At present, the geometry of the universe is only slightly different from the Euclidean model. This imposes very strong limitations on the curvature of the universe in the early stages of its evolution. Such limitations are difficult to explain within the framework of the standard cosmological model. This problem can be solved with the help of the assumption that at the initial moment the universe was in a pure quantum state.
Melkikh A.V. A pure quantum universe as an alternative to inflation
In the pure phase of the expansion of the universe it does not act on itself, then, the curvature of the universe remains zero throughout this entire phase.
After the transition of the universe into a mixed state, it is already so large that the curvature does not change significantly with further expansion.
Article A pure quantum universe as an alternative to inflation
Our Universe is not flat. The distance between every observer and horizon of events (radius of the Universe a) is very great, and the body of every observer is very small. We compare themselves with a, therefore the space of the Universe seems as a flat. For example, we consider the space of Universe as homogeneous, because distances between cosmic bodies ave very great if we compare them with our body.
In this paper I mean that average density of the universe is very close now to critical density.
I agree with Larissa. The universe is infinite. Even though it is elliptical or spherical, it appears to be flat like our Earth appears to us as flat.
See about flatness problem in wikipedia
https://en.wikipedia.org/wiki/Flatness_problem
Alexey,
It is not a co-incidence that the universe is flat (omega(m)=1), it is from the scale-invariance symmetry principle. Imagine that our universe could change scale, with every length dimension changing in equal proportions. It would look the same as before - such a change is a symmetry and should be reflected in the laws of physics. It is. Gravity is the result of this symmetry and has the strength to ensure conservation of energy if the universe 'rescaled'. It's discussed in more detail here - a new(ish) proposal ... http://vixra.org/abs/1802.0167 which also shows why omega(m) appears to be about 0.25 or 0.3, whilst really being 1.
The critical density for flatness without dark energy is rho=3H^2/(8*pi*G). The theory says that gravity has the right strength for energy conservation if the universe 'rescales' which is G=3H^2/(8*pi*rho). It's easier to imagine from classical gravity. Imagine a mass, m, with energy E=mc^2. If all lengths change scale including all physical constants, then as the speed of light changes, the energy due to the mass changes and conservation of energy is violated. With gravity included the energy due to m, is now mc^2 - GmM/R, where M represents the mass of the rest of the universe and R the Hubble radius. If it is zero, then the universe can 'rescale' without violating conservation of energy...i.e gravity has the strength G=Rc^2/M, equivalent to the first two equations above, i.e. flatness.
Hi Alexey,
It's a reinterpretation of expansion as a change of all physical constants and lengths in scale-symmetrical way that cannot be observed locally.
It neatly accounts for the flatness of the universe, the omega(m) approx 0.25 observations and the supernovae data too.
It is also a way to understand the existence of gravity from first principles and is all described in the short paper http://vixra.org/abs/1802.0167 , some details we have discussed are in appendix B.
Hope it answers your question!
The Universe isn't flat-it's expanding at an accelerating rate. It's the spatial part of the Universe that, apparently, is very close to flat. However what matters is the spacetime curvature, not the spatial one, since separating spacetime into space and time isn't an invariant operation.
Inflation is relevant for other issues.
In general relativity there are no local observables anyway. While general relativity does have three constants-Newton's constant, the speed of light and the cosmological constant, the solutions to Einstein's equations only depend on two ratios of these constants anyway. That's why any statement about varying physical constants doesn't make sense, if additional fields, beyond the metric, aren't included-that's what this amounts to. And additional fields are quite severely constrained, since they mediate additional forces, whose effects can be measured. For the moment no such effects have been found.
Dear Alexey,
If somebody understands what are the notions/phenomena “Space” and “Time” [see, for example https://www.researchgate.net/publication/320775304_The_Information_as_Absolute_conception_space_and_time DOI: 10.13140/RG.2.2.12789.06887/2] this somebody understands also that the Matter’s spacetime is, and cannot be something else, an Euclidian empty container/spacetime, where Matter [including every material object] exists, and, because of the energy conservation law, constantly changes; and that any material object fundamentally isn’t able to change something in this container. Emptiness doesn’t interact with something and anything can interact with emptiness.
From human’s practice practically for sure seems that it is [5]4D Euclidian empty container, which is formed by (1+1)D temporal dimensions and 3D spatial dimensions for interactions on the energetic macrolevel, i.e. if we don’t consider the QM effects. However these effects are essential on very small [first of all energetic] scales only and practically inessential in the rest interactions that define Matter’s cosmological structure.
As well as all [5]4 dimensions relate to [5]4 independent degrees of freedom of changes of the material objects states, therefore dimensions are mutually independent also, what is observed physically as that the 4D sub-spacetime is not only Euclidian, but it is “Cartesian”, i.e. all its 4 dimensions are mutually orthogonal.
When the GR postulates such strange things, as that the Matter’s spacetime is 4D pseudo Riemannian space where either space or time and many distances between the space’s points are [mathematically] imaginary; that the spatial and temporal dimensions are linked by some unknown way and so “separating spacetime into space and time isn't an invariant operation.”, that the spacetime can be “curved” by material “masses” etc. That is in the GR simply because of the author didn’t understand what are the space and the time. Regrettably a lot of people in physics don’t understand that till now also…
Cheers
The flatness-problem is naturally solved if the universe expanded very rapidly when it was about 10^{-32} seconds old. Then, even if the universe is not described by the k=0 model, today it is so large (i.e. k c^2/a^2 is very, very tiny, where a(t) is the scale factor) that it resembles a flat universe. This is the standard Inflationary paradigm due to Starobinsky, Guth, Linde,.....
“…The flatness-problem is naturally solved if the universe expanded very rapidly when it was about 10^{-32} seconds old…”
the “inflation hypothesis” seems indeed suggests rather natural solution of the “flatness-problem”, however this solution would be much more natural, if at that in this hypothesis some quite natural questions were answered:
where the inflation happened?, i.e. – what is this “where”? [by another words – what is the space? and what is “10^{-32} seconds old”, i.e. what is the time?]; and
how this inflation would happen so that after the “inflation from a point” the distribution of mass and cosmic objects/systems [interstellar gas, stars, galaxies, etc.] become be practically isotropic in whole Matter’s space, as that humans observe now?
The substantive answers, or at least reasonable versions of the answers, on these questions can be obtained only in framework of the Shevchenko’s and Tokarevsky’s “The Information as Absolute” conception and of the physical model that follows from this conception
https://www.researchgate.net/publication/273777630_The_Informational_Conception_and_Basic_Physics DOI 10.5281/zenodo.16494 , and
https://www.researchgate.net/publication/260930711_the_Information_as_Absolute DOI 10.5281/zenodo.268904.
where, first of all the rigorous definitions of the notions/phenomena “Space” and “Time” are obtained, from which follows, including, that there cannot be the “flatness-problem” at all, the Matter’s spacetime is an absolute [5]4D Euclidian empty container, which principally cannot be “non-flat”, including principally cannot be transformed [“contracted”, “dilated”, “curved”, etc.] by anything inside, i.e. by any material object;
as well as the observed isotropy of the mass distribution can be created by some natural way – see in the second link at least the Sec. 6.1.3. “The problem of Beginning and evolution of Universe” . The Sec. “3.3 Planck mass particles” in first link would be useful also.
Cheers
Alexey,
First of all what does it mean for the universe to be flat? It means to have its cosmological parameter Omega have a value of unity, i.e. Ω = 1.
What is Ω? After analysis from Ω = 8πGρ/3H^2, you find Ω = 2GM/rc^2. And that is the problem.
The universe currently has an estimated mass about 10^52kg. Fitting this in a cosmological beginning will make Ω >>> 1. To resolve this, the cosmic radius r in the equation is increased exponentially to make Ω approximate 1, which is the motivation behind ‘inflation theory’.
Underlying this however, is the dogmatic and likely false belief that all the matter/energy in the universe today has existed from the very beginning. This is the source of the ‘flatness’ and ‘temperature’ problems in our cosmology theory of the early era.
A universe having this matter-energy content at the Planck epoch ~10^-35m radius will have a temperature 10^47K, not the model 10^32K of standard theory. To have a model 10^32K, when the universe was at the Planck size, the matter content would have to be about 10^-8kg, not 10^52kg. A temperature higher than this would not permit the primordial nucleo-synthesis that takes place in the first three minutes.
This leads to this hypothesis: The Universe is increasing in mass and radius from an initial zero value in accord with the formula M = rc^2/2G which amounts to about 6.75 X 10^26kg per metre change in radius.
The above hypothesis resolves the flatness, infinite density, and temperature problems. It is what makes the universe always flat and having a value Ω = 1 from the early epochs till the present time.
Regards,
Akinbo
Reference
(1) Does the universe obey the energy conservation law by a constant mass or an increasing mass with radius during its evolution? http://arxiv.org/abs/0810.1629.
(2) ‘Hypothesis Fingo’, (ebook)
- Badges
- Science topic