{"title":"具有最小耦合标量场的相互作用暗能量模型的动力学系统方法","authors":"A. Samaddar, S. S. Singh, Md Khurshid Alam","doi":"10.1142/s0218271823500621","DOIUrl":null,"url":null,"abstract":"We investigated the stability condition of [Formula: see text] gravity theory with interacting and noninteracting models by using dynamical system. We assume the [Formula: see text] function as [Formula: see text], where [Formula: see text] is the free parameter. We evaluated the critical points for this model and examined the stability behavior. We found two stable critical points for interacting model. The phase plots for this system are examined and the physical interpretation is discussed. We illustrate all the cosmological parameters such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] at each fixed point and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is [Formula: see text]. We transform all the parameters in terms of redshift by using this equation and examine the behavior of these parameters. Our model represents the accelerated expansion of the universe. The energy conditions are examined in terms of redshift and strong energy conditions are not satisfied for the model. We also find the statefinder parameters [Formula: see text] in terms of z and discuss the nature of r–s and r–q plane. For both pairs [Formula: see text] and [Formula: see text] our model represents the [Formula: see text]CDM model. Hence, we determine that our [Formula: see text] model is stable and it satisfies all the observational values.","PeriodicalId":50307,"journal":{"name":"International Journal of Modern Physics D","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Dynamical system approach of interacting dark energy models with minimally coupled scalar field\",\"authors\":\"A. Samaddar, S. S. Singh, Md Khurshid Alam\",\"doi\":\"10.1142/s0218271823500621\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigated the stability condition of [Formula: see text] gravity theory with interacting and noninteracting models by using dynamical system. We assume the [Formula: see text] function as [Formula: see text], where [Formula: see text] is the free parameter. We evaluated the critical points for this model and examined the stability behavior. We found two stable critical points for interacting model. The phase plots for this system are examined and the physical interpretation is discussed. We illustrate all the cosmological parameters such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] at each fixed point and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is [Formula: see text]. We transform all the parameters in terms of redshift by using this equation and examine the behavior of these parameters. Our model represents the accelerated expansion of the universe. The energy conditions are examined in terms of redshift and strong energy conditions are not satisfied for the model. We also find the statefinder parameters [Formula: see text] in terms of z and discuss the nature of r–s and r–q plane. For both pairs [Formula: see text] and [Formula: see text] our model represents the [Formula: see text]CDM model. Hence, we determine that our [Formula: see text] model is stable and it satisfies all the observational values.\",\"PeriodicalId\":50307,\"journal\":{\"name\":\"International Journal of Modern Physics D\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-06-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Modern Physics D\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218271823500621\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Modern Physics D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/s0218271823500621","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 1
摘要
用动力系统方法研究了引力理论在相互作用和非相互作用模型下的稳定性条件。我们假设[Formula: see text]函数为[Formula: see text],其中[Formula: see text]是自由参数。我们评估了该模型的临界点,并检查了稳定性行为。我们找到了相互作用模型的两个稳定临界点。研究了该系统的相图,并讨论了物理解释。我们举例说明了每个固定点的所有宇宙学参数,如[公式:见文]、[公式:见文]、[公式:见文]和[公式:见文],并将参数与观测值进行了比较。进一步,我们假设混合尺度因子和红移与时间的方程为[公式:见文]。我们用这个方程将所有参数用红移的形式进行变换,并检验这些参数的行为。我们的模型代表了宇宙的加速膨胀。从红移角度考察了能量条件,发现模型不满足强能量条件。我们还找到了用z表示的寻态器参数[公式:见文],并讨论了r-s和r-q平面的性质。对于这两对[公式:见文本]和[公式:见文本],我们的模型代表[公式:见文本]CDM模型。因此,我们确定我们的[公式:见文]模型是稳定的,它满足所有观测值。
Dynamical system approach of interacting dark energy models with minimally coupled scalar field
We investigated the stability condition of [Formula: see text] gravity theory with interacting and noninteracting models by using dynamical system. We assume the [Formula: see text] function as [Formula: see text], where [Formula: see text] is the free parameter. We evaluated the critical points for this model and examined the stability behavior. We found two stable critical points for interacting model. The phase plots for this system are examined and the physical interpretation is discussed. We illustrate all the cosmological parameters such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] at each fixed point and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is [Formula: see text]. We transform all the parameters in terms of redshift by using this equation and examine the behavior of these parameters. Our model represents the accelerated expansion of the universe. The energy conditions are examined in terms of redshift and strong energy conditions are not satisfied for the model. We also find the statefinder parameters [Formula: see text] in terms of z and discuss the nature of r–s and r–q plane. For both pairs [Formula: see text] and [Formula: see text] our model represents the [Formula: see text]CDM model. Hence, we determine that our [Formula: see text] model is stable and it satisfies all the observational values.
期刊介绍:
Gravitation, astrophysics and cosmology are exciting and rapidly advancing fields of research. This journal aims to accommodate and promote this expansion of information and ideas and it features research papers and reviews on theoretical, observational and experimental findings in these fields. Among the topics covered are general relativity, quantum gravity, gravitational experiments, quantum cosmology, observational cosmology, particle cosmology, large scale structure, high energy astrophysics, compact objects, cosmic particles and radiation.