Gravitational collapse of matter in the presence of Quintessence and Phantom-like scalar fields

Abstract: In this work, we propose a model of the gravitational collapse of dark matter in the presence of quintessence or phantom-like scalar fields. Our treatment is based on the principles of general relativity up to virialization. We have chosen a spherical patch that starts to collapse gravitationally as it happens in top-hat collapse. It is seen that although the dark matter sector collapses the dark energy sector does keep a profile that is almost similar to the dark energy profile for the background expanding Friedmann-Lemaitre-Robertson-Walker (FLRW) universe for suitable model parameters. It is observed that in order to formulate the problem in the general relativistic setting one has to abandon the idea of a closed FLRW isolated collapsing patch. General relativity requires an external generalized Vaidya spacetime to be matched with the internal spherical patch whose dynamics is guided by the FLRW metric. It is shown that almost all collapses are accompanied by some flux of matter and radiation in the generalized Vaidya spacetime. Some of the spherical regions of the universe are seen not to collapse but expand eternally, producing void-like structures. Whether a spherical region will collapse or expand depends upon the initial values of the system and other model parameters. As this work shows that collapsing structures must emit some form of radiation, this may be taken as an observational signature of our proposal.

• The paper presents a general relativistic model that demonstrates how quintessence and phantom-like scalar fields alter the gravitational collapse of dark matter.
• It employs a closed FLRW metric and generalized Vaidya spacetime to simulate energy fluxes, addressing non-conservation issues in traditional models.
• The study finds that specific parameter ranges yield either structure formation or voids, highlighting the dual impact of dark energy on cosmic evolution.

Overview of "Gravitational collapse of matter in the presence of Quintessence and Phantom-like scalar fields"

The paper "Gravitational collapse of matter in the presence of Quintessence and Phantom-like scalar fields" addresses the complex dynamics of gravitational collapse in a universe composed of dark matter and dark energy, represented by scalar fields. The study investigates the influence of quintessence and phantom-like scalar fields on the collapse process, utilizing a framework grounded in general relativity, and moving beyond purely phenomenological methods.

The authors present a model wherein a spherically symmetric over-dense region of dark matter collapses in the presence of a scalar field. Unlike traditional models that neglect the impact of dark energy, this study incorporates a two-component fluid system, where the interaction of dark matter and dynamic dark energy is considered within a closed Friedmann-Lemaître-Robertson-Walker (FLRW) metric. The research seeks to elucidate whether non-linear perturbations lead to the formation of structures or voids in the cosmic web.

Methodology

The study employs a closed FLRW metric to model the dynamics of over-dense regions, while a flat FLRW metric represents the cosmological background. The gravitational collapse is simulated using a general relativistic approach, accounting for the inclusion of a generalized Vaidya spacetime to manage fluxes of matter and radiation during the collapse. This external Vaidya spacetime allows for the exchange of energy across the boundary of the collapsing region, addressing the non-conservation of energy seen in isolated systems.

Key equations from general relativity are utilized to characterize the scalar fields, adopting potentials such as $V(\phi) = V_0 e^{-\lambda \phi}$ prevalent in quintessence and phantom field models. The authors solve these equations numerically to investigate the effects of different parameters on the collapse process.

Results

The study finds that the presence of scalar fields significantly affects the gravitational collapse of dark matter. Crucially, in scenarios where dark energy does not cluster, the scalar field remains unclustered and homogeneous, maintaining a profile similar to that of the expanding background universe. This matches prior theoretical predictions that dynamic dark energy might inhibit or alter the collapse process.

Additionally, the paper discovers that certain parameter ranges lead to eternal expansion of the region, forming void-like structures instead of collapsing. This dual outcome—structures or voids—depends on initial conditions and model parameters, suggesting a complex interplay between dark matter and dark energy during cosmic structure formation.

The use of a generalized Vaidya spacetime successfully resolves the energy conservation issues found in prior models, providing a theoretical basis for observable radiation from collapsing regions. This potentially offers a new avenue for observational verification of the model's predictions.

Implications and Future Directions

The findings have substantial implications for our understanding of cosmic structure formation. By demonstrating that dark energy can lead to both the promotion and inhibition of collapse, the study supports the notion that the nature of dark energy is critical to large-scale cosmic evolution.

Future research could expand on this work by comparing theoretical predictions with observational data, possibly constraining the parameters related to dark energy and refining models of cosmic evolution. Additionally, investigating other forms of scalar field potentials or including non-minimal couplings might yield further insights into the dynamics of dark matter and dark energy interaction.

Overall, this research contributes to a deeper understanding of the role of dark energy, specifically inhomogeneous scalar fields, in the context of gravitational collapse, challenging existing paradigms while providing a robust theoretical framework for further exploration in cosmology.