scholarly journals Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 366
Author(s):  
Alexander Kritov
Keyword(s):  
Clifford Algebra ◽  
Cosmological Term ◽  
Two Dimensional ◽  
De Sitter ◽  
Time Coordinate ◽  
Novel Approach ◽  
Dimensional Spacetime ◽  
Expansion Of The Universe ◽  
Sitter Model ◽  
The Universe

This paper presents a novel approach to the cosmological constant problem by the use of the Clifford algebras of space Cl3,0 and anti-space Cl0,3 with a particular focus on the paravector representation, emphasizing the fact that both algebras have a center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3H0c. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl3,0 corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl0,3 leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.

scholarly journals Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates

2021 ◽  
Author(s):  
Alexander Kritov
Keyword(s):  
Clifford Algebra ◽  
Cosmological Term ◽  
Two Dimensional ◽  
De Sitter ◽  
Time Coordinate ◽  
Dimensional Spacetime ◽  
Expansion Of The Universe ◽  
Sitter Model ◽  
The Universe ◽  
De Sitter Model

The paper briefly reviews the Clifford algebras of space Cl(3,0) and anti-space Cl(0,3) with a particular focus on the paravector representation, emphasizing the fact that both algebras have an isomorphic center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3Hc. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl(3,0) corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl(0,3) leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.

scholarly journals Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates

2021 ◽  
Author(s):  
Alexander Kritov
Keyword(s):  
Clifford Algebra ◽  
Clifford Algebras ◽  
Minkowski Spacetime ◽  
Cosmological Term ◽  
Two Dimensional ◽  
De Sitter ◽  
Dimensional Spacetime ◽  
Proposed Model ◽  
Expansion Of The Universe ◽  
The Universe

The recently proposed model of the "unified two-dimensional spacetime"[18] shows substantial conformity to Clifford algebras Cl3,0 and Cl0,3. As shown, such two-dimensional spacetime of time and volume corresponds to two Clifford coordinates given by a center of the respective algebra. In the application to comoving frame, the model results in the exact form of the scale factor of the FLRW metric of modern cosmology. This paper formulates and formalizes the approach using Clifford algebras. The study concludes that the Clifford algebra of space (APS)Cen(Cl3,0) has an intrinsic correspondence with the anti-de Sitter (AdS) flat universe and the negative cosmological term that results in an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cen(Cl0,3) leads to the de Sitter model with a positive cosmological term. As reviewed, the Clifford algebra has isomorphic algebras and Lie groups corresponding to different from Minkowski spacetime, such as SO(4); therefore, further study may be required regarding their relation to gravitation.

scholarly journals UV surface brightness of galaxies from the local universe to z ~ 5

2014 ◽  
Vol 23 (06) ◽  
pp. 1450058 ◽  
Author(s):  
Eric J. Lerner ◽  
Renato Falomo ◽  
Riccardo Scarpa
Keyword(s):  
Surface Brightness ◽  
Published Data ◽  
De Sitter ◽  
Local Universe ◽  
Static Universe ◽  
Adopted Model ◽  
Expansion Of The Universe ◽  
Sitter Model ◽  
The One ◽  
The Universe

The Tolman test for surface brightness (SB) dimming was originally proposed as a test for the expansion of the universe. The test, which is independent of the details of the assumed cosmology, is based on comparisons of the SB of identical objects at different cosmological distances. Claims have been made that the Tolman test provides compelling evidence against a static model for the universe. In this paper we reconsider this subject by adopting a static Euclidean universe (SEU) with a linear Hubble relation at all z (which is not the standard Einstein–de Sitter model), resulting in a relation between flux and luminosity that is virtually indistinguishable from the one used for ΛCDM models. Based on the analysis of the UV SB of luminous disk galaxies from HUDF and GALEX datasets, reaching from the local universe to z ~ 5, we show that the SB remains constant as expected in a static universe. A re-analysis of previously published data used for the Tolman test at lower redshift, when treated within the same framework, confirms the results of the present analysis by extending our claim to elliptical galaxies. We conclude that available observations of galactic SB are consistent with a SEU model. We do not claim that the consistency of the adopted model with SB data is sufficient by itself to confirm what would be a radical transformation in our understanding of the cosmos. However, we believe this result is more than sufficient reason to examine this combination of hypotheses further.

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.

scholarly journals PRIMORDIAL BLACK HOLE FORMATION FROM INFLATON

2000 ◽  
Vol 09 (06) ◽  
pp. 705-710 ◽  
Author(s):  
XIN HE MENG ◽  
BIN WANG ◽  
S. FENG
Keyword(s):  
Black Hole ◽  
Primordial Black Hole ◽  
Primordial Black Holes ◽  
De Sitter ◽  
Hole Formation ◽  
Black Hole Formation ◽  
Expansion Of The Universe ◽  
Slow Rolling ◽  
The Relationship ◽  
The Universe

Measurements of the distances to SNe Ia have produced strong evidence that the expansion of the Universe is really accelarating, implying the existence of a nearly uniform component of dark energy with the simplest explanation as a cosmological constant. In this paper a small changing cosmological term is proposed, which is a function of a slow-rolling scalar field, by which the de Sitter primordial black holes' properties, for both charged and uncharged cases, are carefully examined and the relationship between the black hole formation and the energy transfer of the inflaton is eluciated. The criterion for primordial black hole formation is given.

scholarly journals A novel teleparallel dark energy model

2016 ◽  
Vol 25 (02) ◽  
pp. 1650025 ◽  
Author(s):  
Giovanni Otalora
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Teleparallel Gravity ◽  
Accelerated Expansion ◽  
Late Time ◽  
De Sitter ◽  
Sitter Group ◽  
Current State ◽  
Expansion Of The Universe ◽  
The Universe

Although equivalent to general relativity, teleparallel gravity (TG) is conceptually speaking a completely different theory. In this theory, the gravitational field is described by torsion, not by curvature. By working in this context, a new model is proposed in which the four-derivative of a canonical scalar field representing dark energy is nonminimally coupled to the “vector torsion”. This type of coupling is motivated by the fact that a scalar field couples to torsion through its four-derivative, which is consistent with local spacetime kinematics regulated by the de Sitter group [Formula: see text]. It is found that the current state of accelerated expansion of the universe corresponds to a late-time attractor that can be (i) a dark energy-dominated de Sitter solution ([Formula: see text]), (ii) a quintessence-type solution with [Formula: see text], or (iii) a phantom-type [Formula: see text] dark energy.

Expanding Universe with a Variable Cosmological Term

2015 ◽  
Vol 70 (11) ◽  
pp. 905-911 ◽  
Author(s):  
Carlos Blanco-Pérez ◽  
Antonio Fernández-Guerrero
Keyword(s):  
Cosmological Constant ◽  
Cosmological Term ◽  
Expanding Universe ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Variable Cosmological Term ◽  
Einstein's Field Equations ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Entropy Of The Universe

AbstractWe propose a model of expansion of the universe in which a minimal, ‘quantised’ rate is dependent upon the value of the cosmological constant Λ in Einstein’s field equations, itself not a constant but a function of the size and the entropy of the universe. From this perspective, we offer an expression which relates Hubble’s constant with the cosmological constant.

scholarly journals Remarks on cosmology

1959 ◽  
Vol 9 ◽  
pp. 533-535
Author(s):  
G. C. Mcvittie
Keyword(s):  
A Priori ◽  
Initial Instant ◽  
De Sitter ◽  
Relativistic Model ◽  
Space Curvature ◽  
Composite Models ◽  
History Of ◽  
Sitter Model ◽  
The Universe ◽  
De Sitter Model

First, I should like to say something about the use of highly specialized models in cosmology. The Einstein—de Sitter model is a relativistic model in which the cosmical constant and the space-curvature constant are both equated to zero. Likewise, the pressure is assumed to be zero throughout the history of the universe, except perhaps at the initial instant. It is well-known that the first two constants can be determined from observation, if not at present, at any rate as the data are refined in the future. Hence, I think it is a weakness to prejudge the issue and assign a priori values. Nor is it self-evident to me that the pressure must always have been zero even if it is zero now. Composite models, with nonzero pressure at first, followed by a zero-pressure condition, need to be examined.

scholarly journals The Discovery of the Expansion of the Universe

Galaxies ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 132
Author(s):  
Øyvind Grøn
Keyword(s):  
De Sitter ◽  
Historical Evidence ◽  
General Acceptance ◽  
Expansion Of The Universe ◽  
Edwin Hubble ◽  
The Universe

Alexander Friedmann, Carl Wilhelm Wirtz, Vesto Slipher, Knut E. Lundmark, Willem de Sitter, Georges H. Lemaître, and Edwin Hubble all contributed to the discovery of the expansion of the universe. If only two persons are to be ranked as the most important ones for the general acceptance of the expansion of the universe, the historical evidence points at Lemaître and Hubble, and the proper answer to the question, “Who discovered the expansion of the universe?”, is Georges H. Lemaître.

Nonminimal derivative coupling: Some cosmological behaviors of John and George models

2014 ◽  
Vol 23 (08) ◽  
pp. 1450067
Author(s):  
A. Kanfon ◽  
G. Edah ◽  
E. Baloïtcha
Keyword(s):  
Exponential Function ◽  
Coupling Parameter ◽  
Big Bang ◽  
De Sitter ◽  
Stiff Matter ◽  
Derivative Coupling ◽  
Sitter Model ◽  
The Big Bang ◽  
The Universe ◽  
De Sitter Model

We examine some nonminimal derivative coupling models with a term of potential in front of the Ricci scalar–tensor. We limited ourselves to three models of this family: — the potential proportional to the square of the field — the potential proportional to the inverse of the field — the potential proportional to the exponential function of the field. The first one leads to an universe which closes a few moment after its creation. The two other models show an accelerated expanding universe after inflation. The model with a potential proportional to the exponential function of the field, pointed out, just after the big bang primordial, the predominance of dark energy guiding inflation. At the end of inflation, in its expansion, the universe tends to de Sitter model dominated by the stiff matter. These results are those obtained by using the potential which is a linear function of the field. What is interesting about this model is that these results are not very sensitive to variations of the coupling parameter and the initial velocity of the field.

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