First Detection of Traces of Extra Dimensions in the Cosmic Microwave Background
Тяжёлые моды и гравитоны Калуцы–Клейна из дополнительных измерений, избегая обнаружения в земных экспериментах, могут рождаться во время инфляции и генерировать первичную негауссовость через неизбежное взаимодействие с возмущениями плотности. В искривлённой пятимерной модели вычислены полные биспектры, опосредованные радионом и КК-гравитонами, и впервые выполнен поиск этих сигналов в данных Planck 2018 по температуре и поляризации. Статистически значимых свидетельств негауссовости не найдено; максимальная значимость составила 1.8σ для массы КК-гравитона около 1.6H (H — параметр Хаббла во время инфляции). Дополнительно идентифицирована 5D-конфигурация, естественно производящая негауссовость с параметром f_NL в диапазоне 1–50, что находится в пределах досягаемости будущих обзоров неба.
Context
Particle physics has long developed within the framework of the Standard Model, yet many mysteries—from the mass hierarchy to the nature of dark matter—call for new ideas. One of the boldest hypotheses suggests that our world contains hidden spatial dimensions, curled up into tiny loops or forming 'branes' in a higher-dimensional space. Testing these ideas in terrestrial accelerators is challenging, as the energy at which they manifest could be unreachably high. However, right after the Big Bang, during the inflationary expansion era, the characteristic energy scale—the Hubble parameter—could have reached 10^13–10^14 GeV, opening a unique window into ultra-high-energy physics. It is this approach, proposed over a century ago by Georges Lemaître and advanced by the discoveries of Edwin Hubble, that allows us to use the cosmic microwave background as a kind of cosmological collider.
Methods
The analysis used Planck mission data on the temperature and polarization of the cosmic microwave background, discovered in 1965 by Arno Penzias. The main method is the search for deviations from Gaussianity in three-point correlation functions (bispectra). Such deviations can arise if massive particles, such as Kaluza-Klein gravitons, were produced and decayed during inflation. According to the uncertainty principle, quantum fluctuations in the rapidly expanding spacetime lead to the creation of particle pairs from the vacuum. Thanks to superposition of states and effects reminiscent of quantum entanglement, the primordial perturbations acquire a characteristic angular dependence, which depends on the particle's spin and mass. This is akin to high-energy spectroscopy, where the signal shape acts as a spectral line. Unlike ordinary gravitational waves, which propagate through spacetime, massive gravitons manifest through non-Gaussian contributions. The calculations were carried out within a warped five-dimensional space model (RS1), stabilized by the Goldberger-Wise field, taking into account the effects of time dilation in the expanding Universe.
Results
The analysis found no statistically significant signal: the maximum local significance for the Kaluza-Klein graviton was 1.8σ at a mass around 1.6 H (where H is the Hubble parameter during inflation). No significant deviations were found for the radion. At the 95% confidence level, the non-Gaussianity parameter f_NL is consistent with zero: for the radion f_NL ≈ 15 ± 34, for the graviton f_NL ≈ −58 ± 32. However, the researchers showed that within a specific five-dimensional model, values of f_NL around 1–50 are naturally expected, within reach of future surveys. The obtained constraints depend strongly on the bispectrum shape: the observed structure proved sensitive to the particles' quantum numbers, making the method a true mass-spin spectroscopy. The bispectrum shapes, when projected onto the celestial sphere, retain characteristic angular dependencies because the perturbations moved at the speed of light in the hot plasma of the early Universe.
Implications
The discovery that even heavy particles from hidden dimensions, inaccessible to colliders, can leave a trace in the cosmic microwave background changes our approach to testing 'grand unification' theories. Observational bounds on non-Gaussianity can now be directly translated into constraints on the parameters of multidimensional models. Interestingly, these results echo the problem of black hole entropy, where the question of information conservation in quantum gravity also arises. Moreover, they confirm the fruitfulness of the cosmological collider idea, proposed to probe physics at scales otherwise inaccessible. In the future, such studies may shed light on the nature of dark matter, if it turns out to consist of Kaluza-Klein particles as well.
Future development
In the coming years, the sensitivity of non-Gaussianity searches will increase thanks to new data on the large-scale structure of the Universe—the distribution of galaxies and clusters—as well as improved measurements of CMB polarization. Projects like Euclid, SPHEREx, and future sky surveys will already allow for a several-fold reduction in errors. Theorists are also working on extending the class of models: for instance, incorporating non-trivial dynamics in the extra dimensions or chemical potential effects that enhance particle production. Of particular interest is the search for four-point functions (trispectra), which could provide additional information. One can expect that within 5–10 years, sensitivity sufficient to test realistic predictions will be achieved, and then cosmology will become a full-fledged tool for high-energy spectroscopy, competing with accelerators.
Impact
The results will directly impact programs searching for non-Gaussianity in future cosmological missions and surveys, and will also stimulate the development of multidimensional models in string theory.
Next steps
The next step will be the analysis of new data with improved sensitivity, as well as combined searches for the radion and gravitons including four-point correlations.
Key open problems
The research links the mass hierarchy problem and the nature of dark matter to observable cosmology. It also touches on the fundamental question of quantum gravity: quantum fluctuations of spacetime in the early Universe could have left an indelible imprint if string theory with extra dimensions is correct.
🎯 Interestingly, the idea of using cosmology to test particle physics dates back to the 1970s, but only now, thanks to the precision of Planck data, has it become a reality.
🎬 In Greg Egan's novel 'Schild's Ladder', a universe with extra dimensions is described, where physicists discover a way to travel through the 'bulk'. While our reality is more modest, searching for messenger particles from hidden dimensions in the cosmic microwave background is a step toward 'hearing' the echo of a multidimensional cosmos.
Key numbers
- inflation energy scale (maximum): 4×10^13 GeV
- fNL constraint for KK graviton (μ=0.5): −58 ± 32 (68% CL)
- fNL constraint for radion (μ≈1.8): 15 ± 34
- mass of lightest KK graviton: ≈1.57 H
- mass of radion: ≈1.80 H