Investigating Cosmological Dynamics of Tachyon Fluid with Varying Mass Dark Matter
arXiv:2404.07243v1 Announce Type: new
Abstract: This paper presents an investigation of cosmological dynamics of tachyon fluid coupled to varyingmass dark matter particles in the background of spatially flat FLRW universe. The mechanism of varying mass particles scenario assumes the mass of the dark matter depends on time t through the scalar field ${phi}$ in the sense that the decaying of dark matter reproduces the scalar field. First, we analyze the model from dynamical systems perspective by converting the cosmological evolution equations into an autonomous system of ordinary differential equations with a suitable transformation of variables. We choose the mass of dark matter as exponential function of scalar field and the exponential potential of the tachyon field is undertaken in such a way that the autonomous system is reduced in three dimensional form. The critical points obtained from the system are non-hyperbolic in nature. The center manifold theory is employed to discuss the nature of the critical points. Numerical investigation also carried out for some critical points. From this analysis, we obtain dust dominated decelerated transient phase of the universe followed by dark energy dominated scaling attractor alleviating the coincidence problem. Next, we perform the statefinder diagnostic approach to compare our model to ${Lambda}$CDM and finally we study the evolution of the Hubble parameter and the distance modulus and compare this with observational data.
Article Title: Investigating Cosmological Dynamics of Tachyon Fluid with Varying-Mass Dark Matter
In this paper, we present a study on the cosmological dynamics of a tachyon fluid coupled to varying-mass dark matter particles in the background of a spatially flat FLRW universe. Our investigation aims to understand the behavior of the universe in terms of its expansion and the role played by the tachyon fluid and varying-mass dark matter.
Roadmap
1. Dynamical Systems Perspective
We start by analyzing the model from a dynamical systems perspective. We convert the cosmological evolution equations into an autonomous system of ordinary differential equations using a suitable transformation of variables. The mass of dark matter is assumed to be an exponential function of a scalar field, and the exponential potential of the tachyon field is specifically chosen to simplify the autonomous system into a three-dimensional form.
One of the key findings of our analysis is the nature of the critical points obtained from the system. We observe that they are non-hyperbolic in nature. To understand the behavior of these critical points, we employ the center manifold theory.
Numerical investigation is also carried out for some critical points to gain additional insights into the dynamics of the system.
2. Cosmological Evolution and Coincidence Problem
Based on our analysis, we find that the universe undergoes a dust-dominated decelerated transient phase, followed by a dark energy-dominated scaling attractor. This solution helps alleviate the coincidence problem, which is the mystery of why we observe the universe being dominated by dark energy at the present epoch.
3. Comparison with ${Lambda}$CDM Model
In order to assess the validity and viability of our model, we perform a comparison with the ${Lambda}$CDM model using the statefinder diagnostic approach. By analyzing the statefinder parameters, we can evaluate the similarity and differences between our model and the standard ${Lambda}$CDM model.
4. Observational Data Comparison
Finally, we study the evolution of the Hubble parameter and the distance modulus in our model and compare it with observational data. This step allows us to assess the compatibility of our model with the observed behavior of the universe.
Challenges and Opportunities
- Challenge: One potential challenge in this study is the assumption of a specific form of the potential for the tachyon field. Different choices of potential could lead to different cosmological dynamics.
- Opportunity: An opportunity lies in exploring alternative forms of the potential for the tachyon field and assessing their impact on the cosmological dynamics. This could provide a richer understanding of the behavior of the universe.
- Challenge: The non-hyperbolic nature of the critical points obtained from the system poses a challenge in analyzing their stability and nature.
- Opportunity: Further research and techniques, such as perturbation theory and numerical simulations, can help overcome this challenge and provide a more comprehensive understanding of the critical points and their stability.
- Challenge: Comparing the model to observational data requires accurate and precise measurements of the Hubble parameter and the distance modulus.
- Opportunity: As observational techniques and instruments continue to improve, the accuracy and precision of cosmological measurements are likely to increase. This will provide more reliable data for model comparison and validation.
Overall, this investigation offers valuable insights into the cosmological dynamics of a tachyon fluid coupled to varying-mass dark matter. It contributes to our understanding of the behavior of the universe and provides a roadmap for further exploration and research in this fascinating field.