Assuming a flat universe expanding under a constant pressure and combining the first and the second Friedmann equations, a new equation, describing the evolution of the scale factor, is derived. The equation is a gene...Assuming a flat universe expanding under a constant pressure and combining the first and the second Friedmann equations, a new equation, describing the evolution of the scale factor, is derived. The equation is a general kinematic equation. It includes all the ingredients composing the universe. An exact closed form solution for this equation is presented. The solution shows remarkable agreement with available observational data for redshifts from a low of z = 0.0152 to as high as z = 8.68. As such, this solution provides an alternative way of describing the expansion of space without involving the controversial dark energy.展开更多
We show that, when measuring the Hubble constant by starting the evaluation from the time of the big bang era, the effect of time dilation results in a decrease in the value of the Hubble constant. But when evaluating...We show that, when measuring the Hubble constant by starting the evaluation from the time of the big bang era, the effect of time dilation results in a decrease in the value of the Hubble constant. But when evaluating the Hubble constant by starting the evaluation from the present time, the effect of time dilation results in an increase in the value of the Hubble constant. To elucidate the process, the time dilation is calculated both directly and through Schwarzschild solution of the Einstein equation for the gravitational time dilation. It is concluded that both measured values are valid but because of time dilation, different starting times for the evaluation of the Hubble constant have resulted in different measured values for the Hubble constant.展开更多
Through an analytical approach, we show that the Hubble constant is not unique and has two distinct values. The first of these values is consistent with the measurements by Riess et al., while the second value is cons...Through an analytical approach, we show that the Hubble constant is not unique and has two distinct values. The first of these values is consistent with the measurements by Riess et al., while the second value is consistent with the measurements by the Planck Collaboration. This is a new alternative approach that does not depend on the standard ΛCDM model and its constraints. Our analysis shows that the tension is due to a geometric mismatch in the comparison of the measurements which is equal to the temporal diameter of the surface of last scattering. Since the calculated values are essentially identical to the corresponding measured values, we conclude that the non-congruency of the ending point of the Riess et al. measurement and the starting point of the Planck Collaboration measurement, on the surface of last scattering, is the source of tension in the measurements. Further, the surprising consistency of the calculated values of the Hubble constant with the corresponding measured values confirms both the extreme fidelity of the measurements and the validity of the proposed approach.展开更多
文摘Assuming a flat universe expanding under a constant pressure and combining the first and the second Friedmann equations, a new equation, describing the evolution of the scale factor, is derived. The equation is a general kinematic equation. It includes all the ingredients composing the universe. An exact closed form solution for this equation is presented. The solution shows remarkable agreement with available observational data for redshifts from a low of z = 0.0152 to as high as z = 8.68. As such, this solution provides an alternative way of describing the expansion of space without involving the controversial dark energy.
文摘We show that, when measuring the Hubble constant by starting the evaluation from the time of the big bang era, the effect of time dilation results in a decrease in the value of the Hubble constant. But when evaluating the Hubble constant by starting the evaluation from the present time, the effect of time dilation results in an increase in the value of the Hubble constant. To elucidate the process, the time dilation is calculated both directly and through Schwarzschild solution of the Einstein equation for the gravitational time dilation. It is concluded that both measured values are valid but because of time dilation, different starting times for the evaluation of the Hubble constant have resulted in different measured values for the Hubble constant.
文摘Through an analytical approach, we show that the Hubble constant is not unique and has two distinct values. The first of these values is consistent with the measurements by Riess et al., while the second value is consistent with the measurements by the Planck Collaboration. This is a new alternative approach that does not depend on the standard ΛCDM model and its constraints. Our analysis shows that the tension is due to a geometric mismatch in the comparison of the measurements which is equal to the temporal diameter of the surface of last scattering. Since the calculated values are essentially identical to the corresponding measured values, we conclude that the non-congruency of the ending point of the Riess et al. measurement and the starting point of the Planck Collaboration measurement, on the surface of last scattering, is the source of tension in the measurements. Further, the surprising consistency of the calculated values of the Hubble constant with the corresponding measured values confirms both the extreme fidelity of the measurements and the validity of the proposed approach.
