scholarly journals Extended Field Equations for Conformally Curved Spacetime

2021 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
Early Universe ◽  
Positive Curvature ◽  
Power Spectra ◽  
Brane World ◽  
Field Equations ◽  
Microwave Background ◽  
Spacetime Curvature ◽  
Extended Field ◽  
Invariance Theory ◽  
Positively Curved

The recent Planck Legacy release has confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level greater than 99%. In addition, the spacetime curvature of the entire galaxy differs from one galaxy to another due to their diverse energy densities. This study considers both the implied positive curvature of the early Universe and the curvature across the entire galaxy as the curvature of ‘the background or the 4D bulk’ and distinguishes it from the localized curvature that is induced in the bulk by the presence of comparably smaller celestial objects that are regarded as ‘relativistic 4D branes’. Branes in different galaxies experience different bulk curvatures, thus their background or bulk curvature should be taken into consideration along with their energy densities when finding their induced curvatures. To account for the interaction between the bulk and branes, this paper presents extended field equations in terms of brane-world modified gravity consisting of conformal Einstein field equations with a boundary term, which could remove the singularities and satisfy a conformal invariance theory. A visualization of the evolution of the 4D relativistic branes over the conformal space-time of the 4D bulk is presented.

scholarly journals Extended General Relativity for a Conformally Curved Universe

2021 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Cold Dark Matter ◽  
Power Spectra ◽  
Boundary Term ◽  
Field Equations ◽  
Microwave Background ◽  
Extended Field ◽  
Background Curvature ◽  
Invariance Theory

The recent Planck Legacy release confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra. Notably, this amplitude is higher than that estimated by the lambda cold dark matter model (ΛCDM), which endorses a positively curved early Universe with a confidence level greater than 99%. Although General Relativity (GR) performs accurately in the local/present Universe where spacetime is almost flat, its lost boundary term, incompatibility with Quantum Mechanics and the necessity of dark matter/energy could indicate its incompleteness. By utilising the Einstein–Hilbert action, this letter presents extended field equations by considering the pre-existing/background curvature and the boundary contribution. The extended field equations consist of Einstein field equations with a conformal transformation feature in addition to the boundary term, which can remove singularities, satisfy a conformal invariance theory and facilitate its quantisation.

scholarly journals Extended General Relativity for a Curved Universe

2021 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Early Universe ◽  
Cold Dark Matter ◽  
Positive Curvature ◽  
Boundary Term ◽  
Radius Of Curvature ◽  
Field Equations ◽  
Extended Field ◽  
Background Curvature

The recent Planck Legacy release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB). Notably, this amplitude is higher than that estimated by the lambda cold dark matter model (ΛCDM), which endorses the positive curvature of the early Universe with a confidence level greater than 99%. Although General Relativity (GR) performs accurately in the local/present Universe where spacetime is almost flat, its lost boundary term, incompatibility with quantum mechanics and the necessity of dark matter and dark energy might indicate its incompleteness. By utilising the Einstein–Hilbert action, this study presents extended field equations considering the pre-existing/background curvature and the boundary contribution. The extended field equations consist of Einstein field equations with a conformal transformation feature in addition to the boundary term, which could remove singularities from the theory and facilitate its quantisation. The extended equations have been utilised to derive the evolution of the Universe with reference to the scale factor of the early Universe and its radius of curvature.

scholarly journals Extended General Relativity for a Curved Universe

2020 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Positive Curvature ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Conformal Curvature ◽  
Present Universe ◽  
Extended Field ◽  
Hilbert Action ◽  
Matter Energy

The Planck Legacy recent release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background, which endorses the early universe positive curvature with a confidence level greater than 99%. Although General Relativity performs accurately in the present universe where spacetime is almost flat, its lost boundary term and the need of dark matter/energy might indicate its incompleteness. By utilising the Einstein–Hilbert action, this letter presents new extended field equations considering pre-existing universal curvatures and boundary contributions. The extended field equations are inclusive of Einstein field equations in addition to the boundary and the conformal curvature terms, which could remove the singularities from the theory.

scholarly journals On Spacetime Duality and Bounce Cosmology of a Dual Universe

2021 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
Wave Function ◽  
Early Universe ◽  
Positive Curvature ◽  
Power Spectra ◽  
Radius Of Curvature ◽  
Second Phase ◽  
Gravitational Acceleration ◽  
Field Equations ◽  
The Universe ◽  
Universe Evolution

The recent Planck Legacy release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra, which endorses the positive curvature of the early Universe with a confidence level exceeding 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the derived wave function of the Universe is utilized to model Universe evolution with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The wave function reveals both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolve in opposite directions as distinct Universe sides. The wave function indicates that a nascent hyperbolic expansion is followed by a first phase of decelerating expansion away from early plasma during the first 10 Gyr, and then, a second phase of accelerating expansion in reverse directions, whereby both Universe sides free-fall towards each other under gravitational acceleration. Simulations of the predicted conformal curvature evolution demonstrate the fast orbital speed of outer stars owing to the external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the wave function predicts an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings reveal that early plasma could have separated and evolved into distinct sides that collectively and geometrically influencing the Universe evolution, physically explanting the effects attributed to dark matter and energy.

scholarly journals Extended General Relativity for a Curved Universe

2020 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Positive Curvature ◽  
Boundary Term ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Conformal Curvature ◽  
Curvature Term ◽  
Extended Field ◽  
Matter Energy

The recent Planck Legacy release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background, which endorses the early universe positive curvature with a confidence level exceeding 99%. Although general relativity performs accurately in the present universe where spacetime is almost flat, the necessity of dark matter/energy and the lost boundary term might be signs of its incompleteness. Utilising Einstein–Hilbert action, I present extended field equations considering the pre-existing universal curvatures. The new extended field equations are inclusive of Einstein field equations in addition to the boundary term and the conformal curvature term contributions.

scholarly journals Early Universe Plasma Separation and the Creation of a Dual Universe

2021 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
Early Universe ◽  
Power Spectra ◽  
Free Fall ◽  
Radius Of Curvature ◽  
Second Phase ◽  
Gravitational Acceleration ◽  
Field Equations ◽  
Conformal Curvature ◽  
Cyclic Universe ◽  
The Universe

The recent Planck Legacy release confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra, which prefers a positively curved early Universe with a confidence level exceeding 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the derived wavefunction of the Universe is utilised to model Universe evolution with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The wavefunction reveals both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolved in opposite directions as distinct Universe sides, corroborating the axis of CMB. The wavefunction indicates that a nascent hyperbolic expansion away from early plasma is followed by a first phase of decelerating expansion during the first 10 Gyr, and then, a second phase of accelerating expansion in reverse directions, whereby both sides free-fall towards each other under gravitational acceleration. The predicted conformal curvature evolution demonstrates the fast orbital speed of outer stars owing to external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the wavefunction predicts an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings show that early plasma could be separated and evolved into distinct sides of the Universe that collectively inducing its evolution, physically explaining the effects attributed to dark energy and dark matter.

scholarly journals White Hole Cosmology - One Best Alternative for Standard Cosmology

2021 ◽  
Author(s):  
U V Satya Seshavatharam ◽  
S Lakshminarayana
Keyword(s):  
Large Scale ◽  
Positive Curvature ◽  
Power Spectra ◽  
Closed Universe ◽  
Theory Of Relativity ◽  
Microwave Background ◽  
White Hole ◽  
Standard Cosmology ◽  
Definition Of ◽  
Large Scale Universe

By modifying the basic definition of cosmic red shift, considering ‘speed of light’ as an absolute cosmic expansion rate and adopting ‘Planck mass’ as the basic seed of the observed large scale universe, it is certainly possible to review and revise the basic picture of ‘standard cosmology’ and in near future, a perfect model of ‘white hole cosmology’ can be developed. In this context we have developed five assumptions. First three assumptions are based on ‘time reversed’ black holes and seem to be well connected with General theory of relativity as well as Quantum mechanics. 4th and 5th assumptions are helpful in understanding current galactic dark matter and flat rotation speeds. It may be noted that, considering our first three assumptions and considering the Planck Legacy 2018 data’s enhanced lensing amplitude in cosmic microwave background power spectra - conceptually, a closed universe having a positive curvature seems to be a best fit for the observed universe. With reference to our recent publication [26], for clarity on the subject, in this short communication, we make an attempt to review and explain our proposed assumptions at fundamental level. Our aim is to see that, professional and non-professional cosmologists must understand the basics of workable quantum cosmology.

scholarly journals Galaxy Formation, Evolution and Rotation as a 4D Relativistic Cloud-World Embedded in a 4D Conformal Bulk: From String to Cloud Theory

2021 ◽  
Author(s):  
Mohammed Al-Fadhli
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Early Universe ◽  
Galaxy Formation ◽  
Positive Curvature ◽  
Recent Observation ◽  
Galactic Centre ◽  
Field Equations ◽  
The Galaxy ◽  
Gas Cloud

The recent observation of the G2 gas cloud orbit around the galactic centre has challenged the model of a mere supermassive black hole that should have destroyed it. In addition, the Planck Legacy 2018 (PL18) release has preferred a positively curved early Universe with a confidence level exceeding 99%. In this study, the formation of a galaxy from the collapse of a supermassive gas cloud in the early Universe is modelled based on extended field equations as a 4D relativistic cloud-world that flows and spins through a 4D conformal bulk of an initial positive curvature considering the preference of the PL18 release. Owning to the curved background, this scenario of galaxy formation reveals that the core of the galaxy undergoes a forced vortex formation with a central event horizon leading to opposite vortices (traversable wormholes) that are spatially shrinking through evolving in the conformal time. It indicates that the galaxy and its core are formed at the same process where the surrounding gas clouds form the spiral arms due to the frame-dragging induced by the fast-rotating core. Further, the bulk conformal curvature evolution demonstrates the fast orbital speed of outer stars owing to external fields exerted on galaxies as they travel through conformally curved space-time. Accordingly, the G2 gas cloud that only faced the drag effects could be explained if its orbit is around the vortex but at a distance from the central event horizon. These findings could explain the fast orbital speed of outer stars where the galaxy formation and its core simultaneously could explain the formation of the supermassive compact galaxy cores with a mass of ~109 M⊙ at just 6% of the current Universe age and thus could resolve the black hole hierarchy problem.

scholarly journals Galaxy Formation and Rotation as a 4D Relativistic Cloud-World Embedded in a 4D Conformal Background: A Cloud Theory

2021 ◽  
Author(s):  
Mohammed Al-Fadhli
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Early Universe ◽  
Galaxy Formation ◽  
Positive Curvature ◽  
Recent Observation ◽  
Galactic Centre ◽  
Field Equations ◽  
The Galaxy ◽  
Gas Cloud

The recent observation of the G2 gas cloud orbit around the galactic centre has challenged the model of a mere supermassive black hole at the centre of our galaxy which should have destroyed it. In addition, the Planck Legacy 2018 (PL18) release has preferred a positively curved early Universe with a confidence level exceeding 99%. In this study, the collapse of a large gas cloud in the early Universe to form a galaxy is modelled based on extended field equations as a 4D relativistic CloudWorld that flows and spins through a 4D independent conformal background of an initial positive curvature considering the preference of the PL18 release. Owning to the curved background, this scenario of galaxy formation indicates that the core of the galaxy undergoes a forced vortex formation with a central event horizon leading to opposite traversable wormholes that are spatially shrinking through the conformal time. It reveals that the galaxy and its core are formed at the same process where the surrounding gas clouds form the spiral arms due to the frame-dragging induced by the fast-rotating core. Accordingly, the G2 gas cloud that only faced the drag effects could be explained if its orbit is around the wormhole but at a distance from the central event horizon. The formation of the galaxy and its core simultaneously could explain the formation of the supermassive compact galaxy cores with a mass of ~109 M⊙ at just 6% of the current Universe age and could resolve the black hole hierarchy problem.

scholarly journals White Hole Cosmology - One Best Alternative for Standard Cosmology

2021 ◽  
Author(s):  
U V Satya Seshavatharam ◽  
S Lakshminarayana
Keyword(s):  
Large Scale ◽  
Positive Curvature ◽  
Power Spectra ◽  
Closed Universe ◽  
Theory Of Relativity ◽  
Microwave Background ◽  
White Hole ◽  
Standard Cosmology ◽  
Definition Of ◽  
Large Scale Universe

By modifying the basic definition of cosmic red shift, considering ‘speed of light’ as an absolute cosmic expansion rate and adopting ‘Planck mass’ as the basic seed of the observed large scale universe, it is certainly possible to review and revise the basic picture of ‘standard cosmology’ and in near future, a perfect model of ‘white hole cosmology’ can be developed. In this context we have developed five assumptions. First three assumptions are based on ‘time reversed’ black holes and seem to be well connected with General theory of relativity as well as Quantum mechanics. 4th and 5th assumptions are helpful in understanding current galactic dark matter and flat rotation speeds. It may be noted that, considering our first three assumptions and considering the Planck Legacy 2018 data’s enhanced lensing amplitude in cosmic microwave background power spectra - conceptually, a closed universe having a positive curvature seems to be a best fit for the observed universe. With reference to our recent publication [26], for clarity on the subject, in this short communication, we make an attempt to review and explain our proposed assumptions at fundamental level. Our aim is to see that, professional and non-professional cosmologists must understand the basics of workable quantum cosmology.

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