Speaker
Description
With our corrected cosmic red shift formula and Hubble-Hawking model of cosmology, we have developed direct relations for fitting the adot and Hubble parameter. Hubble-Hawking model of current Hubble parameter can be expressed as, $\left ( H_{0} \right )_{HH} \cong 2.92 \times 10^{-19} \left ( 2.725 \right )^2\cong 66.9 \textrm{ km/sec/Mpc}$. If $z_{new}\cong \frac{E_{emitted}-E_{Observed}}{E_{emitted}}\cong \frac{\lambda_{Observed}-\lambda_{emitted.}} {\lambda_{Observed}}\cong \frac{z}{z+1}$ and $1+z \cong \frac{1}{1-z_{new}}$, Lambda model of $\left ( a_{dot} \right )_z \cong \left [ \frac{\sqrt{exp\left ( 0.5\left ( z_{new}+sinh\left ( z_{new} \right ) \right ) \right )\left ( 1+z \right )}}{1+2 z_{new}} \right ]\left ( H_0 \right )_\Lambda$. Thus Lambda model of Hubble parameter (HP) can be expressed as, $\left ( H_z \right )_\Lambda \cong \frac{\left ( a_{dot} \right )_z}{a}\cong \left ( 1+z \right )\left ( a_{dot} \right )_z\cong \left[ \frac{\sqrt{exp\left ( 0.5\left ( z_{new}+sinh\left ( z_{new} \right ) \right ) \right )}}{1+2 z_{new}} \right ]\left ( 1+z \right )^{\frac{3}{2}} \left ( H_0 \right )_\Lambda$. For example, if z=1100, obtained $\left ( a_{dot}\right )_{1100}\cong 1274.6\text{ km/sec/Mpc}$ and $\left ( H_{1100}\right )\cong \begin{matrix} 1403355.27 \end{matrix}\text{ km/sec/Mpc}$. Corresponding Lambda model values are, $\left ( a_{dot}\right )_{1100}\cong 1272.2\text{\:km/sec/Mpc}$ and $\left ( H_{1100}\right )\cong 1400680.00\text{\:km/sec/Mpc}$. See our two page PDF submitted by email for Table 1, Fig. 1 and https://cosmocalc.icrar.org/. With reference to our Hubble-Hawking model, $\left ( \frac{H_z}{H_0} \right )_{HH} \cong \frac{T_z^2}{T_0^2} \cong \left ( 1+z \right )^2$. Hence, $\frac{\left ( H_z \right )_\Lambda }{\left ( H_{z} \right )_{HH}}\cong \left[ \frac{\sqrt{\left ( 1-z_{new} \right )exp\left(0.5\left ( z_{new}+sinh\left( z_{new} \right ) \right ) \right )}}{1+2z_{new}}\right]$. One very interesting observation is that, Lambda model of cosmic age up to recombination can be expressed as, $\left ( t_z \right )_ \Lambda \cong \frac{\sqrt{1+z}}{\left ( H_{z} \right )_{HH}}\cong \left [ \left ( \left ( 1+z \right )^\frac{3}{2} \right )\left ( H_0 \right )_\Lambda \right]^{-1}$. Thus, $\left ( t_z H_z \right )_\Lambda \cong \left[ \frac{\sqrt{exp\left ( 0.5\left ( z_{new}+sinh\left ( z_{new} \right ) \right ) \right )}}{1+2 z_{new}} \right ] $. With further study and by considering the corrected cosmic red shift formula, true nature of cosmic expansion rate can be understood. It needs an unbiased review.
