that the null hypothesis (not accelerating) is very unlikely, though not unlikely enough to dismiss.

    Facepalm...

  8. Emmette Davidson Replied to Damien

    Perhaps it is you who should reread the paper, which in summary states "...we find, rather surprisingly, that the data are still quite consistent with a constant rate of expansion." From basic calculus, constant rate means zero acceleration.

  9. Damien Replied to Emmette Davidson

    Facepalm... No.... it doesnt. Figure 2 shows exactly what it asserts. Note how much of the probability contour is above the line no acceleration and how much of it is on or below it... It asserts that the data supports instead of the single extremely likely hypothesis that the expansion is accelerating, the data rather supports the very very likely hypothesis that the expansion is accelerating and that the null hypothesis (not accelerating) is very unlikely, though not unlikely enough to dismiss. From basic algebra... how to read a graph

    In other words, the fact that its plausible (although incredibly unlikely) that they could get this result if the expansion were not accelerating means that the conclusion does not entirely rule out constant rate of expansion.

  10. Emmette Davidson Replied to Damien

    It doesn’t matter how many face-palms you mock or statistics you strain, my quote is directly from the Abstract. It is also in the spirit of the more layman oriented announcement as to implications of these results by Stuart Gillespie of Oxford (http://www.ox.ac.uk/news/sc.... Like it or not, this is a significant challenge to the physics community.

  11. Arbaham

    Cosmic acceleration can result from competition with inreasing gravity. Here are some considerations. https://www.researchgate.ne...

  12. Larry J Van Stone

    Nobody has yet determined that Type 1a supernovae behave exactly the same regardless of metallicity. It is to be expected that the more distant ones will have lower metallicity, with the most distant being quite low in "metals". This ought to affect their brightness in a systematic way. Until this has been established and quantified, no conclusion as to possible acceleration of cosmological expansion is justified.

  13. Abdul Malek Replied to Larry J Van Stone

    It has been reported that there is not much variation of metallicity
    (Iron content for example) even in the inter-galactic media and in the far away galaxies, including the quasars, which are supposed to be at the periphery. For an alternative view of the cosmos please see: "Ambartsumian, Arp and the Breeding Galaxies": http://redshift.vif.com/Jou...

    What is more, there were recent (after the Nobel Award to
    Perlmutter et al.) reports that many supernovas (with similar light curve), which were supposed to be Type 1a, are in fact caused by the collision/merger of two white dwarf stars. If this is the case, then these cannot be used as "Standard Candles" for distance measurements. Moreover there are many stars in all the galaxies that have mass many times more than the mass of the sun (beyond the
    Chandrashekhar limit of 1.4 solar mass) that live for millions of years and potentially could become supernovae any time during their life times, thus complicating the matter even more! I am not sure whether even the authors of this article took these factors into account.

  14. Василий Минковский

    I tould about this in my theory in 2013: https://www.youtube.com/wat...

  15. Warren Smith

    This looks to have been piss-poor work from this entire community!

    When I initially saw all the supernova stuff, I was dubious and thought
    their stats were not good enough and they were overhyping inadequate evidence.

    But then the propaganda kept coming about "well, that was then, but we have two independent teams agreeing on this, we have hundreds of supernovae now and all our conclusions are beyond question" and they got the Nobel prize, so then I just sort of took their collective word for it.

    But if this new paper is believed, then it shows the entire community
    NEVER did the stats right, it is all garbage inadequately supported by
    their evidence, and a mass delusion --
    more precisely, there still to this day remains no statistically
    significant direct evidence for a cosmical constant, despite the Nobel
    and all the hype.

    However, maybe if they keep on collecting evidence until they have 10X
    more, that'd do it.

    Pathetic.

  16. Warren Smith Replied to Warren Smith

    Actually I think the situation is even worse than this paper says,
    because when one tries many models to find the max-likelihood model,
    one gets an artificially high "confidence of correctness." (E.g. consider
    what would happen with random numbers as entirely fake data.)
    That effect needs to be compensated for by a confidence-downgrade, which this paper did not do. Had they done it,
    then the situation would look even worse.

  17. Warren Smith Replied to Warren Smith

    Some of the other commenters have wrong ideas that e.g. the universe is not really expanding (it certainly is and that really is extremely well establihsed by the evidience by now) or that supernovae variation with metallicity was not thought of before (actually, it was thought of, and empirical corrections were devised that were key to their deductions).

    The present paper contrasts the "standard Lambda CDM model" with accelerating expansion due to repulsive Lambda
    term, versus "Milne model." This is however a pretty ridiculous comparison because the so-called Milne model is not even general relativistic at all and hence is clearly wrong? I mean, assuming we are willing to regard general relativity as well-established by now. For anybody taking tnat view, a better comparison would be repulsive Lambda,
    versus attractive, or zero, Lambda. And that comparison
    is not performed by the present paper.

  18. Симон Тыран

    The first sentence is already wrong. The expansion rate (the Hubble parameter) is not accelerating in Standard cosmology, it is decelerating and converging to a constant value (therefore the cosmological constant which leads to an accelerated expansion with a decreasing and later on almost constant expansion rate. Big difference!)

  19. Valeriy Polulyakh

    If we believe that our World has started sometimes ago we are still in the position to decide which hypothesis, Lemaître’s or Gamow’s was closer to reality. There is an opinion that the problems in the standard cosmology could be solved by adjusting of details. Our suggestion is that we have to go back to the conceptions and use the observations accumulated since.
    https://www.academia.edu/12...

  20. Moncy Vilavinal John

    Dear All, I would like to call your attention to a related paper in arXiv posted today, at https://arxiv.org/abs/1610....

  21. Moncy Vilavinal John

    A common misconception is that `no acceleration' means Milne-type empty universe. This is not correct. A nonempty flat universe, with both matter (66.6%) and dark energy (33.3%) can also expand with no acceleration. See a recent paper
    [1610.09885] Realistic coasting cosmology from the Milne model .

    Use of Bayesian theory in comparing cosmological models is now widely discussed. It may be interesting to know that such a work was done way back in 2001 itself and published in a Physical Review D paper. The result was the same as the recent claim: that the supernova data do not provide strong evidence in favour of an accelerating universe, when compared to a `non-accelerating coasting model' while using Bayesian theory.
    http://journals.aps.org/prd...

    This result was confirmed again in The Astrophysical Journal (ApJ) in 2005.
    http://iopscience.iop.org/a...

    The abstract of this paper tells it all:

    "In this paper, using a significantly improved version of the model-independent, cosmographic approach to cosmology, we address an important question: was there a decelerating past for the universe? To answer this, Bayes's probability theory is employed, which is the most appropriate tool for quantifying our knowledge when it changes through the acquisition of new data. The cosmographic approach helps to sort out the models in which the universe was always accelerating from those in which it decelerated for at least some time in the period of interest. The Bayesian model comparison technique is used to discriminate these rival hypotheses with the aid of recent releases of supernova data. We also attempt to provide and improve another example of Bayesian model comparison, performed between some Friedmann models, using the same data. Our conclusion, which is consistent with other approaches, is that the apparent magnitude-redshift data alone cannot discriminate these competing hypotheses. We also argue that the lessons learned using Bayesian theory are extremely valuable to avoid frequent U-turns in cosmology."

  22. Emmette Davidson Replied to Moncy Vilavinal John

    There should be no misconception, with respect to this paper anyway, which specifically states: "In particular the ‘Milne model’ refers here to an equation of state p = −ρ/3 and should not be taken to mean an empty universe."

  23. Chris Bullock

    If the universal expansion is constant as you suggest, then the need for Dark Energy is eliminated with the simple case of an infinite and homogenous universe. It is generally accepted that on the grand scale, the distribution of matter and energy is quite homogenious. If the universe is also infinite, then gravitational forces would cancel in all directions, resulting in no gravitational contraction of the universe. Therefore, no Dark Energy. Mystery solved.

    Of course, for this to be the case, the universe must have been infinite from the beginning, which means it did not start in one point as commonly believed. It would have had to start as an infinite size and expanded from there. The high temperature and density of the early universe would decrease as the universe expanded.

    On the bright side, this would explain the flatness and homogenious nature of the universe, without the need for inflation.

    Our simple minds don't handle infinities well, but that doesn't mean they don't exist.

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