arXiv:2409.02188v1 Announce Type: new
Abstract: Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is the granularity of spacetime, which suggests that free particles would deviate from classical geodesics by following a covariant Brownian motion. This notion is further supported by swerves models in causal set theory, a discrete approach to quantum gravity. At an effective level, such deviations are described by a stochastic correction to the geodesic equation. We show that the form of this correction is strictly restricted by covariance and the mass-shell condition. Under minimal coupling to curvature, the resulting covariant Brownian motion is unique. The process is equivalently described by a covariant diffusion equation for the distribution of massive particles in their relativistic phase space. When applied to dark matter particles, covariant Brownian motion results in spontaneous warming at late times, suppressing the matter power spectrum at small scales in a time-dependent manner. Using bounds on the diffusion rate from CMB and growth history measurements of $fsigma_8$, we show that the model offers a resolution to the $S_8$ tension. Future studies on the model’s behavior at non-linear cosmological scales will provide further constraints and, therefore, critical tests for the viability of stochastic dark matter.
Quantum Gravity and Cosmological Models
In order to bridge the gap between theory and observations in quantum gravity, it is important to develop effective cosmological models that take into account the fundamental aspects of quantum gravity. One key aspect to consider is the granularity of spacetime, which suggests that particles may deviate from classical geodesics and instead follow a covariant Brownian motion. This idea is supported by swerves models in causal set theory, a discrete approach to quantum gravity.
The Stochastic Correction and Covariant Brownian Motion
At an effective level, the deviations from classical geodesics are described by a stochastic correction to the geodesic equation. The form of this correction is strictly restricted by covariance and the mass-shell condition. When considering minimal coupling to curvature, it is found that the resulting covariant Brownian motion is unique. This process can also be described by a covariant diffusion equation for the distribution of massive particles in their relativistic phase space.
Covariant Brownian Motion and Dark Matter
When applied to dark matter particles, covariant Brownian motion leads to spontaneous warming at late times. This has the effect of suppressing the matter power spectrum at small scales in a time-dependent manner.
Resolution to the S8 Tension
By using bounds on the diffusion rate from measurements of the cosmic microwave background (CMB) and the growth history of the universe ($fsigma_8$), it is shown that the model of covariant Brownian motion offers a resolution to the tension in the determination of the parameter $S_8$.
Future Challenges and Opportunities
Future studies on the behavior of the model at non-linear cosmological scales will provide further constraints and critical tests for the viability of stochastic dark matter. This will be crucial in determining the potential of covariant Brownian motion as a model for quantum gravity and its compatibility with observational data.