Chaplygin gas

Chaplygin gas. It is a hypothetical form of exotic matter characterized by an unusual equation of state where pressure is inversely proportional to density. First studied in aerodynamics by the Russian scientist Sergei Chaplygin, its properties were later found to be of significant interest in theoretical cosmology as a potential candidate for dark energy and dark matter. The model provides a unified description for these two dominant but mysterious components of the universe, offering an alternative to the standard Lambda-CDM model.

Definition and basic properties

The defining feature is its specific barotropic equation of state, originally derived in the context of lift (force) calculations on aircraft wings. In this framework, pressure decreases as density increases, a counterintuitive relationship compared to most conventional perfect fluid models. This mathematical property allows it to behave like pressureless dust at high densities, mimicking the clustering behavior of dark matter, while acting like a cosmological constant at low densities, driving accelerated expansion akin to dark energy. The model was significantly revived and extended in cosmological contexts by researchers like Viatcheslav Mukhanov and Alexander Kamenshchik, connecting early 20th-century fluid dynamics to modern problems in physical cosmology. Its simplicity as a single-fluid component within the Friedmann equations makes it an attractive toy model for exploring unified dark sector scenarios, bridging the gap between the eras dominated by the Planck satellite and the James Webb Space Telescope.

Cosmological applications

Its primary application lies in modeling a unified dark fluid, a single entity that accounts for the effects attributed separately to dark matter and dark energy in the standard model of cosmology. In the early universe, when densities were high, it would cluster under gravity similarly to cold dark matter, potentially seeding the formation of structures like the Virgo Cluster and the Sloan Great Wall. As the universe expands and the density drops, its negative pressure begins to dominate, leading to an accelerated expansion phase, reproducing observations from projects like the Supernova Cosmology Project and the Hubble Space Telescope. This transition offers a dynamical alternative to a static cosmological constant, potentially addressing fine-tuning problems associated with Lambda-CDM model. The model has been integrated into studies of cosmic microwave background anisotropies measured by the Wilkinson Microwave Anisotropy Probe and the evolution of large-scale structure cataloged by the Sloan Digital Sky Survey.

Relation to other models

The original formulation is a specific case of a broader class of models known as generalized Chaplygin gas, which introduces an additional parameter for more flexibility in fitting observational data. It is mathematically connected to scalar field theories, such as quintessence, through a Born-Infeld-type Lagrangian, often studied in the context of string theory and brane cosmology. The model can also be seen as a realization of a perfect fluid with an exotic equation of state, standing in contrast to more conventional components like baryonic matter or radiation. Its behavior interpolates between that of a pressureless fluid and a cosmological constant, making it a bridge between the Einstein field equations solutions for matter-dominated and de Sitter universes. Comparisons are frequently made to other unified models like the van der Waals fluid and proposals involving tachyon condensates from works in theoretical physics.

Mathematical formulation

The equation of state is given by \( p = -A/\rho \), where \( p \) is pressure, \( \rho \) is energy density, and \( A \) is a positive constant. This can be derived from the Nambu-Goto action for a scalar field in a certain limit. When inserted into the continuity equation within the framework of the Friedmann equations, the density evolves as \( \rho(a) = \sqrt{A + B/a^6} \), where \( a \) is the scale factor and \( B \) is an integration constant. This solution showcases the interpolating behavior: for small \( a \) (early times), it behaves like \( \rho \sim \sqrt{B}/a^3 \) (dust), and for large \( a \) (late times), \( \rho \sim \sqrt{A} \) (cosmological constant). The model's dynamics are often analyzed using tools from Hamiltonian mechanics and perturbations are studied within the context of linear perturbation theory to assess stability against gravitational collapse, a key concern for structure formation.

Observational constraints and status

The model has been subjected to rigorous tests against modern astrophysical data. Constraints from the cosmic microwave background power spectrum, particularly from the Planck satellite, along with baryon acoustic oscillations data from the Sloan Digital Sky Survey, have limited the parameter space for a pure, unified model. Observations of the Hubble constant from the Hubble Space Telescope and distance measurements from Type Ia supernova surveys like the Supernova Legacy Survey generally favor the standard Lambda-CDM model, but allow some room for alternative components at certain confidence levels. A significant challenge is its tendency to suppress the growth of structure and produce oscillations or non-adiabatic instabilities in the matter power spectrum, which conflict with observations of galaxy clusters and the Lyman-alpha forest. Current research, incorporating data from the Dark Energy Survey and the upcoming Euclid spacecraft, focuses on more complex variants, like the modified or variable Chaplygin gas, to better align with the observed history of the universe while preserving its appealing unified nature.

Category:Dark energy Category:Hypothetical matter Category:Physical cosmology