Ultralight bosons are attractive dark-matter candidates and appear in various
scenarios beyond standard model. They can induce superradiant instabilities
around spinning black holes (BHs), extracting the energy and angular momentum
from BHs, and then dissipated through monochromatic gravitational radiation,
which become promising sources of gravitational wave detectors. In this letter,
we focus on massive tensor fields coupled to BHs and compute the stochastic
gravitational wave backgrounds emitted by these sources. We then undertake a
search for this background within the data from LIGO/Virgo O1$sim$ O3 runs.
Our analysis reveals no discernible evidence of such signals, allowing us to
impose stringent limits on the mass range of tensor bosons. Specifically, we
exclude the existence of tensor bosons with masses ranging from
$4.0times10^{-14}$ to $2.0times10^{-12}$ eV at $95%$ confidence level.

Future Roadmap: Challenges and Opportunities

Based on the conclusions of the text, we can outline a roadmap for readers to understand the potential challenges and opportunities that lie ahead:

1. Exploring Ultralight Bosons

Further research should be conducted to thoroughly examine ultralight bosons as attractive dark-matter candidates. These particles have shown promise in scenarios beyond the standard model and could potentially explain the nature of dark matter. Scientists should focus on understanding the properties of ultralight bosons and their interactions with other particles.

2. Superradiant Instabilities around Black Holes

Investigating the superradiant instabilities around spinning black holes is crucial to understand the extraction of energy and angular momentum from these objects. Researchers should delve into the mechanisms behind these instabilities and explore their implications for gravitational wave detectors. This avenue of study may lead to groundbreaking discoveries in our understanding of black holes and their behavior.

3. Stochastic Gravitational Wave Backgrounds

Future efforts should be directed towards computing the stochastic gravitational wave backgrounds emitted by sources such as massive tensor fields coupled to black holes. Understanding these backgrounds can provide valuable insights into various astrophysical phenomena. Scientists should continue analyzing and modeling these gravitational wave backgrounds to unlock new information about the universe.

4. Searching for Signals

Ongoing searches for gravitational wave signals should be conducted using data from LIGO/Virgo runs, such as O1 through O3 mentioned in the text. These searches will improve our ability to detect and analyze gravitational waves from various sources, including the potential sources associated with ultralight bosons and black holes. Continual advancements in data analysis methods and detector sensitivity are required to enhance our chances of identifying new and significant signals.

5. Imposing Limits on Tensor Boson Masses

Studies like the one mentioned in the article provide important information about the existence and properties of tensor bosons. Researchers should continue imposing limits on the mass range of these particles to further refine our understanding of fundamental physics. Higher confidence level limits, such as the 95% confidence level mentioned, should be pursued to ensure the accuracy and reliability of the findings.


The roadmap outlined above emphasizes the need for continued research and exploration in the field of ultralight bosons, black holes, and gravitational waves. By addressing the challenges and seizing the opportunities presented in these areas of study, scientists can make significant progress towards unraveling the mysteries of the cosmos and developing a deeper understanding of fundamental physics.

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