Phys.org article: http://phys.org/news/2012-10-interstellar-physicist-anomaly.html
The Pioneer anomaly: the Pioneer 10 and 11 spacecraft were launched in 1972 and ‘73 respectively. They are currently leaving the solar system. By bouncing radio waves off the spacecraft (their high-gain antenna probably), both the distance and line-of-sight velocity can be determined by the time-of-flight of the radio waves and a doppler shift upon receiving the radio waves.
The velocity measurements indicated a small but anomalousdeceleration. One proposed explanation was an imbalance of heat caused by the electrical generators, pushing the spacecrafts away from the direction heated more (thermal recoil). Thermal recoil could only account for up to 20% of the deceleration.
The paper cited in this article proposes that the cause of the apparent deceleration is nothing to worry about and is explained neatly by known physics: the expansion of the universe. Our solar system isn’t getting bigger as the universe expands because the local gravity of the Sun keeps everything nice a close together: the solar system is a gravitationally bound system.
But light waves are free to leave the solar system. Light also behaves differently than matter as the universe expands. Light gets stretched along with the scale of the universe, so light waves will slowly become longer in wavelength, lower energy. The paper cited claims that the universal expansion causes an apparent deceleration, but once the expansion is taken into account, everything is as we expect.
This paper was published in Physical Review D, so it is not available to the public.