scholarly journals Reconstructed f(R) Gravity and Its Csmological Consequences in Chameleon Scalar Field with A Scale Factor Describing The Pre-Bounce Ekpyrotic Contraction

2020 ◽  
Author(s):  
Soumyodipta Karmakar ◽  
Kairat Myrzakulov ◽  
Surajit Chattopadhyay ◽  
Ratbay Myrzakulov
Keyword(s):  
Scalar Field ◽  
Sufficient Conditions ◽  
State Parameter ◽  
Realistic Model ◽  
Scale Factor ◽  
Sufficient Condition ◽  
Reconstruction Scheme ◽  
Exponential Expansion ◽  
Big Crunch ◽  
Subsequent Phase

Inspired by the work of S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D 92, 024016 (2015) [1], the present study reports a reconstruction scheme for f (R) gravity with the scale factor a(t) µ (t * - t) c22describing the pre-bounce ekpyrotic contraction, where t is the big crunch time. The reconstructed f (R) is used to derive expressions for density and pressure contributions and the equation of state parameter resulting from this reconstruction is found to behave like "quintom". It has also been observed that the reconstructed f (R) has satisfied a sufficient condition for a realistic model. In the subsequent phase the reconstructed f (R) is applied to the model of chameleon scalar field and the scalar field f and the potential V(f) are tested for quasi-exponential ex pansion. It has been observed that although the reconstructed f (R) satisfies one of the sufficient conditions for realistic model, the quasi-exponential expansion is not available due to this reconstruction. Finally, the consequences pre-bounce ekpyrotic inflation i n f (R) gravity are compared to the background solution for f (R) matter bounce.

scholarly journals Reconstructed f(R) Gravity and Its Cosmological Consequences in theChameleon Scalar Field with a Scale Factor Describing the Pre-Bounce Ekpyrotic Contraction

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1559
Author(s):  
Soumyodipta Karmakar ◽  
Kairat Myrzakulov ◽  
Surajit Chattopadhyay ◽  
Ratbay Myrzakulov
Keyword(s):  
Scalar Field ◽  
Sufficient Conditions ◽  
State Parameter ◽  
Realistic Model ◽  
Scale Factor ◽  
Sufficient Condition ◽  
Reconstruction Scheme ◽  
Exponential Expansion ◽  
Big Crunch ◽  
Subsequent Phase

The present study reports a reconstruction scheme for f(R) gravity with the scale factor a(t)∝(t*−t)2c2 describing the pre-bounce ekpyrotic contraction, where t* is the big crunch time. The reconstructed f(R) is used to derive expressions for density and pressure contributions, and the equation of state parameter resulting from this reconstruction is found to behave like “quintom”. It has also been observed that the reconstructed f(R) has satisfied a sufficient condition for a realistic model. In the subsequent phase, the reconstructed f(R) is applied to the model of the chameleon scalar field, and the scalar field ϕ and the potential V(ϕ) are tested for quasi-exponential expansion. It has been observed that although the reconstructed f(R) satisfies one of the sufficient conditions for realistic model, the quasi-exponential expansion is not available due to this reconstruction. Finally, the consequences of pre-bounce ekpyrotic inflation in f(R) gravity are compared to the background solution for f(R) matter bounce.

scholarly journals A COMPARISON OF QUINTESSENCE AND NON-LINEAR BORN–INFELD SCALAR FIELD USING GOLD SUPERNOVA DATA

2006 ◽  
Vol 15 (11) ◽  
pp. 1947-1961 ◽  
Author(s):  
WEI FANG ◽  
H. Q. LU ◽  
B. LI ◽  
K. F. ZHANG
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Field Model ◽  
State Parameter ◽  
Scale Factor ◽  
Scalar Field Model ◽  
Equation Of State Parameter ◽  
Non Linear ◽  
Quintessence Model

We study the Non-Linear Born–Infeld (NLBI) scalar field model and quintessence model with two different potentials (V(ϕ) = -sϕ and [Formula: see text]). We investigate the differences between these two models. We explore the equation of state parameter w and the evolution of scale factor a(t) in both the NLBI scalar field and quintessence model. The present age of universe and the transition redshift are also obtained. We use the Gold dataset of 157 SN-Ia to constrain the parameters of the two models. All the results show that the NLBI model is slightly superior to the quintessence model.

A new potential for scalar field dark energy

2020 ◽  
Vol 17 (09) ◽  
pp. 2050139
Author(s):  
Abdulla Al Mamon
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Equation Of State ◽  
Hubble Parameter ◽  
Time Derivative ◽  
Field Potential ◽  
State Parameter ◽  
Simple Relation ◽  
Scale Factor ◽  
Equation Of State Parameter

In this paper, we have investigated some cosmological consequences of a quintessence dark energy model. In particular, we have obtained the forms of the equation of state parameter, the deceleration parameter and the field potential by considering a simple relation between the scale factor and the time derivative of the scalar field, instead of assuming any functional form for the scalar field potential or the scale factor or the equation of state parameter. We have found that the model provides the desired early deceleration followed by present acceleration of the universe. The potential derived numerically in this work in the form [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are real constant parameters. It has also been found that our model mimics as the standard [Formula: see text]CDM model in future. Finally, we have also shown the evolution of the normalized Hubble parameter for our model and the [Formula: see text]CDM model and compared that with the latest Hubble parameter data.

A study on modified holographic Ricci dark energy in modified f(R) Hořava–Lifshitz gravity

2014 ◽  
Vol 92 (3) ◽  
pp. 200-205 ◽  
Author(s):  
Surajit Chattopadhyay ◽  
Antonio Pasqua
Keyword(s):  
Dark Energy ◽  
Modified Gravity ◽  
Functional Form ◽  
State Parameter ◽  
Realistic Model ◽  
Sufficient Condition ◽  
Effective Equation ◽  
Ricci Dark Energy ◽  
Equation Of State Parameter ◽  
The Universe

This paper reports a study on modified holographic Ricci dark energy in modified f(R) Hořava–Lifshitz gravity with a power-law form of the scale factor a. The modified Ricci scalar in the said gravity model is denoted [Formula: see text] and, accordingly, the modified gravity has the functional form [Formula: see text]. The analytical solution for the reconstructed [Formula: see text] has been obtained and it satisfies a sufficient condition for a realistic model. The effective equation of state parameter, ωeff, has been observed to have a quintessence-like behavior. Statefinder trajectories have indicated the attainment of the ΛCDM phase of the universe for the reconstructed [Formula: see text].

scholarly journals Noetherian properties in composite generalized power series rings

2020 ◽  
Vol 18 (1) ◽  
pp. 1540-1551
Author(s):  
Jung Wook Lim ◽  
Dong Yeol Oh
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Commutative Rings ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Power Series ◽  
Ordered Monoid ◽  
Power Series Rings ◽  
Necessary And Sufficient ◽  
Equivalent Conditions

Abstract Let ({\mathrm{\Gamma}},\le ) be a strictly ordered monoid, and let {{\mathrm{\Gamma}}}^{\ast }\left={\mathrm{\Gamma}}\backslash \{0\} . Let D\subseteq E be an extension of commutative rings with identity, and let I be a nonzero proper ideal of D. Set \begin{array}{l}D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {E}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(0)\in D\right\}\hspace{.5em}\text{and}\\ \hspace{0.2em}D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {D}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(\alpha )\in I,\hspace{.5em}\text{for}\hspace{.25em}\text{all}\hspace{.5em}\alpha \in {{\mathrm{\Gamma}}}^{\ast }\right\}.\end{array} In this paper, we give necessary conditions for the rings D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively ordered, and sufficient conditions for the rings D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively totally ordered. Moreover, we give a necessary and sufficient condition for the ring D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively totally ordered. As corollaries, we give equivalent conditions for the rings D+({X}_{1},\ldots ,{X}_{n})E{[}{X}_{1},\ldots ,{X}_{n}] and D+({X}_{1},\ldots ,{X}_{n})I{[}{X}_{1},\ldots ,{X}_{n}] to be Noetherian.

SOME SUFFICIENT CONDITIONS OF LEARNABILITY IN THE LIMIT FROM POSITIVE DATA

2000 ◽  
Vol 11 (03) ◽  
pp. 515-524
Author(s):  
TAKESI OKADOME
Keyword(s):  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Conditions For Learning ◽  
Positive Data ◽  
Necessary And Sufficient ◽  
Learning In The Limit

The paper deals with learning in the limit from positive data. After an introduction and overview of earlier results, we strengthen a result of Sato and Umayahara (1991) by establishing a necessary and sufficient condition for the satisfaction of Angluin's (1980) finite tell-tale condition. Our other two results show that two notions introduced here, the finite net property and the weak finite net property, lead to sufficient conditions for learning in the limit from positive data. Examples not solvable by earlier methods are also given.

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

The Maxslope Taxometric Procedure: Mathematical Derivation, Parameter Estimation, Consistency Tests

2004 ◽  
Vol 95 (2) ◽  
pp. 517-550 ◽  
Author(s):  
William M. Grove
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Regression ◽  
Classification Accuracy ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Indicator Variable ◽  
Regression Slope ◽  
The Relationship ◽  
Mathematical Derivation ◽  
Made In

This article first explains concepts in taxometrics, including the meaning of “taxon” in relation to taxometric procedures. It then mathematically develops the MAXSLOPE procedure of Grove and Meehl which relies on nonlinear regression of one taxometric indicator variable on another. Sufficient conditions for MAXSLOPE's validity are set forth. The relationship between the point of maximum regression slope (MAXSLOPE point) and the HITMAX cut, i.e., the point on a variable which, if used as a diagnostic cut-off score, yields maximum classification accuracy, is analyzed. A sufficient condition is given for the MAXSLOPE point to equal the HITMAX cut; however, most distributions have different MAXSLOPE and HITMAX points. Equations and an algorithm are spelled out for making a graphical test for the existence of a taxon, estimating taxometric parameters, and conducting consistency tests; the latter serve as stringent checks on the validity of a taxonic conjecture. The plausibility of assumptions made, in deriving MAXSLOPE equations, is discussed, and the qualitative effects of violations of these assumptions are explained.

scholarly journals Equipartitioning and balancing points of polygons

Pythagoras ◽  
2010 ◽  
Vol 0 (71) ◽  
Author(s):  
Shunmugam Pillay ◽  
Poobhalan Pillay
Keyword(s):  
General Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Sufficient Condition ◽  
Centre Of Mass ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The centre of mass G of a triangle has the property that the rays to the vertices from G sweep out triangles having equal areas. We show that such points, termed equipartitioning points in this paper, need not exist in other polygons. A necessary and sufficient condition for a quadrilateral to have an equipartitioning point is that one of its diagonals bisects the other. The general theorem, namely, necessary and sufficient conditions for equipartitioning points for arbitrary polygons to exist, is also stated and proved. When this happens, they are in general, distinct from the centre of mass. In parallelograms, and only in them, do the two points coincide.

Asymptotic stability of heteroclinic cycles in systems with symmetry. II

2004 ◽  
Vol 134 (6) ◽  
pp. 1177-1197 ◽  
Author(s):  
Martin Krupa ◽  
Ian Melbourne
Keyword(s):  
Asymptotic Stability ◽  
Transition Matrix ◽  
Sufficient Conditions ◽  
Systematic Investigation ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Heteroclinic Cycles ◽  
Higher Dimensional ◽  
Necessary And Sufficient

Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the asymptotic stability of such cycles. In particular, we found a sufficient condition for asymptotic stability, and we gave algebraic criteria for deciding when this condition is also necessary. These criteria are satisfied for cycles in R3.Field and Swift, and Hofbauer, considered examples in R4 for which our sufficient condition for stability is not optimal. They obtained necessary and sufficient conditions for asymptotic stability using a transition-matrix technique.In this paper, we combine our previous methods with the transition-matrix technique and obtain necessary and sufficient conditions for asymptotic stability for a larger class of heteroclinic cycles. In particular, we obtain a complete theory for ‘simple’ heteroclinic cycles in R4 (thereby proving and extending results for homoclinic cycles that were stated without proof by Chossat, Krupa, Melbourne and Scheel). A partial classification of simple heteroclinic cycles in R4 is also given. Finally, our stability results generalize naturally to higher dimensions and many of the higher-dimensional examples in the literature are covered by this theory.

Sign in / Sign up

Export Citation Format

Share Document