Existence of gravitation inverse matter in finite space is shown inevitable. As an example, direction of gravitation of rest mass of electron is opposite to that of positron. That is, electron and positron are gravita...Existence of gravitation inverse matter in finite space is shown inevitable. As an example, direction of gravitation of rest mass of electron is opposite to that of positron. That is, electron and positron are gravitationally repulsive to each other. The physical space has previously been shown of finite extent. Therefore, if gravitation normal matter is found prevailing in the physical space then, according to the law of mass/charge balance in finite space, the Universe, i.e., the physical space and all that it contains/confines, must be a shell-structured black hole in a higher dimensional space.展开更多
Even though dark matter and dark energy have long been accepted as being of fundamental importance in cosmology, in this paper, we will present arguments to show that neither is necessary. Instead, the phenomena they ...Even though dark matter and dark energy have long been accepted as being of fundamental importance in cosmology, in this paper, we will present arguments to show that neither is necessary. Instead, the phenomena they are thought to be responsible for are consequences of a vacuum whose curvature varies with time. We will focus on three phenomena that are thought to require the existence of dark energy and dark matter. The first is the idea that dark energy is responsible for the observed accelerating expansion of the universe. We will show instead that with time-varying curvature, Einstein’s equations demand such an acceleration without reference to dark or any other form of energy. Turning to dark matter, it is supposedly required to explain the observed constant velocity profile of the stars making up the disks of spiral galaxies and to explain the strong gravitational lensing observed in galaxy clusters. We will show, however, that both phenomena can again be understood in terms of the vacuum and its curvature. In the former case, we will show that galaxies exist within a rotating volume of the vacuum and that this leads directly to the observed constant velocity profiles. In the latter case, gradients of the vacuum curvature serving as a varying index of refraction are responsible. Using numerical results from our new model of nucleosynthesis, we estimate the degree of bending to expect and find that the results are in accord with observation. Our new model very naturally explains the phenomena attributed to dark matter and dark energy and since neither has been observed after several decades of looking, Occam’s razor tells us that neither exists.展开更多
In this paper, we present a new cosmology based on the idea of a universe dominated by vacuum energy with time-varying curvature. In this model, the universe began with an exponential Plank era inflation before transi...In this paper, we present a new cosmology based on the idea of a universe dominated by vacuum energy with time-varying curvature. In this model, the universe began with an exponential Plank era inflation before transitioning to a spacetime described by Einstein’s equations. While no explicit model of the Plank era is yet known, we do establish a number of properties that the vacuum of that time must have exhibited. In particular, we show that structures came into existence during that inflation that were later responsible for all cosmic structures. A new solution of Einstein’s equations incorporating time-varying curvature is presented which predicts that the scaling was initially power law with a parameter of <em>y</em>=1/2 before transitioning to an exponential acceleration of the present-day scaling. A formula relating the curvature to the vacuum energy density is also a part of the solution. A non-conventional model of nucleosynthesis provides a solution for the matter/antimatter asymmetry problem and a non-standard origin of the CMB. The CMB power spectrum is shown to be a consequence of uncertainties embedded during the initial inflation and the existence of superclusters. Using Einstein’s equations, we show that so-called dark matter is, in fact, vacuum energy. A number of other issues are discussed.展开更多
Our original intent was to explain the origin of large HI structures. In order to understand HI structures, however, it is first necessary to understand the origin of both galaxies and galaxy clusters. Explaining thei...Our original intent was to explain the origin of large HI structures. In order to understand HI structures, however, it is first necessary to understand the origin of both galaxies and galaxy clusters. Explaining their origin is the purpose of Part 1 of this work. In our new model of cosmology, the creation of protons during nucleosynthesis was regulated by an imprint embedded in the vacuum in a manner that eventually resulted in the cosmic structures we now observe. Immediately after nucleosynthesis and for a considerable period afterward, the evolution was dominated by the expansion of the universe. Gradually, gravitational influences became important until eventually, the two became equal. At that point, the structures ceased to increase in size, and thereafter, their evolution was dominated by the gravitational interaction of the particles. The zero-velocity point for galaxies and galaxy clusters occurred at the usually accepted time of the beginning of galaxy formation. The initial population of stars also started their compaction at that same time but, in this case, partially for reasons having to do with the temperature of the proton gas. Many details of the evolution of the structure are discussed. We discuss the equilibrium of galaxy clusters and present a model that can potentially account for the present-day energy of the intracluster gas. Another outcome is that, at the time when the galaxies reached their zero-velocity point, they were several times larger than their present-day size, a fact that is critical for understanding the origin of the larger HI rings. In Part 2 of this work, we show that the HI structures can readily be understood in terms of the model developed here.展开更多
The author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more...The author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more fundamental interactions than the four, and these fundamental gauge fields are only components on the bottom manifold (i.e. our universe) projected by a unified gauge potential of the principal fiber bundle manifold;these components can satisfy the transformation of gauge potential, or even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, namely the generalized gauge equation expression, corresponding to gauge transformation invariance;so the invariance of gauge transformation is a necessary condition for unified field theory, and the four (or more) fundamental interaction fields of the universe are unified in a unified gauge field defined by the connection on the principal fiber bundle. In this paper, the author continues to propose a model of large-scale (gravitational) fundamental interactions in the universe based on the mathematical and physical picture of the principal fiber bundle, attempting to explain that dark matter and dark energy are merely reflections of these gravitational fundamental interactions that deviate in intensity from the gravitational fundamental interactions of the solar system at galaxy scales or some cosmic scales which are much larger than the solar system. All these “gravitational” fundamental interactions originate from the unified gauge field of the universe, namely the connection or curvature on the principal fiber bundle. These interactions are their projected representations on the bottom manifold (i.e. our universe) by different cross-sections (gauge transformations). These projection representations of the universe certainly are described by the generalized gauge equation or curvature similarity equation, and under the guidance of curvature gauge transformat展开更多
The direct observation of gravitational waves(GWs)opens a new window for exploring new physics from quanta to cosmos and provides a new tool for probing the evolution of universe.GWs detection in space covers a broad ...The direct observation of gravitational waves(GWs)opens a new window for exploring new physics from quanta to cosmos and provides a new tool for probing the evolution of universe.GWs detection in space covers a broad spectrum ranging over more than four orders of magnitude and enables us to study rich physical and astronomical phenomena.Taiji is a proposed space-based gravitational wave(GW)detection mission that will be launched in the 2030s.Taiji will be exposed to numerous overlapping and persistent GW signals buried in the foreground and background,posing various data analysis challenges.In order to empower potential scientific discoveries,the Mock Laser Interferometer Space Antenna(LISA)data challenge and the LISA data challenge(LDC)were developed.While LDC provides a baseline framework,the first LDC needs to be updated with more realistic simulations and adjusted detector responses for Taiji’s constellation.In this paper,we review the scientific objectives and the roadmap for Taiji,as well as the technical difficulties in data analysis and the data generation strategy,and present the associated data challenges.In contrast to LDC,we utilize second-order Keplerian orbit and second-generation time delay interferometry techniques.Additionally,we employ a new model for the extreme-mass-ratio inspiral waveform and stochastic GW background spectrum,which enables us to test general relativity and measure the non-Gaussianity of curvature perturbations.Furthermore,we present a comprehensive showcase of parameter estimation using a toy dataset.This showcase not only demonstrates the scientific potential of the Taiji data challenge(TDC)but also serves to validate the effectiveness of the pipeline.As the first data challenge for Taiji,we aim to build an open ground for data analysis related to Taiji sources and sciences.More details can be found on the official website(taiji-tdc.ictp-ap.org).展开更多
We present a Quantum Space Model (QSM) of cosmic evolution based on the theory that space consists of energy quanta from which our universe came about. We used the Friedmann equations to trace its history and predict ...We present a Quantum Space Model (QSM) of cosmic evolution based on the theory that space consists of energy quanta from which our universe came about. We used the Friedmann equations to trace its history and predict its ultimate fate. Results provide further support to our recent proposal that the accelerating expansion of the universe is due to a scalar space field which has become known as Dark Energy. In our model, the universe started from high energy space quanta which were triggered by quantum fluctuations that caused the Big Bang. It then expanded and cooled undergoing phase transitions to radiation, fundamental particles, and matter. Matter agglomerated and grew into stars, galaxies, etc. and was eventually consolidated by gravity into Black Holes, which finally ended in a Big Crunch in a state of deep freeze inside the Black hole at 1.380 trillion years. Fluctuations, quantum tunneling, or some other mechanisms caused a new Bang to start another cycle in its life. Our results are in good agreement with the theoretical predictions of a cyclic universe by Steinhardt and his associates, and by Penrose. Space and energy are equivalent as embodied in the Planck energy equation. They give rise to the two principal long range forces in the universe: the gravitational force and the space force. The latter may be the fifth force in the universe. The two forces could provide the clockwork mechanism operating our cyclic universe. If the Law of Conservation of Energy is universal, then the cosmos is eternal.展开更多
Researchers have long been aware of the existence of large HI structures and over the past decades, a large observational record of their properties has been assembled. Despite all the work that has been done, however...Researchers have long been aware of the existence of large HI structures and over the past decades, a large observational record of their properties has been assembled. Despite all the work that has been done, however, there is no consensus about their origin. In this paper, we will show that these structures can readily be understood within the framework of a new model of cosmology based on time-varying curvature and an unconventional model of nucleosynthesis. According to this model, all galaxies came into existence at the same time during nucleosynthesis as large proton gas clouds whose detailed structure was fixed by an imprint established in the vacuum during an initial Plank inflation. One of the predictions of the model is that all these proto-galaxy gas clouds reached the zero-velocity point of their expansion with sizes many times larger than their present-day size. The large outer HI rings are simply regions of this gas that remained at the maximum size as the core compacted to its present-day size. Similarly, the inner rings are regions that did compact with the galaxy core.展开更多
Considering Bianchi type III space-time we present the model Universe containing strange quark matter which is expanding, anisotropic, with a sign of dark energy that help in accelerated expansion of this Universe. It...Considering Bianchi type III space-time we present the model Universe containing strange quark matter which is expanding, anisotropic, with a sign of dark energy that help in accelerated expansion of this Universe. It is also seen that the model Universe contains both particles and strings but ultimately will have fluid containing particles only. This model which we consider here is acceptable in view of the present observations of the Universe. Some physical and geometrical properties are also discussed.展开更多
Considering five dimensional plane symmetric metric, we discuss a model universe with different situations, by solving the modified Einstein field equations within the framework of Lyra geometry. We obtain many intere...Considering five dimensional plane symmetric metric, we discuss a model universe with different situations, by solving the modified Einstein field equations within the framework of Lyra geometry. We obtain many interesting realistic solutions governing the present day model of the universe. Physical and kinematical properties of the models are discussed in detail.展开更多
The alignment between satellite and central galaxies serves as a proxy for addressing the issue of galaxy formation and evolution, and has been investigated abundantly in observations and theoretical works.Most scenar...The alignment between satellite and central galaxies serves as a proxy for addressing the issue of galaxy formation and evolution, and has been investigated abundantly in observations and theoretical works.Most scenarios indicate that the satellites preferentially are located along the major axis of their central galaxy. Recent work shows that the strength of alignment signals depends on the large-scale environment in observations. We use the publicly-released data from EAGLE to figure out whether the same effect can be found in the associated hydrodynamic simulation. We found much stronger environmental dependency of alignment signals in the simulation. We also explore change of alignments to address the formation of this effect.展开更多
We consider a generalized quintom （GQ） dark energy model for changing the equal weight of the negative-kinetic scalar field （phantom） and the normal scalar field （quintessence） in quintom dark energy. Though the...We consider a generalized quintom （GQ） dark energy model for changing the equal weight of the negative-kinetic scalar field （phantom） and the normal scalar field （quintessence） in quintom dark energy. Though the phantomdominated scaling solution is a stable late-time attractor, the early evolution of GQ is different from that of the quintom model and the adjustability of the dark energy state equation in the model is improved.展开更多
The evolution of the Robertson-Walker type universes consisting of radiating perfect fluid distribution coupled with zero-mass scalar field in which the gravitational parameter G varies with cosmic time t are studied....The evolution of the Robertson-Walker type universes consisting of radiating perfect fluid distribution coupled with zero-mass scalar field in which the gravitational parameter G varies with cosmic time t are studied. Unified descriptions of the early evolution of the universe consisting of different phases are investigated. The different properties of the cosmological solutions are discussed and the physical behaviour of the model universes during the radiation-dominated era and also during the big bang scenario are studied. Here we obtain models which are geometrically closed and are thereby ever expanding and evolve from rest from a non-singular hot origin with maximum (finite) energy density and temperature and a small minimum (non-zero) gravitational coupling G.展开更多
Based on the gravitational theory, fundamental data, and comprehensible suppositions, an evolution model of the universe was proposed. The universe exists in explosion and constringency mobile equilibrium state. The c...Based on the gravitational theory, fundamental data, and comprehensible suppositions, an evolution model of the universe was proposed. The universe exists in explosion and constringency mobile equilibrium state. The critical sizes of celestial bodies were calculated in their evolution process.展开更多
文摘Existence of gravitation inverse matter in finite space is shown inevitable. As an example, direction of gravitation of rest mass of electron is opposite to that of positron. That is, electron and positron are gravitationally repulsive to each other. The physical space has previously been shown of finite extent. Therefore, if gravitation normal matter is found prevailing in the physical space then, according to the law of mass/charge balance in finite space, the Universe, i.e., the physical space and all that it contains/confines, must be a shell-structured black hole in a higher dimensional space.
文摘Even though dark matter and dark energy have long been accepted as being of fundamental importance in cosmology, in this paper, we will present arguments to show that neither is necessary. Instead, the phenomena they are thought to be responsible for are consequences of a vacuum whose curvature varies with time. We will focus on three phenomena that are thought to require the existence of dark energy and dark matter. The first is the idea that dark energy is responsible for the observed accelerating expansion of the universe. We will show instead that with time-varying curvature, Einstein’s equations demand such an acceleration without reference to dark or any other form of energy. Turning to dark matter, it is supposedly required to explain the observed constant velocity profile of the stars making up the disks of spiral galaxies and to explain the strong gravitational lensing observed in galaxy clusters. We will show, however, that both phenomena can again be understood in terms of the vacuum and its curvature. In the former case, we will show that galaxies exist within a rotating volume of the vacuum and that this leads directly to the observed constant velocity profiles. In the latter case, gradients of the vacuum curvature serving as a varying index of refraction are responsible. Using numerical results from our new model of nucleosynthesis, we estimate the degree of bending to expect and find that the results are in accord with observation. Our new model very naturally explains the phenomena attributed to dark matter and dark energy and since neither has been observed after several decades of looking, Occam’s razor tells us that neither exists.
文摘In this paper, we present a new cosmology based on the idea of a universe dominated by vacuum energy with time-varying curvature. In this model, the universe began with an exponential Plank era inflation before transitioning to a spacetime described by Einstein’s equations. While no explicit model of the Plank era is yet known, we do establish a number of properties that the vacuum of that time must have exhibited. In particular, we show that structures came into existence during that inflation that were later responsible for all cosmic structures. A new solution of Einstein’s equations incorporating time-varying curvature is presented which predicts that the scaling was initially power law with a parameter of <em>y</em>=1/2 before transitioning to an exponential acceleration of the present-day scaling. A formula relating the curvature to the vacuum energy density is also a part of the solution. A non-conventional model of nucleosynthesis provides a solution for the matter/antimatter asymmetry problem and a non-standard origin of the CMB. The CMB power spectrum is shown to be a consequence of uncertainties embedded during the initial inflation and the existence of superclusters. Using Einstein’s equations, we show that so-called dark matter is, in fact, vacuum energy. A number of other issues are discussed.
文摘Our original intent was to explain the origin of large HI structures. In order to understand HI structures, however, it is first necessary to understand the origin of both galaxies and galaxy clusters. Explaining their origin is the purpose of Part 1 of this work. In our new model of cosmology, the creation of protons during nucleosynthesis was regulated by an imprint embedded in the vacuum in a manner that eventually resulted in the cosmic structures we now observe. Immediately after nucleosynthesis and for a considerable period afterward, the evolution was dominated by the expansion of the universe. Gradually, gravitational influences became important until eventually, the two became equal. At that point, the structures ceased to increase in size, and thereafter, their evolution was dominated by the gravitational interaction of the particles. The zero-velocity point for galaxies and galaxy clusters occurred at the usually accepted time of the beginning of galaxy formation. The initial population of stars also started their compaction at that same time but, in this case, partially for reasons having to do with the temperature of the proton gas. Many details of the evolution of the structure are discussed. We discuss the equilibrium of galaxy clusters and present a model that can potentially account for the present-day energy of the intracluster gas. Another outcome is that, at the time when the galaxies reached their zero-velocity point, they were several times larger than their present-day size, a fact that is critical for understanding the origin of the larger HI rings. In Part 2 of this work, we show that the HI structures can readily be understood in terms of the model developed here.
文摘The author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more fundamental interactions than the four, and these fundamental gauge fields are only components on the bottom manifold (i.e. our universe) projected by a unified gauge potential of the principal fiber bundle manifold;these components can satisfy the transformation of gauge potential, or even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, namely the generalized gauge equation expression, corresponding to gauge transformation invariance;so the invariance of gauge transformation is a necessary condition for unified field theory, and the four (or more) fundamental interaction fields of the universe are unified in a unified gauge field defined by the connection on the principal fiber bundle. In this paper, the author continues to propose a model of large-scale (gravitational) fundamental interactions in the universe based on the mathematical and physical picture of the principal fiber bundle, attempting to explain that dark matter and dark energy are merely reflections of these gravitational fundamental interactions that deviate in intensity from the gravitational fundamental interactions of the solar system at galaxy scales or some cosmic scales which are much larger than the solar system. All these “gravitational” fundamental interactions originate from the unified gauge field of the universe, namely the connection or curvature on the principal fiber bundle. These interactions are their projected representations on the bottom manifold (i.e. our universe) by different cross-sections (gauge transformations). These projection representations of the universe certainly are described by the generalized gauge equation or curvature similarity equation, and under the guidance of curvature gauge transformat
基金funding was provided by the National Key Research and Development Program of China (Grant Nos.2021YFC2203001,2020YFC2201501,and 2021YFC2203002)the NSFC (Nos.11920101003,12021003,12173071,12147103,12235019,and No.12075297)+1 种基金supported by the CAS Project for Young Scientists in Basic Research YSBR-006supported by the Interdisciplinary Research Funds of Beijing Normal University.
文摘The direct observation of gravitational waves(GWs)opens a new window for exploring new physics from quanta to cosmos and provides a new tool for probing the evolution of universe.GWs detection in space covers a broad spectrum ranging over more than four orders of magnitude and enables us to study rich physical and astronomical phenomena.Taiji is a proposed space-based gravitational wave(GW)detection mission that will be launched in the 2030s.Taiji will be exposed to numerous overlapping and persistent GW signals buried in the foreground and background,posing various data analysis challenges.In order to empower potential scientific discoveries,the Mock Laser Interferometer Space Antenna(LISA)data challenge and the LISA data challenge(LDC)were developed.While LDC provides a baseline framework,the first LDC needs to be updated with more realistic simulations and adjusted detector responses for Taiji’s constellation.In this paper,we review the scientific objectives and the roadmap for Taiji,as well as the technical difficulties in data analysis and the data generation strategy,and present the associated data challenges.In contrast to LDC,we utilize second-order Keplerian orbit and second-generation time delay interferometry techniques.Additionally,we employ a new model for the extreme-mass-ratio inspiral waveform and stochastic GW background spectrum,which enables us to test general relativity and measure the non-Gaussianity of curvature perturbations.Furthermore,we present a comprehensive showcase of parameter estimation using a toy dataset.This showcase not only demonstrates the scientific potential of the Taiji data challenge(TDC)but also serves to validate the effectiveness of the pipeline.As the first data challenge for Taiji,we aim to build an open ground for data analysis related to Taiji sources and sciences.More details can be found on the official website(taiji-tdc.ictp-ap.org).
文摘We present a Quantum Space Model (QSM) of cosmic evolution based on the theory that space consists of energy quanta from which our universe came about. We used the Friedmann equations to trace its history and predict its ultimate fate. Results provide further support to our recent proposal that the accelerating expansion of the universe is due to a scalar space field which has become known as Dark Energy. In our model, the universe started from high energy space quanta which were triggered by quantum fluctuations that caused the Big Bang. It then expanded and cooled undergoing phase transitions to radiation, fundamental particles, and matter. Matter agglomerated and grew into stars, galaxies, etc. and was eventually consolidated by gravity into Black Holes, which finally ended in a Big Crunch in a state of deep freeze inside the Black hole at 1.380 trillion years. Fluctuations, quantum tunneling, or some other mechanisms caused a new Bang to start another cycle in its life. Our results are in good agreement with the theoretical predictions of a cyclic universe by Steinhardt and his associates, and by Penrose. Space and energy are equivalent as embodied in the Planck energy equation. They give rise to the two principal long range forces in the universe: the gravitational force and the space force. The latter may be the fifth force in the universe. The two forces could provide the clockwork mechanism operating our cyclic universe. If the Law of Conservation of Energy is universal, then the cosmos is eternal.
文摘Researchers have long been aware of the existence of large HI structures and over the past decades, a large observational record of their properties has been assembled. Despite all the work that has been done, however, there is no consensus about their origin. In this paper, we will show that these structures can readily be understood within the framework of a new model of cosmology based on time-varying curvature and an unconventional model of nucleosynthesis. According to this model, all galaxies came into existence at the same time during nucleosynthesis as large proton gas clouds whose detailed structure was fixed by an imprint established in the vacuum during an initial Plank inflation. One of the predictions of the model is that all these proto-galaxy gas clouds reached the zero-velocity point of their expansion with sizes many times larger than their present-day size. The large outer HI rings are simply regions of this gas that remained at the maximum size as the core compacted to its present-day size. Similarly, the inner rings are regions that did compact with the galaxy core.
文摘Considering Bianchi type III space-time we present the model Universe containing strange quark matter which is expanding, anisotropic, with a sign of dark energy that help in accelerated expansion of this Universe. It is also seen that the model Universe contains both particles and strings but ultimately will have fluid containing particles only. This model which we consider here is acceptable in view of the present observations of the Universe. Some physical and geometrical properties are also discussed.
文摘Considering five dimensional plane symmetric metric, we discuss a model universe with different situations, by solving the modified Einstein field equations within the framework of Lyra geometry. We obtain many interesting realistic solutions governing the present day model of the universe. Physical and kinematical properties of the models are discussed in detail.
基金supported by NSFC (No. 11803095)supported by NSFC (No. 11733010)
文摘The alignment between satellite and central galaxies serves as a proxy for addressing the issue of galaxy formation and evolution, and has been investigated abundantly in observations and theoretical works.Most scenarios indicate that the satellites preferentially are located along the major axis of their central galaxy. Recent work shows that the strength of alignment signals depends on the large-scale environment in observations. We use the publicly-released data from EAGLE to figure out whether the same effect can be found in the associated hydrodynamic simulation. We found much stronger environmental dependency of alignment signals in the simulation. We also explore change of alignments to address the formation of this effect.
基金Supported by the National Natural Science Foundation of China under Grant No 10275008.
文摘We consider a generalized quintom （GQ） dark energy model for changing the equal weight of the negative-kinetic scalar field （phantom） and the normal scalar field （quintessence） in quintom dark energy. Though the phantomdominated scaling solution is a stable late-time attractor, the early evolution of GQ is different from that of the quintom model and the adjustability of the dark energy state equation in the model is improved.
文摘The evolution of the Robertson-Walker type universes consisting of radiating perfect fluid distribution coupled with zero-mass scalar field in which the gravitational parameter G varies with cosmic time t are studied. Unified descriptions of the early evolution of the universe consisting of different phases are investigated. The different properties of the cosmological solutions are discussed and the physical behaviour of the model universes during the radiation-dominated era and also during the big bang scenario are studied. Here we obtain models which are geometrically closed and are thereby ever expanding and evolve from rest from a non-singular hot origin with maximum (finite) energy density and temperature and a small minimum (non-zero) gravitational coupling G.
文摘Based on the gravitational theory, fundamental data, and comprehensible suppositions, an evolution model of the universe was proposed. The universe exists in explosion and constringency mobile equilibrium state. The critical sizes of celestial bodies were calculated in their evolution process.
