Researchers made the discovery studying how growth rings of spruce trees have varied over the past half a century.
As yet, they cannot explain the pattern, but variation in cosmic rays impacted tree growth more than changes in temperature or precipitation.
The study is published in the scientific journal New Phytologist.
"We were originally interested in a different topic, the climatological factors influencing forest growth," says Ms Sigrid Dengel a postgraduate researcher at the Institute of Atmospheric and Environmental Science at the University of Edinburgh.
To do this, Ms Dengel and University of Edinburgh colleagues Mr Dominik Aeby and Professor John Grace obtained slices of spruce tree trunks.
These had been freshly-felled from the Forest of Ae in Dumfriesshire, Scotland, by Forest Research, the research branch of the UK's Forestry Commission.
The trees had been planted in 1953 and felled in 2006.
The researchers froze the trunk slices, to prevent the wood shrinking, then scanned them on to a computer and used software to count the number and width of the growth rings.
As the trees aged, they showed a usual decline in growth.
However, during a number of years, the trees' growth also particularly slowed. These years correlated with periods when a relatively low level of cosmic rays reached the Earth's surface.
When the intensity of cosmic rays reaching the Earth's surface was higher, the rate of tree growth was faster.
The effect is not large, but it is statistically significant.
The intensity of cosmic rays also correlates better with the changes in tree growth than any other climatological factor, such as varying levels of temperature or precipitation over the years.
"The correlation between growth and cosmic rays was moderately high, but the correlation with the climatological variables was barely visible," Ms Dengel told the BBC.
Here comes the Sun
Cosmic rays are actually energetic particles, mainly protons, as well as electrons and the nuclei of helium atoms, that stream through space before hitting the Earth's atmosphere.
The levels of cosmic rays reaching the Earth go up and down according to the activity of the Sun, which follows an 11-year cycle.
Every 11 years or so, the Sun becomes more active, producing a peak of sunspots. These sunspots carry a magnetic field that blocks and slows the path of energetic particles.
When the researchers looked at their data, they found that tree growth was highest during periods of low sunspot activity, when most cosmic rays reached Earth.
But growth slowed during the four periods of cosmic ray-blocking high sunspot activity, which have occurred between 1965 and 2005.
"We tried to correlate the width of the rings, i.e. the growth rate, to climatological factors like temperature. We also thought it would be interesting to look for patterns related to solar activity, as a few people previously have suggested such a link," explains Ms Dengel.
"We found them. And the relation of the rings to the solar cycle was much stronger than it was to any of the climatological factors we had looked at. We were quite hesitant at first, as solar cycles have been a controversial topic in climatology."
"As for the mechanism, we are puzzled."
Ms Dengel's team proposes two main hypotheses as to how cosmic ray particles could influence the growth of trees.
The first idea is that cosmic rays ionise gases in the atmosphere, creating molecules around which clouds condense, therefore increasing cloud over.
This mechanism is hotly debated among scientists, and evidence for it is weak.
One study published in 2006 suggested it may account for as little as 2% of the variation in cloud cover across the UK.
But if it does occur, then an increase in cloud cover and haze would diffuse the amount of solar radiation reaching the trees.
As diffuse radiation penetrates forest canopies better than direct light, it would increase the amount of radiation that plants capture, and increase photosynthesis by trees, boosting growth.
Explaining the unexplained
"Or there is some direct effect," says Ms Dengel.
What that might be is unknown, but experiments in space have shown that cosmic rays can have some positive impacts on biological materials.
Ms Dengel says that much more work needs to be done to investigate the effect further, and their results have received a mixed reaction from other scientists.
"We sent the paper to 161 international colleagues. We are still harvesting the emails. We've identified four groups who would like to work with us on this.
"Locally, one of our colleagues is a cloud physicist. He was encouraging but sceptical at the same time."
If further research backs up the team's findings, the implications could be significant.
"We want to repeat this work for larger data sets, and understand the mechanism better, before we speculate," says Ms Dengel.
But the influence of cosmic rays could resolve other as yet unexplained cycles in tree growth found in studies in North America.
It also suggests the amount of aerosols that humans emit into the atmosphere could impact tree growth, as high levels of aerosols cause "global dimming", an effect that occurs when the levels of light reaching the Earth's surface fall.
"If it is true that the mechanism is all about rays enhancing diffuse radiation, it would mean that 'global dimming' and 'global brightening' would have a big effect on tree growth and therefore on the absorption of carbon dioxide," warns Ms Dengel.
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