Sakharov Oscillations in Cosmology

No time for much of a post today, but I couldn’t resist commenting on something I picked up from Twitter just now. Today is the 93rd anniversary of the birth of the nuclear physicist and dissident Andrei Dmitrievich Sakharov who died in 1989. Sakharov is probably more famous for his political campaigning and the award of the Nobel Peace Prize in 1975 than for his work in physics, but I couldn’t resist mentioning a classic paper by him which was first published in Russian in 1965.

Here is the abstract:


The importance of this remarkable paper for modern cosmology can’t be overstated, although many modern cosmologists have either forgotten it or were never aware of it in the first place. The details are a bit out of date, but the idea that density perturbations that grew by a process of gravitational instability to form galaxies and the large-scale structure of the Universe has survived almost fifty years, and plays a central role in the standard cosmological model. Moreover, the Sakharov Oscillations predicted in this paper manifest themselves in the temperature fluctuations of the cosmic microwave background as measured by, e.g., the Planck experiment:


The wiggles in the power spectrum plotted above appear because these fluctuations, generated in the modern theory during an episode of cosmic inflation, are set up in phase and thus reach the epoch of scattering at different phases of their oscillation and hence with different amplitudes. The detailed behaviour of the spectrum displayed above tells us a huge amount about the composition and evolution of the Universe.

When Francesco Lucchin and I were writing the first edition of our cosmology textbook (second edition here) we were careful to acknowledge Sakharov’s role in the development of cosmological theory, which wasn’t generally reflected in texts written outside Russia. I particularly recall the late Leonid Grischuk banging on about Sakharov’s work at many conferences in order to ensure he got proper credit and some books, e.g. Zel’dovich and Novikov’s two-volume Relativistic Astrophysics, do acknowledge him correctly. Somehow, however, the CMB wiggles never acquired the name of Sakharov; the peaks in the spectrum are often still called Doppler Peaks or Acoustic Peaks, when surely they should be Sakharov Peaks. It’s probably too late to change the nomenclature now, but there you go.

Anyway, I’ve now realized that I was working on the First Edition of Coles & Lucchin in 1994 which is now twenty years ago so before I get too depressed about the passage of time I’ll stop writing and get on with something else!

Anyway, I’ve now realized that

3 Responses to “Sakharov Oscillations in Cosmology”

  1. Anton Garrett Says:

    Given that he also designed the Soviet H-bomb he perhaps deserved a Nobel Physics Prize rather than a Nobel Peace Prize. Although the latter is already pretty tainted.

  2. Peter the abstract talks about masses of globular clusters, but the BAO – and the first CMB power spectra peaks – correspond to masses hugely greater than that. So was he in fact talking about the same thing? George

    • telescoper Says:


      The entire cosmological framework was different then so the details are definitely wrong. He didn’t know about dark matter, for example so is talking about the baryonic component only. He also didn’t know about Silk Damping which suppresses fluctuations on small scales so the oscillations do not survive on those scales. However, it is worth mentioning that the first objects to form in the current CDM cosmology have a mass not far from that of a globular cluster so it’s not that far off actually!

      So in detail it’s not right but the concept has survived.


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