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Quark Soup
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I have a function to calculate the Hubble parameter at a given redshift: $$H(z)=\sqrt{\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_{\Lambda}}$$ And I have another function to calculate the conformal time between two redshifts: $$\eta(z1,z0)=\int_{z1}^{z0}\frac{1}{H(z]}dz$$ So now I want to calculate the particle horizon at the time of recombination. I calculate $$D_{PH}=c\space \eta(z_{CMB},\infty )$$ Have I just calculated the particle horizon at $t_{CMB}$ as it would be measured today after the expansion (comoving), or have I calculated the particle horizon as it was at $z_{CMB}$? I want the actual (proper) particle horizon as measured by an observer 380,000 years after the big bang. Do I divide the value returned by the $\eta$ function by $z_{CMB}$?

Another question is: is it even valid to integrate between $z1$ and $z0$? The reference formula I have shows only integration from 0 (present time) to the given redshift.

I have a function to calculate the Hubble parameter at a given redshift: $$H(z)=\sqrt{\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_{\Lambda}}$$ And I have another function to calculate the conformal time between two redshifts: $$\eta(z1,z0)=\int_{z1}^{z0}\frac{1}{H(z]}dz$$ So now I want to calculate the particle horizon at the time of recombination. I calculate $$D_{PH}=c\space \eta(z_{CMB},\infty )$$ Have I just calculated the particle horizon at $t_{CMB}$ as it would be measured today after the expansion (comoving), or have I calculated the particle horizon as it was at $z_{CMB}$? I want the actual (proper) particle horizon as measured by an observer 380,000 years after the big bang. Do I divide the value returned by the $\eta$ function by $z_{CMB}$?

I have a function to calculate the Hubble parameter at a given redshift: $$H(z)=\sqrt{\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_{\Lambda}}$$ And I have another function to calculate the conformal time between two redshifts: $$\eta(z1,z0)=\int_{z1}^{z0}\frac{1}{H(z]}dz$$ So now I want to calculate the particle horizon at the time of recombination. I calculate $$D_{PH}=c\space \eta(z_{CMB},\infty )$$ Have I just calculated the particle horizon at $t_{CMB}$ as it would be measured today after the expansion (comoving), or have I calculated the particle horizon as it was at $z_{CMB}$? I want the actual (proper) particle horizon as measured by an observer 380,000 years after the big bang. Do I divide the value returned by the $\eta$ function by $z_{CMB}$?

Another question is: is it even valid to integrate between $z1$ and $z0$? The reference formula I have shows only integration from 0 (present time) to the given redshift.

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Quark Soup
Quark Soup
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I have a function to calculate the Hubble parameter at a given redshift: $$H(z)=\sqrt{\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_{\Lambda}}$$ And I have another function to calculate the conformal time at a given redshiftbetween two redshifts: $$\eta(z1,z0)=\int_{z1}^{z0}\frac{1}{H(z]}dz$$ So now I want to calculate the particle horizon at the time of recombination. I calculate $$D_{PH}=c\space \eta(z_{CMB},\infty )$$ Have I just calculated the particle horizon at $t_{CMB}$ as it has grown withwould be measured today after the expansion (comoving), or have I calculated the particle horizon as it was at $z_{CMB}$? I want the actual (proper) particle horizon as measured by an observer 380,000 years after the big bang. Do I divide the value returned by the $\eta$ function by $z_{CMB}$?

I have a function to calculate the Hubble parameter at a given redshift: $$H(z)=\sqrt{\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_{\Lambda}}$$ And I have another function to calculate the conformal time at a given redshift: $$\eta(z1,z0)=\int_{z1}^{z0}\frac{1}{H(z]}dz$$ So now I want to calculate the particle horizon at the time of recombination. I calculate $$D_{PH}=c\space \eta(z_{CMB},\infty )$$ Have I just calculated the particle horizon at $t_{CMB}$ as it has grown with the expansion, or have I calculated the particle horizon as it was at $z_{CMB}$? I want the actual (proper) particle horizon as measured by an observer 380,000 years after the big bang. Do I divide the value returned by the $\eta$ function by $z_{CMB}$?

I have a function to calculate the Hubble parameter at a given redshift: $$H(z)=\sqrt{\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_{\Lambda}}$$ And I have another function to calculate the conformal time between two redshifts: $$\eta(z1,z0)=\int_{z1}^{z0}\frac{1}{H(z]}dz$$ So now I want to calculate the particle horizon at the time of recombination. I calculate $$D_{PH}=c\space \eta(z_{CMB},\infty )$$ Have I just calculated the particle horizon at $t_{CMB}$ as it would be measured today after the expansion (comoving), or have I calculated the particle horizon as it was at $z_{CMB}$? I want the actual (proper) particle horizon as measured by an observer 380,000 years after the big bang. Do I divide the value returned by the $\eta$ function by $z_{CMB}$?

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Quark Soup
Quark Soup
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A question about conformal time

I have a function to calculate the Hubble parameter at a given redshift: $$H(z)=\sqrt{\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_{\Lambda}}$$ And I have another function to calculate the conformal time at a given redshift: $$\eta(z1,z0)=\int_{z1}^{z0}\frac{1}{H(z]}dz$$ So now I want to calculate the particle horizon at the time of recombination. I calculate $$D_{PH}=c\space \eta(z_{CMB},\infty )$$ Have I just calculated the particle horizon at $t_{CMB}$ as it has grown with the expansion, or have I calculated the particle horizon as it was at $z_{CMB}$? I want the actual (proper) particle horizon as measured by an observer 380,000 years after the big bang. Do I divide the value returned by the $\eta$ function by $z_{CMB}$?