A New Cosmological Model of the Universe and New Interpretation for the Cosmic Microwave Background and Type Ia Supernovae Redshifts
Branislav Vlahovic North Carolina Central University, Fayetteville St. Durham, NC 27707
Abstract
Presented is new cosmological model that assumes radial expansion of galaxies with a speed close to c, and confinement of the galaxies and motion of light on the sphere defined by the position of galaxies. The model predicts correct values for the Hubble constant H0 = 71.17 ± 0.86 km/s/Mpc, size of the observable universe, and speed of the event horizon. It explains why the observed cosmic microwave background is always the same, regardless of the direction in which the measurement is performed and explains uniformity of the CMB without inflation theory. Through relativistic mass correction, this model also provides an explanation for critical density without use of dark mass and dark matter. The model also explains that type Ia supernovae redshifts are not related to the accelerated expansion of the universe and dark energy. It is in agreement with type Ia data and with Hubble Ultra Deep Field (HUDF) optical and near-infrared survey performed in 2004.
Introduction
The distance to the edge of the observable universe is roughly the same in every direction. Therefore, the observable universe is a spherical volume centered on the observer and from our perspective it appears to be a sphere with a comoving radius of about 14 billion parsecs (about 45.6 billion light-years). It includes signals, inside particle horizon, since the beginning of the cosmological expansion (the Big Bang in traditional cosmology, the end of the inflationary epoch in modern cosmology). Although many theories require a total universe that is much larger (for instance according to the theory of cosmic inflation and its founder, Alan Guth, the lower bound for the diameter of the entire universe should be at least in the range of 1023 to 1026 times as large as the observable universe) it is also possible that the universe is smaller than the observable universe. The reasoning behind the latter case is a possibility that what we take to be very distant galaxies may actually be duplicate images of nearby galaxies, formed by light that has circumnavigated the universe. A lower bound of 24 gigaparsecs on the diameter of the whole universe is predicted in [1] (regardless the difficulties to test this hypothesis experimentally, because different images of the same galaxy might appear quite different in different eras in its history) making it, at most, only slightly smaller than the observable universe.
However, let us here note that if the boundary of the visible universe (which is about 2% smaller than observable universe) approximately corresponds to the physical boundary of the universe at the present time (if such a boundary exists) it would imply that Earth is
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exactly at the center of the universe. This is a non Copernican model which is difficult to believe.
According to the Big Bang model, the radiation from the sky we measure today comes from a spherical surface called the surface of last scattering, which represents the collection of spots in space at which the decoupling event is believed to have occurred when the universe was approximately 380,000 years old and at a point in time such that the photons from that distance have just reached observers. Observing the background radiation coming from opposite directions, we are looking at the two regions billions of light years apart on opposite sides of our observable universe, but we are seeing them as they were when they were only 380,000 years old. When we are looking at the early universe, we are looking at the image of a sphere with the size of only 36 Mly. That sphere has expanded to 1292 times the size it was when the CMB photons were released; hence, the most distant matter that is observable at present, 46 billion light-years away, was only 36 million light-years away from the matter that would eventually become Earth when the microwaves we are currently receiving were emitted.
The uniformity of CMB and the general sameness of the observable universe at very large scales are explained by the inflation model, which assumes that tiny region much smaller than the nucleus of an atom expanded to become entire part of the observable universe. Let us here note that inflation ended when universe was only 10-32 second old. From that time to the era of decoupling the universe went through the period of the most significant transformations, with the densities changed from 1038 kg/m3 to 10-17 kg/m3 and temperature changed from 1029 K to about 3000 K. The high degree of isotropy observed in the microwave background indicates that any density variations from one region of space to another at the time of decoupling must have been small, at most a few parts in 105 and that the temperature variations are smaller than 30-40 millionths of a Kelvin from place to place in the sky. Keeping in mind that during this period of transformation some regions of universe were separated by as much as 36 Mly and were not able to communicate for the period of 380,000 years, it is at least surprising that all of them will end with almost exactly the same density and temperature. It is also important to note that this almost perfect uniformity in CMB cannot explain formation of larger structures such as galaxies and clusters without introducing cold dark mater. We will show that there is another possible solution without inflation theory and dark matter and dark energy if a Copernican model for interpretation of the universe and CMB is applied.
The proposed model
Modern cosmological models are isotropic and homogenous on large scale. This means that all observers in all galaxies will find themselves to be in the “center” of expansion, with all other galaxies moving away with velocities proportional to their relative distances v = Hod. This statement means that there is no center and no preferred position. However, when this is combined with the definition of the visible universe (as comoving distance of 14 Bly in any direction from Earth) and with the interpretation of the CMB
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(as a sphere that surrounds us, Fig. 1.), it appears to be the origin for the misconceptions incorporated in the current cosmological models.
Origin of CMB
Fig 1. a) visible universe and expansion of space and b) CMB as visible from the Earth.
It has been always emphasized that galaxies do not move through space and that the universe is not expanding into empty space around it, for space does not exist apart from the universe. An argument for this is that, for example, Earthly occurrences must involve motions through space and that we have no such experience in our everyday lives. However, this argument is similar to the Aristotle’s argument that Earth is not moving (since if it is moving we will always experience strong wind) and can be easily refuted because, as it is well known by special relativity that we cannot measure our absolute speed.
Having all that in mind, let us be for a moment open minded and devise another possible interpretation for the observable universe and also a different interpretation for the CMB, which are both as it will be shown consistent with cosmological observations and are actually more aligned with Copernicus principle. The proposed model will incorporate both motion of the galaxies through space and expansion of space.
The presence of matter or energy causes warping, or curvature, of spacetime. In a high- density universe (Ω0 > 1), space is curved so much that it bends back on itself and “closes off”. It is difficult to visualize a three-dimensional volume arching back on itself in this way, but a two dimensional version is the surface of the sphere. Just for purpose of visualization, let us assume for a moment that we cannot visualize or experience in any way the third dimension perpendicular to the sphere’s surface; that we and the light rays are confined to the sphere’s surface, just as we are in reality confined to the three- dimensional volume of our universe. In this model the universe can be schematically represented by Fig. 2.
In this model galaxies are expanding from the center of the universe (place of Big Bang) with the speed (as it will be shown later) close to the speed of the light. All galaxies are
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on the surface of the sphere and, just for example, our galaxy is marked by A. As mentioned earlier, the light is confined to the surface and can only travel on the surface of the sphere; for that reason we cannot point to the center of the universe. As seen from our galaxy all other galaxies are moving away from us (and from each other) with the speed v = v0Θ, which is actually Hubble law v = H0 x distance. In this schematic, looking from the position of our galaxy, the place of decoupling (the surface of last scattering) is on the opposite side of the sphere and it is marked by B. We can see B regardless which observation direction we will choose. Taking into account that the universe is 13.7 ± 0.17 By old [2], it gives the radius of the sphere R = 13.75 ± 0.17 Bly and distance from A to B, which represents in comoving distances the size of the observable universe equal to about 43 Bly. Using v = v0Θ = H0RΘ and expressing R in Mpc, it is easy to calculate value for the Hubble’s constant H0 = 71.17 ± 0.86 km/s/Mpc, which is in the agreement with the experimental data.
Fig. 2. a) Expansion of the universe with speed close to the speed of light, b) CMB visible from Earth, c) CMB visible from another place in the universe.
In this model, regardless of the direction we chose to measure CMB (for instance from point A looking in any arbitrary chosen direction), we will always measure CMB in the point B and we will always obtain the same value for the CMB. It is important to notice that measuring the same CMB by looking in the opposite directions of the universe does not represent or reflect the uniformity of the universe, because regardless of direction in which we will observe it, we will always measure CMB in the same point and for that
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reason we always must obtain the same result. Small variations for the CMB are possible and they are observed, but they are the result of the interaction between matter and light during its travel. For instance, depending on the direction we choose to measure CMB, light will travel from point A to B through different galaxies and will interact with different amounts of matter, which may result in the small observed variations of CMB.
To establish connection between the uniformity of the earlier universe at time of decoupling or uniformity of the present universe and CMB we will need to make a completely different kind of measurement of the CMB. We can see the CMB in any direction we can look in the sky. However, we must keep in mind that the CMB emitted by the matter that would ultimately form for instance Milky Way is long gone. It left our part of the universe at the speed of light billions of years ago and now forms part of the CMB for observers in remote parts of the universe, actually exactly for observer in the point B. For instance, if we perform measurement of the CMB at the point C, we will measure the CMB emitted by matter in the point D. To measure uniformity of the universe we will need to measure the CMB in at least two different points on the sphere. If, for instance, the measurements from points A and C give the same result, then and only then may we speak about the uniformity of the universe. However, such measurements are not possible at the present time.
The presented model has significant consequences for current cosmological theories. It explains uniformity in the CMB without inflation theory. The model also removes any superluminal speed, since all galaxies in the model are by definition moving with speeds less or equal to the speed of light. However, the radius of the observable universe or the radius of the particle horizon is πct0 where t0 is the present age of the universe. This is -1 between the values 2cH0 = 3cto, which corresponds to the particle horizon in Einstein-de Sitter universe (Ωm = 1 and ΩΛ = 0) and 3.4ct0, which corresponds to the currently favorable cosmological model Ωm = 0.3 and ΩΛ = 0.7 universe [3]. The velocity of particle horizon of this model is 2c which is the same as in the Einstein-de Sitter model.
The motion of galaxies with the speed of light incorporated in this model provides a valid reason for applying special relativity, for instance for the interpretation of redshifts or time dilatation for Type Ia supernovae. It also allows us to introduce an interesting new idea for interpretation of the missing mass, dark matter, and dark energy. The current assumption is that universe contains 4% of matter, 23% of dark matter, and 73% of dark energy. However, if galaxies are moving with the speeds close to c, we should take into account increase of the mass or energy due to this relativistic speed. The mass which we are observing corresponds to rest mass m0. However, in the models to calculate, for instance, critical density we should take into account mass increase due to the motion of the galaxies m = m0/ 1/ 1 . To account for the 96% of the missing mass galaxies should have speed equal to 99.995% of the speed of light, which is in agreement with the model.
One of the global methods for determining the mass density of the universe is by measuring the rate of cosmic expansion in the distant past. It is accepted that
5 observations of type Ia supernovae (SNe Ia) at redshift z < 1 provide startling and puzzling evidence that the expansion of the Universe at the present time appears to be accelerating, behavior attributed to “dark energy” with negative pressure [4,5].
This conclusion is based on the measurements of supernovae distances without using Hubble’s law and their redshifts, the rate of the cosmic expansion in the distant past. According to the data, galaxies at large distances are receding less rapidly than Hubble’s law would predict. A purely kinematic interpretation of the SN Ia sample provides evidence at the > 99% confidence level for a transition from deceleration to acceleration or similarly strong evidence for a cosmic jerk [6].
Our model provides an alternative explanation. It predicts, with the statistical significance that there is no acceleration. It clearly demonstrates that the deviation from Hubble’s law is misinterpreted, and that it is not related to the acceleration of the universe. The deviation is related to kinematics, to our position in the universe, and our point of sight.
Fig. 3. Hubble’s velocity is represented by dashed line. The speed, as seen by an observer on the surface of the sphere, as a function of the distance on the sphere, is represented by red curve. The experimental data from [6] are plotted as points with assigned errors.
To demonstrate this, let us stay consistent with our model and assume that galaxies are moving with a radial speed close to c, as explained in figure 2a. Let us again assume that our position in the galaxy is noted with point A. To measure the speed of another galaxy located on the line of sight from point A to point B, we will divide that arc into n segments. Let us assume that one observer is located in each of the n points on the
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segment from A to B. Each of these observers measures relative speed, dv, to its next neighbors (all will measure the same dv, since the segments have the same length). The observer in the point A will obtain the speed of the m-th observer by adding m times differences dv measured by each observer. Since the total sum will increase in value, the observer will need to apply the relativistic equation for the speed addition. It is easy to show that a simple recurrence relation for the speed at segment m has a form:
2 vi= (vi-1+dv)/(1+vi-1dv/c ), with m iterations.
Applying this equation plotted is the curve in Fig. 3. that represents the speed (as seen by observer in point A) as a function of the distance (the length of the arc from the point A to the point of the measurement). Plotted are on the same graph Hubble’s law v(Hubble)=dv*m and the experimental data from [6], where speed is obtained through redshift z as v=cz, and luminosity distance dL (in units of megaparsecs) is obtained from extinction-corrected distance moduli, μ = 5 log dL + 25. Fig. 3. clearly demonstrates that there is no acceleration of the universe, and that the effect is introduced by relativity. This result also underlines our earlier statement that there is no a reason for introduction of dark energy, because the observations for the universe acceleration can be explained by the model and kinematics.
The model can be tested. Assuming that matter is homogenously distributed in the universe, a simple experiment which will count the number of galaxies as function of redshift could provide a test for space curvature. If space is curved, the number of galaxies as function of altitude on the sphere, or function of redshift, should first increase and then decrease. This test is more complex than it appears, since it should include into the account expansion of the space with time and also detection limits of current instrumentation, but it is feasible at the present time. The Hubble Ultra Deep Field (HUDF) optical and near-infrared survey performed in 2004 covered only a tiny patch of the sky, just 3.5 arc minutes across, but due to the significant sensitivity and long exposure time extends thousands of megaparsecs away. HUDF shows a uniform distribution of matter by distance. This is consistent with the model, since integration by longitude could result in different number of galaxies for different redshifts, but a survey that will confirm this needs to be performed.
Conclusion
The presented model assumes radial expansion of the galaxies with the speed close to c and confinement of the galaxies and motion of light to the sphere R=ct0. The model gives an explanation for the Hubble law and predicts a value for the Hubble’s constant of H0 = 71.17 ± 0.86 km/s/Mpc. It also explains that the observed CMB belongs to the single point on the opposite side of the sphere and for that reason the measured CMB must be exactly the same for all directions of measurements. It explains uniformity of the CMB without the inflation theory. The model predicts correct values for the particle horizon πct0 and the velocity of the particle horizon 2c. It also accounts for the missing mass and explains critical density by applying relativistic mass or energy correction without
7 introducing dark mass and dark energy. The model also explains that type Ia supernovae redshifts are not related to the accelerated expansion of the universe, but are rather caused by our position in the universe and kinematics. It is in agreement with type Ia data and with Hubble Ultra Deep Field (HUDF) optical and near-infrared survey performed in 2004.
Acknowledgment
This work is supported by NSF award HRD-0833184 and NASA grant NNX09AV07A.
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