The basic framework of ΛCDM is the curved spacetime of general relativity. However, precise cosmological observations show that the universe is indeed a flat space with a zero curvature, and high degree of homogeneity and isotropy. The flatness of the cosmic vacuum indicates that the ubiquity of attractive gravity is only a hypothesis derived from infinite extrapolation of local physical phenomena. On a cosmological scale, space might be gravitationally neutral. Measurements of the expansion of the universe indicate that there exist undeniable repulsive material components in the universe, such as dark energy. The gravitationally neutral universe composed of attractive dark matter (and a small amount of baryonic matter) coupled with repulsive dark energy is the true object of cosmic expansion dynamics. In addition, time in cosmic dynamics must be the absolute time that describes the overall expansion of the universe; Even the Friedman equations of standard cosmology require the use of the Robertson-Wolker metric to derive from the gravitational field equation of general relativity, and the time in the Robertson-Wolker metric is the absolute time of the universe that is independent of spatial position. Therefore, cosmic dynamics should be constructed in a flat spacetime composed of uniform fload time and three-dimensional space. The author [2] has constructed a gravitationally neutral universe model in flat spacetime, the Dark-Energy-Matter Coupled model (DEMC). The standard model ΛCDM with curved spacetime and the gravitationally neutral model DEMC with flat spacetime have proposed completely different theoretical predictions for the expansion rate, thermal process, and age of the universe, which can be clearly tested by observations.

Cosmic dynamics is the dynamics of cosmic vacuum. The cosmic vacuum is not a system of particle dynamics, but a thermodynamic system, its dynamics is neither classical mechanics nor relativistic mechanics. The basic physical quantities of cosmic dynamics are energy density and temperature, and the basic processes are density fluctuations, collective oscillations (thermal phonons) and critical phase transitions between attractive and repulsive fields. The expanding universe originates from the phase transition in a limited region in the primitive static vacuum of the attraction-repulsion equilibrium, the inflation caused by the transformation of the attraction field to the repulsive field, the inflation process produces material particles with inertial mass, the local interactions, and the high temperature neutral vacuum of uniform isotropic expansion. The time sequence of the whole process of the universe can only be characterized by the thermodynamic variables of vacuum-temperature or energy density. The uniform and isotropic space-time of the universe is composed of cosmic time $\tau$ and three dimensional Euclidean space. The expansion of the cosmic radius $R\left(\tau \right)$ is not any mechanical movement of material particles. Only the process of phase transition of the background vacuum (interconversion between dark energy and matter) itself can affect the uniform expansion of the universe as a whole.

For the expending universe, let $M_m$ and $M_{\lambda }$ be the inertial mass of gravitational matter and that of repulsive matter (dark energy) respectively, $E_{rad}$ be the radiation energy, then the total inertial mass $M_{\text{I}}=M_m+M_{\lambda }+E_{rad}$, total gravitational mass $M_g=M_m-M_{\lambda }$. Relative to the primitive static vacuum, the cosmic kinetic energy $E_k=M_{\text{I}}{\stackrel{\dot{}}{R}}^2/2$, and gravitational potential energy $E_p=-G{M}_{\text{I}}{M}_g{R}^{-1}$. The uniform and isotropic expanding vacuum has no relativistic effect of translational motion and no transfer of mechanical energy-radiation energy (therefore, the comoving system of the expanding vacuum can be regarded as a static inertial frame); From the conservation of mechanical energy

$E_{mech}=E_k+E_p=\text{const}$

the energy equation of the expanding universe can be derived as

${\stackrel{\dot{}}{a}}^2=\frac{8\pi G}{3}{\rho }_g{a}^2+ϵ$(1)

where the scale factor of the universe $a=R/R_0$, the current radius of the universe $R_0$, the gravitational mass density ${\rho }_g$, and the constant $ϵ=2E_{mech}/R_0^2{M}_{\text{I}}$. The equation of motion of the expanding universe is the Lagrangian equation

$\frac{\partial L}{\partial R}-\frac{\text{d}}{\text{d}\tau }\left(\frac{\partial L}{\partial \stackrel{\dot{}}{R}}\right)=0$(2)

where the Lagrangian of the universe

$L=M_{\text{I}}{\stackrel{\dot{}}{R}}^2/2+G{M}_{\text{I}}{M}_g{R}^{-1}$(3)

The laws of conservation, including the gauge invariance, require that the cosmic vacuum be a gravitationally neutral vacuum, ${\rho }_g=0$. According to the cosmic energy Equation (1), the normal state of the expanding universe is uniform expansion at the speed

$\stackrel{\dot{}}{a}=\sqrt{ϵ}$(4)

The data points in Figure 1 are measurement results of the cosmic expansion velocity $\stackrel{\dot{}}{a}$ at different cosmological redshifts $z$, from which we can see that the two most accurate observational results, the expansion velocity of the early ( $z=2.3$) and the current ( $z=0$), have the largest time interval but their values are very close; Starting from $z=z_c~1$, the recent universe is likely to have a phase transition process during which attractive matter $M_m$ and repulsive matter $M_{\lambda }$ convert each other and the universe firstly deviate from and then recovery again to the inertial expansion. For the phase transition starting from the critical redshift $z_c$ with critical temperature $T_c$ and critical radius $R_c$, taking the gravitational mass $M_g$ as the thermodynamic potential of the universe, and adopting the methodology of Landau mean-field theory for continuous phase transition [3] , we expand $M_g$ in power series of $\left(R-R_c\right)/R_c$ about the transition point $R_c$ as

$M_g=b_0+b_1\left(R-R_c\right)/R_c+\cdots$(5)

with $b_0=M_g\left(R=R_c\right)=0$. For the decelerating phase of $z\le z_c$, only the first two terms in the power series are used

$M_g=-b\left(R-R_c\right)$(6)

where $b>0$. Substituting (6) into Equation (2) we get the equation of motion for the decelerating phase

$\ddot{R}=-G\left(M_g{R}^{-2}+b{R}^{-1}\right)$(7)

Combining Equation (1) of energy and Equation (7) of motion, we get the evolution equation for the decelerating phase

$\ddot{a}=-\frac{1}{2}\left({\stackrel{\dot{}}{a}}^2-\alpha ϵ\right)a^{-1}$(8)

with the constant $\alpha =1-2Gb/R_0^2$. The solution of Equation (8) is

$\stackrel{\dot{}}{a}=\sqrt{\xi \left(1+z\right)-\alpha ϵ}\left(z_t\le z<z_c\right)$(9)

where $z_t$ is the end redshift of the decelerating phase, the positive integral constant $\xi =ϵ\left(1+\alpha \right)/\left(1+z_c\right)$.

During the deceleration phase, part of dark matter in the universe is converted into dark energy. After the decelerating phase, the universe at $z<z_t$ relaxed to an equilibrium state again through a part of dark energy converting back into dark matter. For a continuous phase transition at $z_t$, the acceleration $\ddot{a}\left(z=z_t\right)=0$, from Equation (8) the expansion rate is

$\stackrel{\dot{}}{a}\left(z=z_t\right)=\sqrt{\alpha ϵ}$(10)

Substituting Equation (10) into Equation (9) we get

$z_t=\frac{2\alpha }{1+\alpha }\left(1+z_c\right)-1$(11)

From $0<z_t<z_c$ we find

$\frac{1}{2z_c+1}<\alpha <1$(12)

Define a dimensionless relative density of gravitational mass

$\eta =\frac{{\rho }_g}{{\rho }_c}=\frac{{\stackrel{\dot{}}{a}}^2}{ϵ}-1$(13)

where the critical density

${\rho }_c=\frac{3}{8\pi G}ϵ{\left(1+z\right)}^3$

By Onsager’s principle of the symmetry of the kinetic coefficients ( [3] §120), $\eta$ should be symmetric around $z=z_t$, i.e. $\eta$ at $z_e\le z<z_t$ is the same with that at $z^{\prime }=2z_t-z$, where $z_e$ is the red shift at the end of the phase transition

$z_e=2z_t-z_c.$(14)

Then from Equation (9) we can get the evolution equation of the accelerated expansion phase

$\stackrel{\dot{}}{a}=\sqrt{\eta \left(1+2z_t-z\right)-\alpha ϵ}\left(z_e\le z<z_t\right)$(15)

Using Equations (11) and (14), the number of undetermined parameters in three evolution Equations (4), (9) and (15) can be reduced to three. The values of the undetermined parameters estimated by fitting the data shown in Figure 2 with Equation (4), (9) and (15) are as follows: $\sqrt{ϵ}=66.7\pm 0.9$ km∙s⁻¹∙Mpc⁻¹, $\alpha =0.64\pm 0.04$ and $z_c=1.08\pm 0.15$. From Equations (11) and (14) we have $z_{\text{t}}=0.62$ and $z_e=0.16$. The solid line in Figure 2 is the evolution curve obtained by fitting the model of uniform expansion + phase transition to date: from $z_c=1.08$ the universe of uniform expansion began to decelerate, the relaxation process of phase transition started from $z_t=0.62$, and from $z_e=0.16$ the universe has recovered to an uniform expansion.

The Friedmann equation of the standard universe model ΛCDM is a general relativistic equation of an ideal fluid, a particle system. The Friedmann equation predicts that under the action of gravity, velocity of particles that make up the cosmic fluid monotonously drop until to the critical point of $z_t$, and then infinitely rise accelerated by the cosmological constant. For the future of $z<0$, it is impossible to confirm whether the universe is an inertial expansion with occasional phase transition or an infinite acceleration to tearing; However, for the early universe of $z\ge 4$, the expansion speed of the universe expected by the standard model is far greater than the current speed, so it will be possible to make a clear choice between the two models of universe.

In the gravitationally neutral universe, there is no Big Bang singularity that puzzles physics: the universe was generated by an inflation of a limited region in an infinite vacuum ocean (see Figure 2 ). The vacuum before inflation is a gravitationally neutral vacuum in which the attractive and repulsive fields were balanced to each other and no mechanical motion and thermal motion existed, it is an absolutely rest frame of reference (cosmic rest system) for motions of cosmic and local systems. The inflation was driven by the phase transition in the limited vacuum region: part of the attractive field was transformed into the repulsive field, which made the repulsive field in this region dominant, and the net repulsive field drove the vacuum to be uniform and isotropic inflation.

On the map of CMB temperature anisotropies shown in Figure 3 , there exist a few tens of thousands of hot and cold spots with typical angular scale $\theta ~1^{\circ }$, each one will form a sub expending universe. Therefore, the expending universe consists of a few tens of thousands of parallel sub expending universes. Our Milky Way belongs to a parent sub universe which comes from a certain 1˚-diameter spot, say a parent cold spot.

In ΛCDM, all spots on CMB anisotropy maps are the product of the Big Bang. However, there is a most prominent 10˚-diameter cold spot located at $\left(b,l\right)=\left(-{55.8}^{\circ },{209.4}^{\circ }\right)$ on CMB maps made by WMAP and Planck satellites, which should be a topological defect in the very early universe, but the energy scale required to produce it is too high [15] , leading Gurzadyan and Penrose [16] to argue that it was a supermassive black hole before the Big Bang.

In DEMC, spots of 1˚-diameter on CMB maps come from a phase transition of the cosmic medium at $z~1$, when the age of the universe was about 14 billion years. The 10˚-diameter spot can be naturally interpreted as a product of an earlier cosmic phase transition at $z~10$, which was about 12 billion years earler than the last phase transition at $z~1$.

It is worth noting that the high red shift galaxies and black holes found by JWST that challenge the standard model are all within the scope of this big cold spot. Furthermore, Liu and Li [17] pointed out that the temperature map of this cold spot has a characteristic structure: a circular ring about 4˚ from the center has the largest temperature fluctuation (see the upper left panel of Figure 4 ); and that quite a few other 10˚-diameter cold or hot spots with similar characteristic temperature structure have also found in WMAP maps (as shown in the remaining panels in Figure 4 ) and in Plank maps as well.

As previously mentioned, for the gravitationally neutral universe DEMC, cold/hot spots of ~1˚ on all-sky CMB maps are sub universes formed during the phase transition at redshift of $z~1$ about 14 billion years ago, while these cold/hot spots of ~10˚ should be sub universes formed during a phase transition at redshift of $z~10$ about 25 billion years ago. The average temperature difference distribution obtained by superimposing 1˚ cold or hot CMB spots after aligning with their extreme temperature points [18] presents a feature of standing wave effect of disturbance propagation within ~1˚ horizon when $z~1$; For the characteristic feature of cold/hot spots shown in Figure 4 —largest temperature fluctuations at ~4˚ rings—should be attributed to standing wave effects of disturbance propagation within ~10˚ horizon when $z~10$.

On the CMB angular power spectrum shown in Figure 5 , the acoustic peak at multipole moment index $l~200$ (angular scale $\theta ~1^{\circ }$) and overtones are the results of local acoustic oscillations within horizons in the beginning of the cosmic phase transition at $z~1$; In the large-scale spectrum of Figure 5 , there is also an obvious concave structure at $l~20$ ( $\theta ~{10}^{\circ }$), supporting that the earlier phase transition of the expanding universe at $z~10$ really occurred.

Thus, much richer than expected by the Big Bang model, the observed expending universe has undergone at least two phase transitions, each produced a large number of sub universes expanding in parallel: ~10⁴ sub universes from the last phase transition at $z~1$ and ~10² ones from the previous phase transition at $z~10$. Parallelly expending universes form the observable universe. Each sub universe is composed of clusters of galaxies and voids. Most of observed objects and voids almost uniform distributed in the sky belong to the parent sub universe where the Milky Way galaxy is located, and a small number of celestial bodies belonging to other sub universes may also be observed in their corresponding ~1˚ or ~10˚ sky range, respectively. It can be expected that with the development of optical and radio telescopes and through in-depth observations to the universe, human understanding of the temporal and spatial scales of the universe and physical processes in the universe could be essentially expanded.