Zero-energy space cancels the need for dark energy Tuomo Suntola

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1 Short notes on Zero-energy space cancels the need for dark energy Tuomo Suntola, Faculty of Science of Eötvös University, Budapest Zero-energy space cancels the need for dark energy Tuomo Suntola, Finland Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory Following news was released in July this year: Latest PhysicsWeb Summaries : Dark-energy teams win cosmology prize (Jul 7) Two independent teams of researchers who discovered that the expansion of the universe is accelerating have been awarded this year's Gruber Cosmology Prize. The prize, worth $500,000, has been given to the groups led by Saul Perlmutter and Brian Schmidt, who reported their discovery in 998. Their work provided the first convincing evidence for the existence of "dark energy" -- a mysterious and so-far invisible entity that physicists believe works against gravity to boost the expansion of the universe. 2

2 The work by Perlmutter s and Schmidt s teams certainly was worth the award, but what actually was discovered was not acceleration of the expansion of space but the magnitudes of distant supernovas an alternative way of wording the news had been Latest PhysicsWeb Summaries : Dark-energy teams win cosmology prize (Jul 7) an alternative way of wording the news: Two independent teams of researchers who discovered that the magnitudes of high redshift supernovae do not follow the prediction of the standard cosmology model have been awarded a concept of dark energy working against gravitation between galaxies has been suggested to fix the problem. 4 What exactly was observed, was the magnitudes of supernovas with different redshift Magnitude versus redshift: Supernova observations 50 μ + SN Ia observations Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) 30 0,00 0,0 0, z 0 5 2

3 the pink curve illustrates the basic prediction of the standard model which shows small but observable deviation from the observations at high redshifts 50 μ Magnitude versus redshift: Supernova observations + SN Ia observations Standard model with Ω m =, Ω Λ = RH μ = 5log 0 pc Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) z + 5log ( + z) dz 0 ( z) 2 ( m z) z( 2 z + +Ω + ) Ωλ 30 0,00 0,0 0, z 0 6 the prediction for magnitudes can be twisted upwards by replacing part of the mass in space with mass with negative gravitation, referred to as dark energy 50 μ Magnitude versus redshift: Supernova observations + SN Ia observations Standard model with Ω m =, Ω Λ = 0 Standard model with Ω m = 0.3, Ω Λ = RH μ = 5log 0 pc z + 5log ( + z) dz 0 ( z) 2 ( m z) z( 2 z + +Ω + ) Ωλ 30 0,00 0,0 0, z 0 Data: A. G. Riess, et al., Astrophys. J., 607, 665 (2004) Suggested correction: Ω m = 0.3 Ω Λ = 0.7 (dark energy) 7 Dark energy works like Einstein s cosmology constant which he introduced to prevent contraction of spherically closed space in his cosmology outline in 97. The fit of magnitude prediction to observations up to redshift z = 2 becomes fixed with the dark energy the problem is solved or is it? 3

4 Magnitude versus redshift is not the only problem met with the predictions of the standard cosmology model. It has been known for quite some time that the observed angular sizes of galaxies and quasars decrease in direct proportion to their redshift which means Euclidean appearance of galaxy space as shown by the blue Euclidean lines in the figure on the right Angular size of galaxies and quasars Euclidean (a) z 0.00 (b) z Largest angular size (LAS), Open circles: galaxies Filled circles: quasars Collection of data: K. Nilsson et al., Astrophys. J., 43, 453 (993) 9 The basic prediction without dark energy of the standard model looks quite different: at redshifts z > the predicted angular size turns upward as shown by the red curves in the lower figure on the left when the effect of dark energy is added to the prediction the turning point is shifted slightly to higher redshifts but it is still far from the observed Euclidean appearance as shown by the lower figure on the right Angular size of galaxies and quasars Euclidean (a) (b) Largest angular size (LAS), Open circles: galaxies Filled circles: quasars (c) Standard model Ω m = Ω m = 0.3 Ω Λ = 0.7 (d) Standard model + dark energy Collection of data: K. Nilsson et al., Astrophys. J., 43, 453 (993) Suggested explanation: high z galaxies are young; sizes are still developing (not supported by spectral data!) z z 2 4

5 The suggested explanation to the deviation of the predicted angular size from the Euclidean appearance is that galaxies and quasars with redshift z > are young and their sizes are still developing such explanation, however, is not supported by spectral data from the objects We should ask: Does the dark energy really solve problem or do the observations reflect a more fundamental problem in the Standard Cosmology Model or the Relativity Theory? The standard model, the solution of GR field equations by Friedman, Lemaître, Robertson and Walker relies on the assumptions of general relativity including the conservation of energy in local systems but not in whole space Standard Cosmology Solution of GR field equations by Friedman, Lemaître, Robertson, and Walker assuming - the cosmological principle - space-time metrics and the assumptions of general relativity - Lorentz transformation - relativity principle - equivalence principle - constancy of the velocity of light - local conservation of energy galaxies conserve their dimension 4 An alternative to the Standard Cosmology Model, the Dynamic Universe model, or the zeroenergy space concept is a holistic view of space as a spherically closed entity with zero-energy balance between the potential energy and the energy of motion in the system Local phenomena are derived by conserving the total energy in all interactions in space Zero-energy space Solution of zero-energy condition in spherically closed space assuming - minimum volume for closing 3-space the surface of a 4-sphere - conservation of total energy in all interactions in space - homogeneity as the initial condition cosmological principle - absolute time and distance units 5 5

6 In zero-energy space, the fourth dimension is metric by its nature it is not time-like like in GR space. Metric fourth dimension allows the definition of space as the 3-dimensional surface of an orthodox 4-dimensional sphere. Gravitation between masses in space result in a shrinkage force putting the structure into contraction towards singularity by converting the energy of gravitation into the energy of motion like a pendulum on the way down The energy of motion gained in contraction is paid to gravitation in expansion after singularity just like in the case of pendulum on the way back up Zero-energy space Solution of zero-energy condition in spherically closed space assuming - minimum volume for closing 3-space the surface of a 4-sphere - conservation of total energy in all interactions in space - homogeneity as the initial condition cosmological principle - absolute time and distance units E m R 4 F n m n E g contraction expansion 8 In real space we are subject to gravitation and motion in a system of nested energy frames (Solar system, Milky Way galaxy, local galaxy group, etc.). Combining the effects of motion and gravitation in each frame the locally available rest energy is reduced by motion and gravitation in the local gravitational frame and in all the related parent frames E rest = E δ β δ, β 2 ( ) rest( 0,0) ( ) i i i i i The system of nested energy frames Hypothetical homogeneous space zero-energy space appears as a structured system of nested energy frames where universal time and distance applies, the local state of rest is an attribute of the local frame, relativity is the measure of locally available share of total energy n 2 ( ) 2 rest = 0 0 i i i= E m c δ β 26 6

7 Physical distance in spherically closed space can be expressed in terms the size angle from the 4-center of space. In practice, the distance observed is the length of the propagation path of light from the object observed Because the velocity of light in zero-energy space is equal to the velocity of space in the direction of the 4-radius, the optical distance obtains a simple mathematical form α z D = R4( e ) = R4 + z Physical distance of objects in zero-energy space Optical distance of objects in zero-energy space c 0 observer c 0 object t c 0 R 4 observer D phys R 4 R 4 α t (0) α R 4(0) c 0(0) emitting object O (a) O (b) Dphys = α R 4 D opt α z = R4 R40 ( ) = R4( e ) = R4 + z 3 As a consequence of the conservation of energy in zero-energy space, gravitationally bound systems like galaxies and quasars expand with the expansion of space The angular sizes of galaxies and quasars in zero-energy space obtain the Euclidean appearance which is very good news regarding a fit with observations, see the blue upper figure on the right in the slide below Angular size of galaxies and quasars (a) (b) Euclidean, zero-energy space Zero-energy space: complete agreement with observations r0 θ = R z Largest angular size (LAS), Open circles: galaxies Filled circles: quasars 4 (c) Standard model Ω m = Ω m = 0.3 Ω Λ = 0.7 (d) Standard model + dark energy Collection of data: K. Nilsson et al., Astrophys. J., 43, 453 (993) Suggested explanation: high z galaxies are young; sizes are still developing (not supported by spectral data!) z z 38 7

8 The prediction for the magnitude obtains a simple, parameter-free form, with excellent fit to the supernova observations without assumptions of dark energy or accelerating expansion. 50 μ 45 Magnitude versus redshift: Supernova observations + SN Ia observations Zero-energy space Zero-energy space R4 μ = 5log 0 pc + 5log z + 2.5log ( + z) ,00 0,0 0, 0 44 CONCLUSIONS: There is a fundamental problem in the FLRW metrics observed at the extremes: at large distances and at local singularities the problem is related to the local nature of general relativity and the missing linkage between the energy of local systems and the total energy in space AND The zero-energy approach is a holistic analysis of zero-energy condition in spherically closed space It shows the essence of relativity as the measure of locally available share of total energy, produces precise predictions to local and cosmological phenomena in closed mathematical forms, and re-establishes the use of absolute coordinate quantities, time and distance, essential for human conception, and in merging relativity into the framework of quantum mechanics 8