In Einstein’s General Relativity, gravitational interactions are mediated by a massless particle, the graviton. However, there is a general class of modified gravity theories that endow the graviton with a mass. What are the implications of massive gravitons?
First, the existence of a graviton mass causes a time delay in the propagation of gravitational waves as collections of gravitons, relative to the speed of light. Second, in many of these modified gravity theories, a massive graviton enables gravitational interactions only out to a limited distance, dictated by its quantum-mechanical Compton wavelength. This wavelength is given by h/mc, where h is Planck’s constant, m is the graviton mass and c is the speed of light. For a graviton mass that is 40 orders of magnitude lighter than the proton, this scale is 1.2 billion light years, about a tenth of the distance to the edge of the observable universe.
With a massive graviton, the gravitational influence of any object is suppressed exponentially below the Newtonian potential at distances larger than graviton Compton wavelength. This exponential suppression is commonly named after the Japanese physicist Hideki Yukawa who won the Nobel Prize in 1949 for describing the strong interaction as an exchange of massive particles named mesons, which exhibit the same exponential suppression on the meson Compton wavelength.
In past decades, many limits were set of the graviton mass based on a variety of astrophysical data sets all the way from the Solar system out to the Universe at large. Most recently, analysis of gravitational-wave data from the three observing runs of the LIGO-Virgo-KAGRA collaboration used the propagation speed constraint to derive a limit on the graviton mass that is 32 orders of magnitude below the proton mass. Thanks to an idea I had before my morning jog, I submitted for publication a new paper in which I improved this limit by a factor of 250 million.
My idea is simple. Our motion relative to the cosmic frame of reference introduces a Doppler effect through which the Cosmic Microwave Background (CMB) appears brighter in the direction we move. The increased CMB flux ahead of us is analogous to the experience of getting more wet at the front compared to the back when running through rain. Most recently, the Planck satellite measured this effect to an exquisite precision, implying a local peculiar velocity of about a thousandth of the speed of light relative to the cosmic frame of reference. Where does this velocity come from?
To a good approximation, the Universe is uniform. However, small density inhomogeneities in the early universe grew over time and resulted in large-scales structure today. These structures first collapsed along one axis, creating sheets that look like pancakes. Their collapse along a second axis created large-scale filaments. Eventually, the mass drained along the third axis of the filaments to form bound objects like galaxies or clusters of galaxies.
These large-scale concentrations of mass pull and push us relative to the cosmic frame. They are traced by the distribution of galaxies which behave as test particles on larger scales. An extensive infrared survey of galaxies, called 2MASS, traced the distribution of large-scale structure out to a distance of 1.2 billion light years. A detailed analysis of the clustering of matter in the 2MASS data set showed converge of the pulling and pushing to agree with our measured motion relative to the cosmic frame, but only if the net gravitational acceleration is integrated out to at least 1.2 billion light years.
My calculation showed that if the Compton wavelength of the graviton was smaller than 2.4 billion light-years, then the agreement between the 2MASS survey and the CMB dipole would have been spoiled. Hence, I concluded that the graviton mass must be smaller by 41.3 orders of magnitude of the proton mass, or equivalently less than 10 to the power -64 grams.
This new limit is tighter by 8.4 orders of magnitude than the LIGO-Virgo-KARGA limit and constitutes the best Yukawa-limit on the graviton mass so far.
In summary, it is very likely that the graviton mass is zero. This was expected in Einstein’s version of gravity from 1915 but not in more recent theories. Just as with fine wine, sometimes older is better.
Link to Related scientific paper: https://lweb.cfa.harvard.edu/~loeb/arXiv_Graviton.pdf
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. The paperback edition of his new book, titled “Interstellar”, was published in August 2024.
