Should there be a cosmological constant Λ term in the GR field equations? Is the Λ term symmetric with Gμν?
"According to Einstein's theory of General Relativity, gravity should lead to a slowing of the cosmic expansion. Yet, in 1998, two teams of astronomers studying distant supernovae made the remarkable discovery that the expansion of the universe is speeding up. To explain cosmic acceleration, cosmologists are faced with two possibilities: either 70% of the universe exists in an exotic form, now called dark energy, that exhibits a gravitational force opposite to the attractive gravity of ordinary matter, or General Relativity must be replaced by a new theory of gravity on cosmic scales."[1] In order to match the phenomenon of cosmic expansion, the general theory of relativity introduced the cosmological constant term and various speculations on its cause have been made [2]. However, these studies have rarely addressed the possible solutions in the structural aspects of the universe [3].
If there is only gravitational force, it looks like there is a deficiency. We believe that if there is a gravitational force, there is a corresponding repulsive force. But who should cause it and under what circumstances? It is important to know that in electromagnetic interactions, both positive and negative forces are formed by charges, and our goal is to unify the electromagnetic and gravitational forces. Would dark energy be a repulsive force symmetrical to gravity? Where does their symmetry come into play? If the result is to be symmetrical, the cause must first have symmetry. According to the assumptions of modern physics, the dark energy that causes the expansion of the universe is background and not symmetrical with the energy in GR. Regular energies are floating above the dark energy background, so they cannot have symmetry. In Einstein's gravitational field equation, Gµν + Λgµν = G*Tµν, the energy Tµν leads to an unmeasurable intrinsic Space-Time Curvature Gµν [4] while Λgµν is assumed to be a measurable extrinsic Space-Time Expansion due to the universal energy [5]. Specific and background, intrinsic and extrinsic, curvature and expansion do not have any symmetrical meaning. It would then not be appropriate to arrange them in a GR field equation.
Philosophically speaking, there should be no difference with ‘existence’ at this time and the other time, this place and the other place, i.e., when space and time are considered as background *, ‘existence’ does not depend on space-time coordinates. Therefore, the equations of the universe should not require boundary and initial conditions. Physics, by analysing observational data, has proposed the ‘Big Bang Theory’ and the ‘Accelerated Expansion Theory’ of the Universe, both of which are inconsistent with this. Therefore, the hypothesis of dark energy based on this foundation is questionable.
Our Questions:
Does the existence of ‘energy’ necessitate the existence of ‘dark energy’ or ‘anti-energy’? The hypothesis of the existence of dark energy is based only on the observation of the expansion of the universe. Is it the only explanation for the expansion of the universe? [6]
The function of energy is to drive interactions, and energy is presented in discrete forms, which can be manifested in a variety of forms, including gravity. Is the function of dark energy only to cause negative gravity? Is there only one form of dark energy?
Conservation of energy is an important physical principle, is dark energy conserved?
If gravity and negative gravity cancel each other out, why can't energy and dark energy cancel each other out directly?
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Notes
* We believe that existence itself has a space-time parameter, but not a coordinate parameter.
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References
[1] Dark Energy Survey, Collaboration. https://www.darkenergysurvey.org/the-des-project/overview/
[2] Peebles, P. J. E., & Ratra, B. (2003). The cosmological constant and dark energy. Reviews of Modern Physics, 75(2), 559.
[3] Fan, C. (2023). Convergent and Disperse Cyclic Multiverse Model (CDCMM). https://www.preprints.org/manuscript/202309.0784/v2
[4] Doubts about General Relativity (7) - Is Space-Time Bend a Motion? https://www.researchgate.net/post/NO42Doubts_about_General_Relativity_7-Is_Space-Time_Bend_a_Motion；
Doubts about General Relativity (5) - Should there be "negative gravity" in General Relativity?，https://www.researchgate.net/post/NO40Doubts_about_General_Relativity_5-Should_there_be_negative_gravity_in_General_Relativity.
[5] Doubts about General Relativity (3) - Are Space-Time Curvature and Expansion Two Different Geometrical Mechanical Properties? https://www.researchgate.net/post/NO38Doubts_about_General_Relativity_3-Are_Space-Time_Curvature_and_Expansion_Two_Different_Geometrical_Mechanical_Properties.
[6] Is there a reasonable alternative to the theory of the expanding universe?
https://www.researchgate.net/post/Is_there_a_reasonable_alternative_to_the_theory_of_the_expanding_universe
Th answer to the first question is, No. The answer to the second question is, also, No. The answer to the third question is that the statement doesn't make sense.
The answer to the penultimate question is Yes. The answer to the last question is that it doesn't make sense.
The cosmological constant is as inevitable a feature of general relativity as Newton's constant is. It's a dimensionsful quantity, whose presence i dictated by the symmetry of gravity, general coordinate invariance. What's not fixed by symmetry is its value and its sign: Einstein's equations admit solutions whatever the sign and whatever the value of the cosmological constant. For a long time it was assumed that the cosmological constant was equal to 0 and there was a lot of effort put into imagining the mechanism that would select the value 0. No mechanism was found and, in the 1980s it was realized from the measurement of what quantities it could be possible to deduce its value (and its sign) and the results became known in 1998: Its value is positive. And it was realized that what's called ``dark energy'' can be accounted for by the cosmological constant.
Dear Stam Nicolis
Thank you very much for your professional comments, which I always see as a yardstick to judge the deviation of my question and whether that deviation is reasonable or not.
My question or can be specifically described as if there must be dark energy, then can we write the Einstein field equation as two independent from each other, with
Gµν=G*Tµν, (eq.1)
gµν=G'*T(dark) (eq.2)
(eq.1) contains only the energy Tµν, (eq.2) contains only the dark energy T(dark), or some other element，and G' is a G like factor. Do these two equations still have mathematically adequate and reasonable solutions? And their solutions will not conflict? Are such equations still consistent with astronomical observations?
Best Regatds. Chian Fan
No, it's not possible to separate the energy-momentum tensor in this way. There's one set of Einstein's equations.
Dear Stam Nicolis
Thank you very much for your reply.
I think the most important thing here is ‘inevitable’, although I haven't realised the conditions and sufficient reasons for ‘No’ yet. I continue to try to learn and understand them. Hopefully everything will eventually make Its own sense.
Best Regards, Chian Fan
The reason for the fact that the presence of the cosmological constant is inevitable is that the corresponding term in the Einstein-Hilbert action, Λg^(1/2), where g is the determinant of the metric is invariant under diffeomorphisms and contributes the term Λg_(μν) to the Einstein equations, that doesn't contain any derivatives of the metric, therefore must be included, since the classical action of any physical system contains all terms, functions of the dynamical variables, in the case at hand, these are the components of the metric, that are invariant under the symmetries assumed-in this case the diffeomorphisms of spacetime-and that lead to the appearance of terms in the equations of motion that contain up to two time derivatives of the dynamical variables, in order for the space of solutions to be well-defined.
This does not imply that the value of the cosmological constant must be non-zero, however! It just implies that there's no reason, due to symmetry, that it must be zero-and, indeed, it was measured and found to be positive.
Dear Stam Nicolis
You provide, and reinforce, the perception that there is growing evidence that the laws of nature are ‘unique’ and ‘unavoidable’. This may be the essential relationship between physics and maths, and their defining characteristic. It could guides our thinking and determines our conclusions. We look forward to learning and discovering more such revelations.
Best Regards, Chian Fan
Yes, dark energy must exist. No, it is not discrete. It can be consumed and created. Yes, it has a symmetry with the energy density of gravitational fields.
If a particle with a mass gets accelerated by a collision, a kink of the static gravitational field lines moves outwards with the speed of light. Before the kink has passed, the field lines correspond to the particle's state before the collision happened. After the kink has passed, the field lines correspond to the new state of the particle in the new inertial rest frame.
The outmoving field, which warps the lines of the static gravitational field to such a kink, has a positive energy density and therefor is a contribution to dark energy.
It is beyond question that any accelerated mass (not only rest-mass but also relativistic mass, including photon mass) emits such a radiation with the purpose to adapt its static gravitational field to the new inertial reference system. This field repair is obligatory, because no mass exists which has "forgotten" its static gravitational field in its old inertial reference system.
In the electrostatic analogy this field repair is called "Larmor radiation".
It is also obligatory that the energy content of such a pulse of gravitational radiation contains a positive amount of energy. Otherwise, the emission of such a pulse would further accelerate the source, instead of consuming a small part of the energy, which was externally provided for the acceleration.
Because of these two obligatory facts, the dark energy as a counter player of the negative energy density of gravitational fields must exist.
It is also obligatory that the energy density of the dark energy must even be high enough to compensate for the negative energy density of the extremely strong gravitational fields around neutron stars.
The unbelievable fact is that the existence of such a strong dark energy field turns current cosmology inside out, but nobody cares.
I already noted in the previous discussion that dark energy in nonsense, it is not needed because the data on cosmological acceleration can be explained without uncertainty in the framework of semiclassical approximation to quantum de Sitter symmetry - see e.g., Axioms vol. 13, paper No. 138 (2024) https://doi.org/10.3390/axioms13030138. Historically, the problem of dark energy has arisen because Einstein said that introducing Λ was the biggest blunder of his life, and for many physicists Einstein's words are almost a law.
Felix Lev "Solving Particle–Antiparticle and Cosmological Constant Problems"
"So, the statement that at early stages of the universe the numbers of baryons and antibaryons were the same, also does not have a physical meaning, and, as a consequence, the "Barion Assymetry of the Universe" problem does not arise."
Don't you think denying natural laws is a too simple solution for the BAU problem?
Felix Lev "If you think that I am wrong then please indicate explicitly why my conclusions are erroneous."
I only had a deeper look at your consideration of the BAU problem, and there I don't claim that your conclusions are wrong, because I have not seen any conclusion at all.
Over many many pages you are rising the expectation for a mathematically justified conclusion about the BAU problem. But finally you only end up with the trivial claim, that in the early universe the natural laws, as we are currently knowing them, are not exactly fulfilled.
Chian Fan
Dark energy may be the erroneous interpretation of the experiment. The observed dimming of the supernovas at z~1 may be explained by the completely new phenomenon - scattering of light. Recent observations of supernovas at Z~3 by James Webb Space Telescope delivered an unusual observation - they all too big (much larger than the diffraction limit of telescope). Thus the observed dimming of supernovas (discovery of "dark energy" has the second explanation - the scattered light causes the supernovas image be larger than the diffraction limit and thus dimmer).
See my publications here:
Tipikin: Tired light hypothesis and "accelerated expansion of Universe" - no need for dark energy.
https://tipikin.blogspot.com/2024/05/tired-light-hypothesis-and-accelerated.html
2406.0162v1.pdf (vixra.org)
https://vixra.org/pdf/2406.0162v1.pdf
Dmitriy Tipikin "In addition to the blurred images of far galaxies the observation of the supernovas (well researched object with many standard features present) confirms once again the tired light hypothesis (great accuracy of the fit of the experimentally observed angle size is achieved) and disproves Big Bang Theory."
I fully admit to that interpretation of observations and I think that I can contribute to the explanation:
The universe is filled with a dark energy medium, which compensates for the negative energy density contained in gravitational fields. This medium warps the space and causes a homogenous Ricci curvature 1/R². The total volume of the universe therefor is 2π²R³. Geodesics are circles with radius R.
Light propagation around a circle causes a geometrical red shift, compared to a propagation across a straight line. The factor achieved by crossing the universe is πR instead of 2R.
However this geometrical red shift is not sufficient to explain the observed red shift. But we know that every photon has a mass equivalent of its energy content and therefor also carries a gravitational field. This gravitational field causes a tiny density dent in the dark energy medium. The moving dent implies depositing some kinetic energy in that medium. This energy is taken from the photon and therefor causes the red shift.
The scientifically rational answers to the questions in
“【NO.49】Must dark energy exist? Is it discrete? Does it have symmetry with energy?”
- are given in a couple of SS posts in https://www.researchgate.net/post/NO50Should_the_Entire_Universe_Have_any_Symmetry_Can_a_Finite_Universe_Avoid_a_Centre/1, so more see the posts and links in the posts, first of all to the Shevchenko-Tokarevsky’s really philosophical 2007 “The Information as Absolute” conception and to the Planck scale informational physical model; here only briefly:
- to the above: some “dark energy” practically for sure exist, and was spent at least in two points
– at creation of the primary version of the Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which is placed in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct), FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP, c= lP/tP; and
- at seems real expansion of [fundamentally not of Matter’s space] of the FLE lattice later.
At that the problem “what was/is this energy?” is fundamentally outside physics, at least till the really completely transcendent/mystic for humans phenomenon/notion “Energy” will be really scientifically defined; though from what is known now it looks as that “Energy” is continuous, though it can be spending in concrete cases discretely.
Besides the wording “have symmetry with energy?” looks as too concretely vague, more clear would be, say, as “is the energy that acts on FLEs the same as the energy that acts at observable experimentally interactions in matter?”, but, again, though the “ordinary” energy eventually fundamentally acts on FLEs, nonetheless it looks as practically for sure at interactions in matter fundamentally no new FLEs are created – in contrast to that the “dark energy” makes.
And to
“…We believe that existence itself has a space-time parameter, but not a coordinate parameter..….”
- that above looks as again too vague claim. Spacetime is absolutely necessary for Matter existence [see also SS post in https://www.researchgate.net/post/what_is_the_most_important_problem_in_the_theoretical_physics_now#view=6664575e41c39451ce08b623/1680/1681/1680/1683/1683/1683/1683/1684/1683/1685/1685/1686/1685/1685/1686/1685/1687/1686/1685/1689/1689/1688/1690/1691/1700/1758/1758/1759/1764/1765/1764/1765/1766/1768/1768/1769/1768/1769/1769/1769/1770/1769/1770/1769, page 1769, 5 days ago now],
- while all/every material objects have as main primary parameters their coordinates [relating to rather probably existent center, see SS posts in the first link], which very essentially determine, say, strengths of interactions in matter.
Cheers
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