182. Competing bounds on the present-day time variation of fundamental constants

This is a guest blog post by Thomas Dent from the U. of Heidelberg. Dmitry.

My recent preprint [arxiv:0812.4130] with Steffen Stern and Christof Wetterich from Heidelberg is perhaps more experimentally minded than most. We consider a question that has been attracting attention periodically since about 2001 – are the parameters of the Standard Model constant over all (observationally accessible) space and time, or are there variations away from the present measured values?

These “parameters” are the set of (apparently arbitrary) numbers that are necessary to match the SM to experiment, but do not follow from any established theory. The gauge sector, Higgs sector and flavour (i.e. elementary fermion) sector are all riddled with these numbers, whose present values are becoming better and better known by the efforts of experimentalists. And not to forget one force necessary to get correct experimental results: I also count the strength of semiclassical gravity, or the Planck mass, as a parameter.

Suppose we had some Theory of Everything we wished to test – assuming that it predicts some nontrivial relations between the SM parameters, one way to do it would be to see whether their values continue to satisfy such relations as they are more and more precisely measured. Still, the amount of information contained these values at any given time is not all that large. What if we were able to use not just the present values of the SM parameters, but their derivatives with respect to some other parameter… for example, time. In principle we could have twice as much information to test the Theory of Everything via the derivatives.

That is one tantalizing possibility of “varying constants”: if there is a unified theory with at least one variable parameter, it can be tested by nonzero time variations in a way that is independent from its consistency with present-day values.

Of course, we are limited by the ways in which time variations could be observed. Since 2001 there have been a series of papers by Webb, Murphy, Flambaum et al. which seemed to show a different value of the fine structure ‘constant’ alpha in absorption systems around redshift 1 or 2 compared to today, by a fractional amount of about or 0.001%. Such a measurement is possible because different absorption lines have strongly different dependences on alpha (due to relativistic corrections). Contrary to the expected behaviour of statistical glitches, the significance of the variation increased when further systems were added to the sample. The most recent value from the Murphy group is from 2003 [astro-ph/0310318]: the variation away from today’s alpha is

for a sample of 143 systems over a wide range of z. Yes, five sigma! The time difference is about years, so the linearly extrapolated variation rate would be a little below per year.

To probe any unified or beyond-the-standard model we need at least one more observable. Astrophysical spectra can also indicate variations in the ratio of proton and electron masses . This is sensitive both to the strong interaction (via ) and the Higgs vev (via ), so its theoretical dependence is rather more complex than alpha. Actually no significant variation of mu has been found, although the sensitivity is comparable to alpha: this is rather a problem for unified theories, where the strong interaction scale and the electroweak scale may both depend non-perturbatively on the unified couplings.

Since 2003 progress seems slow for astrophysical spectra. Other groups claimed to have more precise results showing null variation from smaller samples, but many of these were too optimistic about their errors. Improving the result robustly requires many high-quality spectra (already there from the VLT), and much computational effort to fit them correctly… which may take some years.

In the meantime, different probes of variation have been catching up and surpassing the sensitivity of absorption spectra. Most impressive has been the improvement in atomic clocks, which can be operated in optical frequencies [http://www.sciencemag.org/cgi/content/abstract/1154622] and are stable to a few parts in over a year’s operation. This bounds alpha variation to a few /year, inconsistent with a linear time variation extrapolated from at or .

Is this a reasonable extrapolation? This is where we come in as theorists! Varying alpha makes no theoretical sense without a new scalar degree of freedom whose dynamics should determine the space-time dependence. The behaviour of a cosmologically-varying scalar was already investigated, since it can be connected with another big observational puzzle, the acceleration of the Universe’s expansion, which seems to have switched on some time between and now. The energy of the scalar could drive the acceleration, but only if its kinetic energy is relatively small and it behaves almost like a vacuum energy or cosmological constant at present. This means that the evolution of the scalar has slowed since , and we cannot use a linear extrapolation over such a range of time. But with a significant slowing of evolution we could get down from /year to a few . We looked at a few models of ‘quintessence’ (ie scalar field with some choice of action and couplings) in arXiv:0809.4628 and it is possible but not automatic to get a reasonable fit.

Alternatively, you could just focus on the last few billion years, after the accelerated expansion has kicked in. This is less dependent on details of scalar field model-building. Bounds on variation in this epoch come from atomic clocks, but also the isotopic composition of meteorites, sensitive to variations in nuclear forces and alpha over the last 5 by, and neutron cross-sections in the Oklo natural nuclear reactor (1.8 by ago), which depend strongly on alpha, and possibly other parameters of particle physics.

What we did in arxiv:0812.4130 was to evaluate the bounds in general, since not only alpha but ratios of masses and energy scales in the SM may vary. We also incorporated bounds from Weak Equivalence Principle violations, which arise because the scalar has to couple differently to different constituents of matter, and so produces forces that depend on the composition of the bodies they act on. The ‘Eot-Wash’ group in Seattle has measured the gravitational acceleration of bodies with different composition and they are the same to few parts in , so the scalar couplings have to be very weak… Together with the cosmological bound on the kinetic energy of any field in the last few billion years, this severely limits any possible variation.

What are the results? If only alpha and no other parameter varies, the atomic clocks give by far the strictest bound on ‘recent’ variation. However, if there are also variations in the masses and energy scales of the SM, bounds from Equivalence Principle tests + cosmology are often competitive and even stronger. If there is ever a clear detection of nonzero variation over recent cosmological time, we could discriminate between different models of variation, and possibly unified models, by seeing where the variation arose. We could also put a lower bound on the equation of state of ‘dark energy’ since a nonzero time variation implies that some cosmological field has non-vanishing kinetic energy.

So much interesting physics could be done with a variation that it seems slightly disappointing that nature seems to have made it, if not zero, then so extremely small…