It's a pretty simple-minded analysis, so I doubt it will be taken very seriously. That's not to say that astronomers are particularly attached to the cosmological constant model of the universe. Many (including myself) suspect that we will eventually find a non-trivial equation of state for the "dark energy". It's going to require more precision than this, however.

There's a limit to how much I trust Type Ia supernovae as a standard candle -- well, two limits, really. First, I don't trust them to arbitrary precision. We account for the zeroth order (the average energy output) and first order (the correction for energy output from the light curve) terms in the "standard candle" expansion, but there are no doubt higher order corrections that need to be made. Second, I don't trust them to arbitrary redshift. It appears that Type Ia SNe aren't evolving very much at low redshift, but that doesn't mean we can extrapolate those conclusions to arbitrary z.

It's for exactly these reasons that a lot of astronomers are skeptical about the usefulness of the planned Supernova/Acceleration Probe (SNAP). It's basically a satellite for doing supernova and weak lensing cosmology, with the principle goal of constraining the properties of the dark energy. In theory, it could provide some interesting results, but there's maybe a bit more uncertainty than some are comfortable with. It has also been argued that similar-quality measurements of the properties of the dark energy can be obtained from ground-based weak lensing analyses. It never hurts to get independent confirmation, though.

In short, we won't be able to say much more about the dark energy for another 5 years, at least. There's a lot of uncertainty in analyses like that done in this paper, so I would be prone to disregard it for the time being.

I tend to think this was a tongue in cheek poke by Vishwakarma. ST makes good points. It is very risky to extrapolate data that is already shaky. And I think most theorists are fully aware of that and do so carefully. We should not get terribly attached to the occasional confirming observation. It is encouraging, but, not compelling.

One thing I have always found discomforting is the potential role of metallicity in SN light curves. I think it reasonable to assume metallicity tends to decrease with distance, and might be a spoiler in the 'standard candle' scheme of things.

It could also just be statistical noise. A P-value of 3.4% (as in the Vishwakarma paper) isn't as bad as it seems. This article explains how you can extract minimum Bayes factors from P-values. It has a handy little table. It assumes normal distributions rather than chi-squared, though, so I'm not sure to what extent the exact numbers carry over.

I've skimmed the paper; two quick comments:
- it's not clear to me how well the author applied the 'first order' corrections (per ST's post), or even if he did; each of the independent studies/papers he combines almost certainly applied these in slightly different ways, to their datasets
- this kind of meta-analysis can work very well ... provided you have a minimum of 'angles' you can apply to the stats (and you work those angles properly); it was unclear to me, in my quick skim, how thoroughly, and rigorously, Vishwakarma handled all the stats (my impression is, not at all well; for example, did he mention Bayes, even once?).