When can an "Expanding Universe" look "Static" and vice versa: A comprehensive study

2015 ◽  
Vol 24 (05) ◽  
pp. 1550032 ◽  
Author(s):  
Abhas Mitra
Keyword(s):  
Energy Density ◽  
A Priori ◽  
Net Energy ◽  
Expanding Universe ◽  
Minkowski Metric ◽  
Static Universe ◽  
Frw Model ◽  
Frw Metric ◽  
Friedmann Robertson Walker ◽  
Comprehensive Study

The Friedmann–Robertson–Walker (FRW) metric expressed, in terms of comoving coordinates (r, t), always looks nonstatic. But by employing the recently derived curvature/Schwarzschild form, (R, T), of FRW metric (A. Mitra, Gravit. Cosmol. 19 (2013) 134), we show here that FRW metric can assume static forms when the net energy density (ρe) is solely due to the vacuum contribution. Earlier this question was explored by Florides (Gen. Relativ. Gravit. 12 (1980) 563) whose approach was complex and of purely mathematical nature. Also, unlike Florides, we do not assume any a priori separability of T(r, t) = F(r)G(t) and thus our treatment is truly general and yet simpler. More interestingly, even if the net energy density involved in a certain FRW model may appear to be nonzero from its algebric appearance, it may still be possible that tacitly ρe = 0 and the model actually corresponds to a vacuum Minkowski metric. For instance, it has been found that FRW universes which appear to be expanding with a fixed speed in comoving coordinates are intrinsically static universes. While such a linearly expanding universe having k = -1 is well-known as the Milne universe, the corresponding k = 0 case has recently been shown to be vacuum in disguise (A. Mitra, Mon. Not. Roy. Astron. Soc. 442 (2014) 382). In addition, here we show that even the k = +1 linearly "expanding" universe (in comoving coordinates) tacitly corresponds to Einstein's static universe.

scholarly journals Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method

Open Physics ◽  
2006 ◽  
Vol 4 (4) ◽  
Author(s):  
Dumitru Baleanu
Keyword(s):  
Scalar Field ◽  
Degrees Of Freedom ◽  
Cosmological Perturbations ◽  
Consistency Conditions ◽  
Jacobi Formalism ◽  
Frw Model ◽  
Frw Metric ◽  
Friedmann Robertson Walker ◽  
Gauge Conditions

AbstractThe Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW) metric. The gauge conditions are determined from the consistency conditions. The physical degrees of freedom of the model are obtained by the symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in the Hamilton-Jacobi formalism is discussed.

Signature change in p-adic and noncommutative FRW cosmology

2014 ◽  
Vol 29 (27) ◽  
pp. 1450155 ◽  
Author(s):  
Goran S. Djordjevic ◽  
Ljubisa Nesic ◽  
Darko Radovancevic
Keyword(s):  
Loop Quantum Gravity ◽  
Initial Conditions ◽  
Planck Scale ◽  
The Other ◽  
Frw Cosmology ◽  
Signature Change ◽  
Discrete Nature ◽  
Frw Metric ◽  
The Universe ◽  
Friedmann Robertson Walker

The significant matter for the construction of the so-called no-boundary proposal is the assumption of signature transition, which has been a way to deal with the problem of initial conditions of the universe. On the other hand, results of Loop Quantum Gravity indicate that the signature change is related to the discrete nature of space at the Planck scale. Motivated by possibility of non-Archimedean and/or noncommutative structure of space–time at the Planck scale, in this work we consider the classical, p-adic and (spatial) noncommutative form of a cosmological model with Friedmann–Robertson–Walker (FRW) metric coupled with a self-interacting scalar field.

CHAOTIC INFLATIONARY SCENARIO IN BIANCHI TYPE I SPACETIME

2012 ◽  
Vol 27 (09) ◽  
pp. 1250049 ◽  
Author(s):  
RAJ BALI
Keyword(s):  
Energy Density ◽  
Bianchi Type ◽  
Type I ◽  
Inflationary Model ◽  
Bianchi Type I ◽  
Inflationary Scenario ◽  
Inflationary Phase ◽  
Chaotic Model ◽  
Frw Model ◽  
Frame Work

Chaotic inflationary model of the early universe proposed by Linde7 is investigated in the frame work of Bianchi type I spacetime. To determine inflationary scenario, we assume that scale factor [Formula: see text], λ being a constant, m the mass, V(ϕ) the potential energy density. It is shown that chaotic model leads to an inflationary phase which also helps in isotropization process. The Higg's field (ϕ) is initially large but decreases due to lapse of time in both cases. The assumption R3 = ABC~e3Ht does not lead to FRW model immediately but for large values of t, it reduces to FRW model since shear σ = 0 in FRW model and shear σ ≠ 0 in Bianchi type I model. The physical aspects of the model are also discussed.

Relativistic dynamics for the expanding universe

2020 ◽  
Vol 33 (2) ◽  
pp. 200-207
Author(s):  
Brian B. K. Min
Keyword(s):  
Large Scale ◽  
Cold Dark Matter ◽  
Critical Density ◽  
Newtonian Gravity ◽  
Relativistic Dynamic ◽  
Expanding Universe ◽  
Dynamic Effects ◽  
Relativistic Dynamics ◽  
Two Parameters ◽  
Friedmann Robertson Walker

An analysis according to the principles of special and general relativity and less restrictive Newtonian gravity proves the dynamic effects to be substantial for the expanding universe. With the resulting dynamic critical density, typically greater than the standard critical density, I am able to identify the hypothetical cold dark matter (CDM) as being an artifact of the Friedmann‐Robertson‐Walker equation that is insufficient to describe the dynamic effects. With the included special-relativistic dynamic effects, I can now predict the cosmic data with two parameters, matter and the cosmological constant, without the CDM at least on a large scale.

XXIV.—On the Equation of Motion of a Free Particle in the Expanding Universe of Kinematical Relativity

1943 ◽  
Vol 61 (3) ◽  
pp. 288-297
Author(s):  
E. A. Milne
Keyword(s):  
Additional Assumption ◽  
A Priori ◽  
Free Particle ◽  
Equation Of Motion ◽  
Expanding Universe ◽  
Image Position ◽  
Special Case

In a recent paper in these Proceedings, Dr G. C. McVittie has published some criticisms of kinematical relativity. These criticisms are to a large extent based on his formula (4.10), namely,It must be stated at the outset that McVittie's interpretation of his derivation of (1) as a derivation of “Milne's formula for the acceleration of a ‘free particle moving in the presence of a substratum,’ for the special case of one spatial co-ordinate only” is wrong. McVittie does not derive the result, as he claims, from what he calls the “axioms of kinematical relativity” alone; he deduces it from these axioms together with an additional assumption, which is equivalent to begging the answer to the whole problem it was my object to solve. Instead of considering a free particle, as I did—that is, a particle whose motion we do not a priori know—he prescribes a priori the motion of his particle as being constrained to obey the rule, in his notation,

scholarly journals SECOND-ORDER INVARIANTS AND HOLOGRAPHY

2012 ◽  
Vol 21 (12) ◽  
pp. 1250091 ◽  
Author(s):  
ORLANDO LUONGO ◽  
LUCA BONANNO ◽  
GERARDO IANNONE
Keyword(s):  
Dark Energy ◽  
Energy Density ◽  
Holographic Dark Energy ◽  
Statistical Tests ◽  
A Priori ◽  
Second Order ◽  
Fine Tuning ◽  
Dark Energy Density ◽  
Event Horizons

Motivated by recent works on the role of the holographic principle in cosmology, we relate a class of second-order Ricci invariants to the IR cutoff characterizing the holographic dark energy density. The choice of second-order invariants provides an invariant way to account the problem of causality for the correct cosmological cutoff, since the presence of event horizons is not an a priori assumption. We find that these models work fairly well, by fitting the observational data, through a combined cosmological test with the use of SNeIa, BAO and CMB. This class of models is also able to overcome the fine-tuning and coincidence problems. Finally, to make a comparison with other recent models, we adopt the statistical tests AIC and BIC.

Dynamic cohesive fracture: Models and analysis

2014 ◽  
Vol 24 (09) ◽  
pp. 1857-1875 ◽  
Author(s):  
Christopher J. Larsen ◽  
Valeriy Slastikov
Keyword(s):  
Energy Density ◽  
Existence Of Solutions ◽  
A Priori ◽  
Regular Case ◽  
Mathematical Study ◽  
Cohesive Fracture ◽  
One Dimensional ◽  
Cohesive Energy Density ◽  
Fracture Models ◽  
The One

Our goal in this paper is to initiate a mathematical study of dynamic cohesive fracture. Mathematical models of static cohesive fracture are quite well understood, and existence of solutions is known to rest on properties of the cohesive energy density ψ, which is a function of the jump in displacement. In particular, a relaxation is required (and a relaxation formula is known) if ψ′(0+) ≠ ∞. However, formulating a model for dynamic fracture when ψ′(0+) = ∞ is not straightforward, compared to when ψ′(0+) is finite, and especially compared to when ψ is smooth. We therefore formulate a model that is suitable when ψ′(0+) = ∞ and also agrees with established models in the more regular case. We then analyze the one-dimensional case and show existence when a finite number of potential fracture points are specified a priori, independent of the regularity of ψ. We also show that if ψ′(0+) < ∞, then relaxation is necessary without this constraint, at least for some initial data.

Intuition versus Semantics: Problem of A priori

2021 ◽  
pp. 87-97
Author(s):  
Konstantin A. Pavlov-Pinus ◽  
Keyword(s):  
A Priori ◽  
Logical Positivism ◽  
Original Version ◽  
Future Research ◽  
The Right ◽  
Comprehensive Study

The article is an excursus to several significant episodes of history related to de­velopment of semantic and Kantian traditions of reasoning within the framework of logical positivism. It is focused on an increasing role of meaning in philoso­phy, and on a struggle of “meaning” with “intuition” for the right to be consid­ered as a key constituent of justifiable knowledge. The material is presented from Alberto Coffa’s book perspective named “Semantic tradition from Kant to Carnap” which was translated in Russian in 2019, and original version of which was published in 1991. This book is historically the first comprehensive study of the development of logical positivism. It is an indispensable source for all future research in this area.

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