Question CYCLIC UNIVERSE

[Harry Costas]

Cyclic Universe
A comprehensive analysis of the compact phase space for Hu-Sawicki f(R) dark energy models including spatial curvature
Kelly MacDevette, Peter Dunsby, Saikat Chakraborty

We present a comprehensive dynamical systems analysis of homogeneous and isotropic Friedmann-Laîmatre-Robertson-Walker cosmologies in the Hu-Sawicki f(R) dark energy model for the parameter choice {n,C1}={1,1}. For a generic f(R) theory, we outline the procedures of compactification of the phase space, which in general is 4-dimensional. We also outline how, given an f(R) model, one can determine the coordinate of the phase space point that corresponds to the present day universe and the equation of a surface in the phase space that represents the ΛCDM evolution history. Next, we apply these procedures to the Hu-Sawicki model under consideration. We identify some novel features of the phase space of the model such as the existence of invariant submanifolds and 2-dimensional sheets of fixed points. We determine the physically viable region of the phase space, the fixed point corresponding to possible matter dominated epochs and discuss the possibility of a non-singular bounce, re-collapse and cyclic evolution. We also provide a numerical analysis comparing the ΛCDM evolution and the Hu-Sawicki evolution.

Although we look at the Cyclic universe as one theory to explain the working of the universe, one should not discard the Big Bang Theory.
Keep on looking for theories
Advance yourself
Don’t be convinced by my threads and the papers i post
Work through what ever theories with an open mind.

 

[Harry Costas]

They’re many scientists who are looking at the possibility that the parts within the universe recycle from small to mega large

This is one explanation that explains how our SUN has long Jeopardy

[Submitted on 25 Apr 2022]
A non-singular closed bouncing universe without violation of null energy condition
Nasr Ahmed, Tarek M. Kamel, Mohamed I Nouh

A matter bouncing entropy-corrected cosmological model has been suggested. The model allows only positive curvature with negative pressure and no violation of the null energy condition. The result obtained in this paper is supported by some recent theoretical works where the combination of positive spatial curvature and vacuum energy leads to non-singular bounces with no violation of the null energy condition. An important feature of the current model is that evolutions of the cosmic pressure, energy density and equation of state parameter are independent of the values of the prefactors α and β in the corrected entropy-area relation. The validity of the classical and the new nonlinear energy conditions has been discussed. The cosmographic parameters have been analyzed

 

[Harry Costas]

[Submitted on 3 Aug 2022]
Regular black holes, universes without singularities, and phantom-scalar field transitions
Leonardo Chataignier, Alexander Yu. Kamenshchik, Alessandro Tronconi, Giovanni Venturi

We consider a procedure of elimination of cosmological singularities similar to that suggested in the recent paper by Simpson and Visser for the construction of regular black holes. It is shown that by imposing a non-singular cosmological evolution with a bounce in a flat Friedmann universe filled with a minimally coupled scalar field, we obtain a transition between the standard scalar field and its phantom counterpart. The potential of the scalar field has in this case a non-analyticity of the cusp type. This result is readily reproduced also in the case of an anisotropic Bianchi I universe.

In search of how the universe function in a never ending cycle.
Since we cannot destroy Matter or Energy
We look at how matter and energy transform from one phase or state to another.
We look a Neutron Stars with Quark matter cores and expand our thinking of the possibilities of denser matter, Transients of Condensates and their properties.
Imagine a core that is able to attract with extreme vector fields preventing EM wave from escaping mimicking a black hole.
We also note a property that we can observe, a dipolar electromagnetic vortex that expels matter.

Put these together and you have a system that is able to recycle matter.

 

[Harry Costas]

Quantum Effects in Cosmology
Emmanuel Frion

“Quantum effects play an essential role in modern cosmology. Perhaps the most striking example comes from large-scale structures, generally assumed to originate from vacuum quantum fluctuations and stretched by an expansion phase. Inflation is the leading paradigm in explaining this process. The various observational successes of inflationary models drive the scientific community into elaborating more and more stringent tests, which can simultaneously be used to probe beyond the simple slow-roll, single field inflation. However, inflation is not a theory, and going beyond inflation is a necessity. Various alternatives and/or complementary mechanisms to inflation have been invoked in the literature. The best-known cosmological models endowed with the capacity of explaining large-scale observations while avoiding the singularity form a class called non-singular bouncing models. The main features of these models are the presence of a contraction phase before expansion, and a never-vanishing scale factor. A non-singular bounce generally appears when quantum effects are part of the model, playing the role of a regulator leading to the avoidance of singularities. This thesis focuses on a Hamiltonian formulation of quantum effects in cosmology. We first explore stochastic perturbations in a collapsing universe. Then, we show that quantum cosmology with Bohmian mechanics resolves the initial singularity. Adding a non-minimal coupling of gravity with electromagnetism, we show that the generation of magnetic fields is possible. Finally, we apply the affine quantisation on the Brans-Dicke Theory, the prototype of modified gravity theories, and we discuss the quantum equivalence of the Jordan and Einstein frames within this framework. We show that in both frames a smooth bounce is expected, and that equivalence between frames holds at the quantum level.”

OK
Quantum mechanics to explain the properties of condensed matter.

Condensates may have particles condensed relented to the mass.
Neutron Stars have Neutron matter
Within Neutron stars, the core maybe Quark matter.
Quark Stars may have Partonic and so on.

The properties of such condensed matter being Dipolar Electromagnetic is very important to explaining many images that we can observe ot there.

 

[Harry Costas]

We think of the universe evolving from the Big Bang Theory and the nucleosynthesis as a resultant.
I say that the universe is in a constant state of recycling in a never ending time.

So how does it recycle, what states of matter undergo to make the cycle.

Do we have all the answers?

Not yet, although we can discuss some processes.


[Submitted on 1 Sep 2022]
Free Fermion Cyclic/Symmetric Orbifold CFTs and Entanglement Entropy
Tadashi Takayanagi, Takashi Tsuda

In this paper we study the properties of two-dimensional CFTs defined by cyclic and symmetric orbifolds of free Dirac fermions, especially by focusing on the partition function and entanglement entropy. Via the bosonization, we construct the twist operators which glue two complex planes to calculate the partition function of Z_2 orbifold CFT on a torus. We also find an expression of Z_N cyclic orbifold in terms of Hecke operators, which provides an explicit relation between the partition functions of cyclic orbifolds and those of symmetric ones. We compute the entanglement entropy and Renyi entropy in cyclic orbifolds on a circle both for finite temperature states and for time-dependent states under quantum quenches. We find that the replica method calculation is highly non-trivial and new because of the contributions from replicas with different boundary conditions. We find the full expression for the Z_2 orbifold and show that the periodicity gets doubled. Finally, we discuss extensions of our results on entanglement entropy to symmetric orbifold CFTs and make a heuristic argument towards holographic CFTs.

 

[Harry Costas]

We observe the:
Birth and death of Stars.
Black Holes or center cores of galaxies eating up stars.
Dipolar vector fields expelling matter.
We assume these processes are part of a cyclic process.


[Submitted on 17 Nov 2022 (v1), last revised 6 Dec 2022 (this version, v2)]
A note on the arrow of time in nonminimally coupled scalar field FRW cosmology
L. León Andonayre, M. Skugoreva, A. Toporensky. T. Vargas

"We revisit the cyclic Universe scenario in scalar field FRW cosmology and check its applicability for a nonminimally coupled scalar field. We show that for the most popular case of a quartic potential and the standard nonminimal coupling this scenario does work. On the other hand, we identify certain cases where cyclic model fails to work and present corresponding reasons for this".

 

[Harry Costas]

Food for thought
I added this paper for those that want to research.
Giving my thoughts on the paper, should not influence your findings.

[Submitted on 11 Aug 2022]
Conformal Cyclic Cosmology Signatures and Anomalies of the CMB Sky
Eve Bodnia, Vlad Isenbaev, Kellan Colburn, Joe Swearngin, Dirk Bouwmeester

"Circles of low-variance and Hawking points in the Cosmic Microwave Background (CMB), resulting from black hole mergers and black hole evaporation, respectively, in a previous cycle of the universe, have been predicted as possible evidence for the Conformal Cyclic Cosmology model (CCC) introduced by R. Penrose. We present a high-resolution search for such low-variance circles in the Planck and WMAP CMB data, and introduce HawkingNet, our machine learning open-source software based on a ResNet18 algorithm, to search for Hawking points in the CMB. We find that CMB anomalies, consisting of a single or a few bright pixels, erroneously lead to regions with many low-variance circles when applying the search criteria used in previous works [V.G. Gurzadyan, R. Penrose]. After removing the anomalies from the data no statistically significant low-variance circles can be found. Concerning Hawking points, also no statistically significant evidence is found when using a Gaussian temperature amplitude model over 1 degree opening angle and after accounting for CMB anomalies. That CMB anomalies themselves might be remnants of Hawking points is not supported by low-variance and/or high-temperature circles around them. The absence of such distinct features in the CMB does not disprove CCC because if the density of such circles and Hawking points is large an interference speckle pattern in the CMB might arise instead. This would lead to non-Gaussian fluctuation in the CMB, a feature not unique to CCC. We do observe significant local deviation of the real CMB sky from Gaussian noise on a local scale when using best-fit Lambda-CDM and COM PowerSpect CBM TT-full power spectra."

 

[Harry Costas]

It's all in the game of science information. Keep looking for answers and never assume we know everything.
I'm sorry that I keep on posting papers.

[Submitted on 28 Dec 2022]
Tunneling wavefunction proposal with loop quantum geometry effects
Meysam Motaharfar, Parampreet Singh

In Vilenkin's tunneling wavefunction proposal our expanding universe is born via a tunneling through a barrier from nothing at the zero scale factor. We explore the viability of this proposal for the spatially closed FLRW model with a positive cosmological constant including quantum gravity modifications in the Planck regime. Our setting is the effective spacetime description of loop quantum cosmology (LQC) which is known to replace the big bang singularity with a bounce due to the holonomy modifications. Due to the bounce, the barrier potential of the Wheeler-DeWitt theory is replaced by a step like potential which makes the tunneling proposal incompatible. But for a complete picture of singularity resolution, inverse scale factor modifications from quantum geometry must be included which play an important role at very small scale factors in the spatially closed models. We show that with inclusion of inverse scale factor modifications the resulting potential is again a barrier potential. The universe at the vanishing scale factor is dynamically non-singular and in an Einstein static like phase. We show that quantum geometric effects in LQC provide a non-singular completion of Vilenkin's tunneling proposal. We also find that quantum geometric effects result in a possibility of a tunneling to a quantum cyclic universe albeit for a very large value of cosmological constant determined by the quantum geometry.

 

[Harry Costas]

I we accept the Big Bang Nucleosynthesis than we must accept the reversal.
And this leads us to a cyclic event.

 

[billslugg]

Just because something is capable of being reversed does not necessarily mean it will. The Hubble Constant is steadily decreasing and will stabilize at around 45 km/s-mpc. The Universe will never stop expanding. There will be no Big Crunch. Perlmutter/Smith/Riess got the Nobel Prize in 2011 for discerning this.

 

[Harry Costas]

We see this in our observation. M87
We observe stars been pulled into the cores.
We observe jets expelling matter.
This is a cyclic process.
Our Sun has a cyclic process and is the reason for long life.

 

[Harry Costas]

Our universe is infinite.
The Big Bang is only a theory.
A cyclic process can go both ways.

[Submitted on 2 Dec 2022]
Observables for cyclic causal set cosmologies
Fay Dowker, Stav Zalel

In causal set theory, cycles of cosmic expansion and collapse are modelled by causal sets with "breaks" and "posts" and a special role is played by cyclic dynamics in which the universe goes through perpetual cycles. We identify and characterise two algebras of observables for cyclic dynamics in which the causal set universe has infinitely many breaks. The first algebra is constructed from the cylinder sets associated with finite causal sets that have a single maximal element and offers a new framework for defining cyclic dynamics as random walks on a novel tree. The second algebra is generated by a collection of stem-sets and offers a physical interpretation of the observables in these models as statements about unlabeled stems with a single maximal element. There are analogous theorems for cyclic dynamics in which the causal set universe has infinitely many posts.

 

[Harry Costas]

Understanding how matter works and the phases of Condensate Transients.


[Submitted on 10 May 2018 (v1), last revised 31 Aug 2018 (this version, v3)]
Magnetic fields in the Galactic halo restrict fountain-driven recycling and accretion
Asger Grønnow, Thor Tepper-García, Joss Bland-Hawthorn

The Galactic halo contains a complex ecosystem of multiphase intermediate-velocity and high-velocity gas clouds whose origin has defied clear explanation. They are generally believed to be involved in a Galaxy-wide recycling process, either through an accretion flow or a large-scale fountain flow, or both. We examine the evolution of these clouds in light of recent claims that they may trigger condensation of gas from the Galactic corona as they move through it. We measure condensation along a cloud's wake, with and without the presence of an ambient magnetic field, using two- (2D) and three-dimensional (3D), high-resolution simulations. We find that 3D simulations are essential to correctly capture the condensation in all cases. Magnetic fields significantly inhibit condensation in the wake of clouds at t≳25 Myr, preventing the sharp upturn in cold gas mass seen in previous non-magnetic studies. The magnetic field suppresses the Kelvin-Helmholtz instability responsible for the ablation and consequent mixing of a cloud with halo gas which drives the condensation. This effect is universal across different cloud properties (density, metallicity, velocity) and magnetic field properties (strength and orientation). Simple convergence tests demonstrate that resolving the gas on progressively smaller scales leads to even less condensation. While condensation still occurs in all cases, our results show that an ambient magnetic field drastically lowers the efficiency of fountain-driven accretion and likely also accretion from condensation around high-velocity clouds. These lower specific accretion rates are in better agreement with observational constraints compared to 3D, non-magnetic simulations.

 

[Harry Costas]

[Submitted on 28 Dec 2022]
Tunneling wavefunction proposal with loop quantum geometry effects
Meysam Motaharfar, Parampreet Singh

In Vilenkin's tunneling wavefunction proposal our expanding universe is born via a tunneling through a barrier from nothing at the zero scale factor. We explore the viability of this proposal for the spatially closed FLRW model with a positive cosmological constant including quantum gravity modifications in the Planck regime. Our setting is the effective spacetime description of loop quantum cosmology (LQC) which is known to replace the big bang singularity with a bounce due to the holonomy modifications. Due to the bounce, the barrier potential of the Wheeler-DeWitt theory is replaced by a step like potential which makes the tunneling proposal incompatible. But for a complete picture of singularity resolution, inverse scale factor modifications from quantum geometry must be included which play an important role at very small scale factors in the spatially closed models. We show that with inclusion of inverse scale factor modifications the resulting potential is again a barrier potential. The universe at the vanishing scale factor is dynamically non-singular and in an Einstein static like phase. We show that quantum geometric effects in LQC provide a non-singular completion of Vilenkin's tunneling proposal. We also find that quantum geometric effects result in a possibility of a tunneling to a quantum cyclic universe albeit for a very large value of cosmological constant determined by the quantum geometry.

In my opinion there has never been a ZERO to the universe.
If we discuss cyclic events, ZERO will designate the start of a new event through various local time scale.
A cyclic event must occur in an infinite universe.

 

[Harry Costas]

[Submitted on 4 Feb 2023]
Complex Berry phase and imperfect non-Hermitian phase transitions
Stefano Longhi, Liang Feng

In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time (PT) symmetry, where the energy spectrum remains entirely real in the unbroken PT phase while a transition to complex energies is observed in the unbroken PT phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e. imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT-symmetric class of two-band non-Hermitian lattices subjected to an external dc field, unraveling that a non-vanishing imaginary part of the Zak phase -- the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone -- is responsible for imperfect spectral phase transitions

The answer to cyclic universe is on-going journey. It's not black or white.
But! to understand cyclic process, you need to understand condensates from Axion matter to Neutron matter and vice versa.

 

[Harry Costas]

[Submitted on 7 Feb 2023]
Bouncing cosmology from nonlinear dark energy with two cosmological constants
Molly Burkmar, Marco Bruni

We explore the dynamics of FLRW cosmologies which consist of dark matter, radiation and dark energy with a quadratic equation of state. Standard cosmological singularities arise due to energy conditions which are violated by dark energy, therefore we focus our analysis on non-singular bouncing and cyclic cosmologies, in particular focusing on the possibility of closed models always having a bounce for any initial conditions. We analyse the range of dynamical behaviour admitted by the system, and find a class of closed models that admit a non-singular bounce, with early- and late-time accelerated expansion connected by a decelerating phase. In all cases, we find the bouncing models are only relevant when dark matter and radiation appear at a certain energy scale, and so require a period such as reheating. We then investigate imposing an upper bound on the dark matter and radiation, such that their energy densities cannot become infinite. We find that bounces are always the general closed model, and a class of models exist with early- and late-time acceleration, connected by a decelerating phase. We also consider parameter values for the dark energy component, such that the discrepancy between the observed value of Λ and the theoretical estimates of the contributions to the effective cosmological constant expected from quantum field theory would be explained. However, we find that the class of models left does not allow for an early- and late-time accelerated expansion, connected by a decelerating period where large-scale structure could form. Nonetheless, our qualitative analysis serves as a basis for the construction of more realistic models with realistic quantitative behaviour.

Sharing these papers, I hope you do not think that I have originated the works.
Giving Credit to the scientists that have written the papers.
Do I think that the universe parts are recycling?
Yes

 

[Harry Costas]

[Submitted on 17 Feb 2023]
Non-singular flat universes in braneworld and Loop Quantum Cosmology
Rikpratik Sengupta, B. C. Paul, M. Kalam, P. Paul, A. Aich

In this paper we take matter source with non-linear Equation of state (EoS) that has produced non-singular Emergent cosmology for spatially flat universe in General Relativity and minimally coupled scalar field with two different potentials that produce an inflationary emergent universe for positive spatial curvature in the relativistic context. We study all these three cases both in the context of Randall-Sundrum braneworld and effective Loop quantum cosmology (LQC) for zero spatial curvature that is observationally favoured and in the absence of any effective cosmological constant term. We solve the modified Friedmann equation in each case to obtain the time evolution of the scale factor and use it to check whether the initial singularity can be averted. In almost all the cases we find the initial singularity is absent. We study the nature of the slow roll inflation in the cases where we obtain inflationary emergent universes. The inflationary scenario is found to be improved than in a standard relatvistic context and we compare the improved scenario for both the braneworld and LQC models. Interestingly, we also obtain bouncing and cyclic universes from our analysis in some cases. We find that the initial singularity can be averted for a spatially flat universe with specific choice of matter EoS or scalar field potential, which do not violate the Null Energy condition in most cases, taking into account effective high energy (curvature) corrections with or without extra dimensions.

An update to the same paper from 12 months ago.
Keep searching for the answers.
The old saying goes like this.
The more we look and accumulate information the more we find how little we know.

 

[Atlan0001]

There is no "age calculation" of the universe that means anything, the observation of those "enormous distant galaxies that should not exist" proves. What it may mean though is that the Big Bang Horizon (I call the 'Big Bang / Planck / Infinity Horizon') is the forever continuing steady state "emergent" condition of universe that the rest of our universe, ever cycling and recycling from that [never anything but distant horizon to the other end of the "life zone"] continuing constant of Horizon to any and all [coming and going] infinities of black hole horizons [at the opposite end of the "life zone"], Horizon (H) to horizon (h) and re-turn ("turn": "verse"), isn't!

In order to envision what I'm talking about, though, you have to be able to envision a multi-dimensional, multi-level multiplex of Multiverse-Universe. Flat universe horizontally infinite in universes (loaded to infinity with those "enormous distant galaxies that should not exist" at / in / through every 'point' of the distant horizon), multileveled vertically -- as described in Chaos Theory's "zoom" (zoom out/ zoom in) -- to infinity (as I see and describe in 'The Largest Black Hole' here in forum 'Cosmology').

So, again, there is no "age calculation" of [the universe / the infinity of universes] that means anything between a steady state constant condition (H) in one dimension, and a forever cycling / recycling condition (h) in another dimension. Two ((H) (h))! eternally linked in the "turn" / the "verse".

Infinity can never be observed as such. It collapses into a constant of non-local "horizon", and into purpose from being Infinity's constant of horizon as well. The "speed of light" constant (+/- 'c') is one identical constant of non-local collapsed "horizon".

 

[Harry Costas]

What do we know?
The more we see the more we know that Trillions of Galaxies are found in deep field images.
Deep Field 13.4 billion years.
The monster galaxies themselves would be over 20 billion years to evolve and that's been conservative.
Trying to prove the Big Bang is an up-hill battle.
We also know that over 9 super clusters of galaxies, cluster.

Matter tends to cluster together.

If we look at an infinite universe we need to look at the cyclic process that occur.

 

[Atlan0001]

Universes have eternally begun and ended; are eternally beginning and ending; will eternally begin and end, a cycling and recycling always occurring right now. Stephen Hawking recounted the story of some physicists having done the math reducing the universe to a finality of 0-point and going bonkers over their discovery. He didn't know why they were so concerned because, he said, that is where the universe (I add: every universe of a flat 'horizontal' -- and Chaos Theory "zoom accelerative" leveled 'vertical' -- infinity of universes) is right now, has always been, and will always be, so no need to be bothered about it.

 

[Harry Costas]

Many scientists around the world have many opinions.
But! only a few have an idea of how things work.
Either way
It's fun to express your thoughts.
Most are still hooked on the BIG BANG

 

[Harry Costas]

The universe is infinite.

The universe has matter that cannot be destroyed and cannot create more matter.

What we see out there and beyond.

Stars, clusters of stars, galaxies and clusters of galaxies, our Milkyway is a cluster of galaxies and is part of a local cluster of galaxies with over 250 galaxies with M87 being the gravity center.

Our local group of Galaxies belongs to a super cluster of similar local Galaxies and we have observed over 19 super clusters similar.

The word is cluster.

Since the universe is infinite than we can assume the common property is clustering.

Super clusters have a non-classical black hole meaning without a singularity, its property being a condensate that have dipolar electromagnetic vector fields. These dipolar fields expel matter away from the core creating and expansion field that is large enough to fit galaxies in, and if you were in the area, you would be seeing expansion of the known universe.
The vector fields also are pulled into the core with the strength of a black hole, these fields are away from the expelling jet Vortex and we notice stars and galaxies of various sizes pulled in. We are talking about areas larger than our local group of galaxies and if you are in the area, you would be seeing contraction.

Expansion and contraction can be explained by the location, similarly, accelerated expansion and contraction can be explained.

This is my opinion in a nutshell.

 

[Harry Costas]

Just added this to the reading list.
It's interesting and yet questionable.
Like always keep researching, it's never ending.

[Submitted on 4 Mar 2023]
Exploring Higher Dimensional Solutions for Conformal Cyclic Cosmology with DeSitter Space via Eternal Inflation
Natarajan Shriethar

According to conformal cyclic cosmology, a two-surface (Penrose 2-surface) must exist between successive conformal aeons. To understand the quantum gravitational effects of the Penrose 2-surface, a few higher dimensional solutions are required. The higher dimensional metric for the Penrose 2-surface is obtained in the current work. The evolution of the conformal factor is discussed in this work.This article discusses the importance of higher dimensional solutions in understanding the final stages of the universe, particularly in the context of conformal cyclic cosmology. The article explores the behaviour of de Sitter space via eternal inflation, with the aim of providing a more complete understanding of the evolution of the universe and the role that higher dimensions may play in its final stages. The article concludes that without the availability of higher dimensions, the conformal birth of a new aeon will not be possible, and that the use of only three spatial dimensions in the final 2-surface of an aeon will fall short in accounting for the influence of quantum gravity. The article also presents a 5-dimensional metric that describes the behaviour of 5-dimensional spacetime, along with the corresponding 5-dimensional Friedmann-Robertson-Walker equations of the conformal surface in the late-time evolution of the universe. The results of this work have important implications for our understanding of the nature of space and time and how they behave in extreme conditions, such as the final stages of the universe.

 

[Catastrophe]

Harry,
You may have seen my previous posts on cyclic models.
I have suggested that there may be some analogy obtainable by looking at flatlander 'experience'.
A flatlander living 'on' the surface of a sphere experiences expansion of the surface of his spherical universe. However, to a being able to access (n + 1) dimensions, it is evident that the flatlander's sphere is expanding in its radius, which, of course, is not accessible to the flatlander.

That means that expansion is relative to / governed by the sensory input available to the 'beholder'.

Does this fit with your posts, please?

Cat

 

[Atlan0001]

The initial conditions and the final conditions are permanently with us as is Hawking's "life zone" as he indicated in his 'A Brief History of Time'. You simply run the cycling to infinite parallel.

So, there is a time limit to a cycle, every single 1-dimensional cycle, a time to die, to end, in black hole, and yet no time limit whatsoever to the infinite offset parallels (to the infinity of offset parallels) of that cycling. It puts the Big Bang / Planck / Infinite (collapsed) Horizon on a permanent footing as a constant of the Multiverse-Universe (as opposed to the inconstant of 'finite' and 1-dimensional string 'universe' (u) locked into one each 'finite' cycle playing on the playing field but in no way the playing field itself (independent due to infinite offset parallel)).

Now someone might come back with sooner or later the infinity of black holes throughout space and time will finalize, come together, in / to one space and time, one largest Black Hole and Horizon of them all. The answer to that is Hawking's answer, "already there" at 0-point, eternally "already there" (never being, never to be, anywhere, any-when, else). The vertical universe / the "zoom" universe / the Big (but again independent) Vortex of all constituent vortices, too. "Already there!!!"