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Qmechanic ♦
Qmechanic ♦
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I'm studdingstudying the age of the universe for a universe dark energy dominated. Using Friedmann equation $$ \left( \frac{\dot{a}}{a} \right)^2 = H_0^2 \left[ \Omega_R \cdot a^{-4} + \Omega_{NR} \cdot a^{-3} + \Omega_k \cdot a^{-2} + \Omega_{\Lambda} \right] $$ with the conditions $\Omega_R=\Omega_{NR}=\Omega_k=0$, $\Omega_\Lambda=1$, I have found the following expression $$ \frac{\dot{a}}{a} = H_0 \quad \to \quad \frac{da}{a} =H_0 \cdot dt $$ If I integrate from the Big-Bang $(t=0, a(0)=0)$ to the present $(t=T, a(T)=1)$ $$ \int_0^1 \frac{da}{a} =H_0 \cdot \int_0^T dt $$ but I have a singularity in the first integral. Does it mean that is impossible to find a universe full made of dark energy from the Big-Bang?

I'm studding the age of the universe for a universe dark energy dominated. Using Friedmann equation $$ \left( \frac{\dot{a}}{a} \right)^2 = H_0^2 \left[ \Omega_R \cdot a^{-4} + \Omega_{NR} \cdot a^{-3} + \Omega_k \cdot a^{-2} + \Omega_{\Lambda} \right] $$ with the conditions $\Omega_R=\Omega_{NR}=\Omega_k=0$, $\Omega_\Lambda=1$, I have found the following expression $$ \frac{\dot{a}}{a} = H_0 \quad \to \quad \frac{da}{a} =H_0 \cdot dt $$ If I integrate from the Big-Bang $(t=0, a(0)=0)$ to the present $(t=T, a(T)=1)$ $$ \int_0^1 \frac{da}{a} =H_0 \cdot \int_0^T dt $$ but I have a singularity in the first integral. Does it mean that is impossible to find a universe full made of dark energy from the Big-Bang?

I'm studying the age of the universe for a universe dark energy dominated. Using Friedmann equation $$ \left( \frac{\dot{a}}{a} \right)^2 = H_0^2 \left[ \Omega_R \cdot a^{-4} + \Omega_{NR} \cdot a^{-3} + \Omega_k \cdot a^{-2} + \Omega_{\Lambda} \right] $$ with the conditions $\Omega_R=\Omega_{NR}=\Omega_k=0$, $\Omega_\Lambda=1$, I have found the following expression $$ \frac{\dot{a}}{a} = H_0 \quad \to \quad \frac{da}{a} =H_0 \cdot dt $$ If I integrate from the Big-Bang $(t=0, a(0)=0)$ to the present $(t=T, a(T)=1)$ $$ \int_0^1 \frac{da}{a} =H_0 \cdot \int_0^T dt $$ but I have a singularity in the first integral. Does it mean that is impossible to find a universe full made of dark energy from the Big-Bang?

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user239504
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Can dark energy dominate from the Big-Bang?

I'm studding the age of the universe for a universe dark energy dominated. Using Friedmann equation $$ \left( \frac{\dot{a}}{a} \right)^2 = H_0^2 \left[ \Omega_R \cdot a^{-4} + \Omega_{NR} \cdot a^{-3} + \Omega_k \cdot a^{-2} + \Omega_{\Lambda} \right] $$ with the conditions $\Omega_R=\Omega_{NR}=\Omega_k=0$, $\Omega_\Lambda=1$, I have found the following expression $$ \frac{\dot{a}}{a} = H_0 \quad \to \quad \frac{da}{a} =H_0 \cdot dt $$ If I integrate from the Big-Bang $(t=0, a(0)=0)$ to the present $(t=T, a(T)=1)$ $$ \int_0^1 \frac{da}{a} =H_0 \cdot \int_0^T dt $$ but I have a singularity in the first integral. Does it mean that is impossible to find a universe full made of dark energy from the Big-Bang?