scholarly journals Cosmographic analysis of the equation of state of the universe through Padé approximations

2014 ◽  
Vol 89 (10) ◽  
Author(s):  
Christine Gruber ◽  
Orlando Luongo
Keyword(s):  
Equation Of State ◽  
Padé Approximations ◽  
Pade Approximations ◽  
The Universe

scholarly journals High-redshift cosmography: auxiliary variables versus Padé polynomials

2020 ◽  
Vol 494 (2) ◽  
pp. 2576-2590 ◽  
Author(s):  
S Capozziello ◽  
R D’Agostino ◽  
O Luongo
Keyword(s):  
High Redshift ◽  
Padé Approximation ◽  
Monte Carlo Analysis ◽  
Pade Approximation ◽  
Shift Parameter ◽  
Padé Approximations ◽  
Pade Approximations ◽  
Optimal Approach ◽  
Fifth Order ◽  
The Universe

ABSTRACT Cosmography becomes non-predictive when cosmic data span beyond the redshift limit z ≃ 1. This leads to a strong convergence issue that jeopardizes its viability. In this work, we critically compare the two main solutions of the convergence problem, i.e. the y-parametrizations of the redshift and the alternatives to Taylor expansions based on Padé series. In particular, among several possibilities, we consider two widely adopted parametrizations, namely y1 = 1−a and $y_2=\arctan (a^{-1}-1)$, being a the scale factor of the Universe. We find that the y2-parametrization performs relatively better than the y1-parametrization over the whole redshift domain. Even though y2 overcomes the issues of y1, we get that the most viable approximations of the luminosity distance dL(z) are given in terms of Padé approximations. In order to check this result by means of cosmic data, we analyse the Padé approximations up to the fifth order, and compare these series with the corresponding y-variables of the same orders. We investigate two distinct domains involving Monte Carlo analysis on the Pantheon Superovae Ia data, H(z) and shift parameter measurements. We conclude that the (2,1) Padé approximation is statistically the optimal approach to explain low- and high-redshift data, together with the fifth-order y2-parametrization. At high redshifts, the (3,2) Padé approximation cannot be fully excluded, while the (2,2) Padé one is essentially ruled out.

scholarly journals Dynamical system analysis of FLRW models with Modified Chaplygin gas

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ali Osman Yılmaz ◽  
Ertan Güdekli
Keyword(s):  
Dynamical System ◽  
Equation Of State ◽  
Energy Density ◽  
System Analysis ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
State Spaces ◽  
The Universe ◽  
Matter Energy ◽  
Far Future

AbstractWe investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods. We assume $$p=(\gamma -1)\mu -\dfrac{A}{\mu ^\alpha }$$ p = ( γ - 1 ) μ - A μ α as equation of state where $$\mu$$ μ is the matter-energy density, p is the pressure, $$\alpha$$ α is a parameter which can take on values $$0<\alpha \le 1$$ 0 < α ≤ 1 as well as A and $$\gamma$$ γ are positive constants. We draw the state spaces and analyze the nature of the singularity at the beginning, as well as the fate of the universe in the far future. In particular, we address the question whether there is a solution which is stable for all the cases.

scholarly journals Almost-Pseudo-Ricci Symmetric FRW Universe with a Dynamic Cosmological Term and Equation of State

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 205
Author(s):  
Sanjay Mandal ◽  
Avik De ◽  
Tee-How Loo ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Equation Of State ◽  
Cosmological Parameters ◽  
Cosmological Term ◽  
Ricci Scalar ◽  
Energy Conditions ◽  
Late Time ◽  
Frw Universe ◽  
Accelerating Expansion ◽  
Expansion Of The Universe ◽  
The Universe

The objective of the present paper is to investigate an almost-pseudo-Ricci symmetric FRW spacetime with a constant Ricci scalar in a dynamic cosmological term Λ(t) and equation of state (EoS) ω(t) scenario. Several cosmological parameters are calculated in this setting and thoroughly studied, which shows that the model satisfies the late-time accelerating expansion of the universe. We also examine all of the energy conditions to check our model’s self-stability.

Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation

2006 ◽  
Vol 11 (2) ◽  
pp. 139-158 ◽  
Author(s):  
Kathy Driver ◽  
Helmut Prodinger ◽  
Carsten Schneider ◽  
J. A. C. Weideman
Keyword(s):  
Symbolic Computation ◽  
Padé Approximations ◽  
Pade Approximations

scholarly journals Neutron stars as probes of dark matter

2020 ◽  
Vol 29 (14) ◽  
pp. 2043028
Author(s):  
M. Ángeles Pérez-García ◽  
Joseph Silk
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Equation Of State ◽  
Neutron Stars ◽  
Internal Structure ◽  
Stellar Objects ◽  
Ordinary Matter ◽  
Stable Solutions ◽  
The Universe

Neutron Stars (NSs) are compact stellar objects that are stable solutions in General Relativity. Their internal structure is usually described using an equation of state that involves the presence of ordinary matter and its interactions. However there is now a large consensus that an elusive sector of matter in the universe, described as dark matter, remains as yet undiscovered. In such a case, NSs should contain both, baryonic and dark matter. We argue that depending on the nature of the dark matter and in certain circumstances, the two matter components would form a mixture inside NSs that could trigger further changes, some of them observable. The very existence of NSs constrains the nature and interactions of dark matter in the universe.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

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