Skip to main content
Physics

Return to Answer

added 19 characters in body
Source Link
Andrew
Andrew
  • 55.5k
  • 4
  • 91
  • 172

There isn't really such a thing as "the" velocity of expansion. Perhaps you have in mind "the velocity at which galaxies recede from us." However, the apparent velocity of galaxies moving away from us due to the expansion of the Universe depends on how far away they are, via Hubble's law \begin{equation} v = H_0 d \end{equation} where $v$ is the recessional velocity we observe, $H_0$ is the Hubble constant, and $d$ is the distance. (As a warning, this law is only valid when $v\ll c$, where $c$ is the speed of light, or in other words for galaxies that are not "too far.")

However, $H_0$ -- the Hubble "constant" -- is a good measure of the expansion rate of the Universe. It is related to the scale factor $a(t)$ via \begin{equation} H = \frac{\dot{a}}{a} \end{equation} where antwo unbound objects (unboundlike two galaxy clusters) object that has lengthare separated by a distance $L$$d$ at time $t_1$ will have a lengthbe separated by $a(t_2)/a(t_1) \times L$$a(t_2)/a(t_1) \times d$ at time $t_2$. So, $H$ measures how fast the scale factor is changing with time, and is therefore perhaps a more refined notion than "expansion velocity" for the question you are getting at. The Hubble constant $H_0$ corresponds to the value of the Hubble parameter we observe today, but the Hubble parameter has evolved throughout the Universe's history according to the Friedmann equation (generally it used to be larger and has gotten smaller over time).

The second part of your question is about "the" beginning of the dark energy era. In fact there is not a precise moment in time where we can say that "the dark energy era" starts. Loosely speaking, the "radiation era" occurs when the energy density in radiation is much larger than the energy density in other forms of matter; the "matter era" occurs when the energy density in baryonic and dark matter is much larger than other forms of energy density; and the dark energy era would correspond to times when dark energy was dominant over other forms of energy density.

In fact, the energy density in dark energy and the energy density in baryonic and dark matter are approximately equal today. The Universe's energy density budget is about $2/3$ dark energy and $1/3$ baryonic and dark matter (mostly dark matter). So we are not even really in "the dark energy era" today, but rather transitioning from the matter era to the dark energy era. (The fact that we happen to be living at a "special time" where the Universe is transitioning between two eras, instead of clearly in one or the other, is sometimes called "the coincidence problem.")

Therefore, I would argue that a more refined version of your question would be:

What is the approximate value of the Hubble parameter during the period of transition between the matter and dark energy eras?

In which case, the value of the Hubble constant is a decent approximate answer:

\begin{equation} H_0 \approx 70\ {\rm km\ s^{-1}\ Mpc^{-1}} \end{equation} This number is good to one significant figure. Partly this is because the Hubble parameter will evolve somewhat over the course of the transition. However, additionally there are multiple methods to measure the Hubble constant which achieve more decimal places, but these methods currently disagree with each other given their claimed uncertainties; this is known as the Hubble tension.

There isn't really such a thing as "the" velocity of expansion. Perhaps you have in mind "the velocity at which galaxies recede from us." However, the apparent velocity of galaxies moving away from us due to the expansion of the Universe depends on how far away they are, via Hubble's law \begin{equation} v = H_0 d \end{equation} where $v$ is the recessional velocity we observe, $H_0$ is the Hubble constant, and $d$ is the distance. (As a warning, this law is only valid when $v\ll c$, where $c$ is the speed of light, or in other words for galaxies that are not "too far.")

However, $H_0$ -- the Hubble "constant" -- is a good measure of the expansion rate of the Universe. It is related to the scale factor $a(t)$ via \begin{equation} H = \frac{\dot{a}}{a} \end{equation} where an (unbound) object that has length $L$ at time $t_1$ will have a length $a(t_2)/a(t_1) \times L$ at time $t_2$. So, $H$ measures how fast the scale factor is changing with time, and is therefore perhaps a more refined notion than "expansion velocity" for the question you are getting at. The Hubble constant $H_0$ corresponds to the value of the Hubble parameter we observe today, but the Hubble parameter has evolved throughout the Universe's history according to the Friedmann equation (generally it used to be larger and has gotten smaller over time).

The second part of your question is about "the" beginning of the dark energy era. In fact there is not a precise moment in time where we can say that "the dark energy era" starts. Loosely speaking, the "radiation era" occurs when the energy density in radiation is much larger than the energy density in other forms of matter; the "matter era" occurs when the energy density in baryonic and dark matter is much larger than other forms of energy density; and the dark energy era would correspond to times when dark energy was dominant over other forms of energy density.

In fact, the energy density in dark energy and the energy density in baryonic and dark matter are approximately equal today. The Universe's energy density budget is about $2/3$ dark energy and $1/3$ baryonic and dark matter (mostly dark matter). So we are not even really in "the dark energy era" today, but rather transitioning from the matter era to the dark energy era. (The fact that we happen to be living at a "special time" where the Universe is transitioning between two eras, instead of clearly in one or the other, is sometimes called "the coincidence problem.")

Therefore, I would argue that a more refined version of your question would be:

What is the approximate value of the Hubble parameter during the period of transition between the matter and dark energy eras?

In which case, the value of the Hubble constant is a decent approximate answer:

\begin{equation} H_0 \approx 70\ {\rm km\ s^{-1}\ Mpc^{-1}} \end{equation} This number is good to one significant figure. Partly this is because the Hubble parameter will evolve somewhat over the course of the transition. However, additionally there are multiple methods to measure the Hubble constant which achieve more decimal places, but these methods currently disagree with each other given their claimed uncertainties; this is known as the Hubble tension.

There isn't really such a thing as "the" velocity of expansion. Perhaps you have in mind "the velocity at which galaxies recede from us." However, the apparent velocity of galaxies moving away from us due to the expansion of the Universe depends on how far away they are, via Hubble's law \begin{equation} v = H_0 d \end{equation} where $v$ is the recessional velocity we observe, $H_0$ is the Hubble constant, and $d$ is the distance. (As a warning, this law is only valid when $v\ll c$, where $c$ is the speed of light, or in other words for galaxies that are not "too far.")

However, $H_0$ -- the Hubble "constant" -- is a good measure of the expansion rate of the Universe. It is related to the scale factor $a(t)$ via \begin{equation} H = \frac{\dot{a}}{a} \end{equation} where two unbound objects (like two galaxy clusters) that are separated by a distance $d$ at time $t_1$ will be separated by $a(t_2)/a(t_1) \times d$ at time $t_2$. So, $H$ measures how fast the scale factor is changing with time, and is therefore perhaps a more refined notion than "expansion velocity" for the question you are getting at. The Hubble constant $H_0$ corresponds to the value of the Hubble parameter we observe today, but the Hubble parameter has evolved throughout the Universe's history according to the Friedmann equation (generally it used to be larger and has gotten smaller over time).

The second part of your question is about "the" beginning of the dark energy era. In fact there is not a precise moment in time where we can say that "the dark energy era" starts. Loosely speaking, the "radiation era" occurs when the energy density in radiation is much larger than the energy density in other forms of matter; the "matter era" occurs when the energy density in baryonic and dark matter is much larger than other forms of energy density; and the dark energy era would correspond to times when dark energy was dominant over other forms of energy density.

In fact, the energy density in dark energy and the energy density in baryonic and dark matter are approximately equal today. The Universe's energy density budget is about $2/3$ dark energy and $1/3$ baryonic and dark matter (mostly dark matter). So we are not even really in "the dark energy era" today, but rather transitioning from the matter era to the dark energy era. (The fact that we happen to be living at a "special time" where the Universe is transitioning between two eras, instead of clearly in one or the other, is sometimes called "the coincidence problem.")

Therefore, I would argue that a more refined version of your question would be:

What is the approximate value of the Hubble parameter during the period of transition between the matter and dark energy eras?

In which case, the value of the Hubble constant is a decent approximate answer:

\begin{equation} H_0 \approx 70\ {\rm km\ s^{-1}\ Mpc^{-1}} \end{equation} This number is good to one significant figure. Partly this is because the Hubble parameter will evolve somewhat over the course of the transition. However, additionally there are multiple methods to measure the Hubble constant which achieve more decimal places, but these methods currently disagree with each other given their claimed uncertainties; this is known as the Hubble tension.

Source Link
Andrew
Andrew
  • 55.5k
  • 4
  • 91
  • 172

There isn't really such a thing as "the" velocity of expansion. Perhaps you have in mind "the velocity at which galaxies recede from us." However, the apparent velocity of galaxies moving away from us due to the expansion of the Universe depends on how far away they are, via Hubble's law \begin{equation} v = H_0 d \end{equation} where $v$ is the recessional velocity we observe, $H_0$ is the Hubble constant, and $d$ is the distance. (As a warning, this law is only valid when $v\ll c$, where $c$ is the speed of light, or in other words for galaxies that are not "too far.")

However, $H_0$ -- the Hubble "constant" -- is a good measure of the expansion rate of the Universe. It is related to the scale factor $a(t)$ via \begin{equation} H = \frac{\dot{a}}{a} \end{equation} where an (unbound) object that has length $L$ at time $t_1$ will have a length $a(t_2)/a(t_1) \times L$ at time $t_2$. So, $H$ measures how fast the scale factor is changing with time, and is therefore perhaps a more refined notion than "expansion velocity" for the question you are getting at. The Hubble constant $H_0$ corresponds to the value of the Hubble parameter we observe today, but the Hubble parameter has evolved throughout the Universe's history according to the Friedmann equation (generally it used to be larger and has gotten smaller over time).

The second part of your question is about "the" beginning of the dark energy era. In fact there is not a precise moment in time where we can say that "the dark energy era" starts. Loosely speaking, the "radiation era" occurs when the energy density in radiation is much larger than the energy density in other forms of matter; the "matter era" occurs when the energy density in baryonic and dark matter is much larger than other forms of energy density; and the dark energy era would correspond to times when dark energy was dominant over other forms of energy density.

In fact, the energy density in dark energy and the energy density in baryonic and dark matter are approximately equal today. The Universe's energy density budget is about $2/3$ dark energy and $1/3$ baryonic and dark matter (mostly dark matter). So we are not even really in "the dark energy era" today, but rather transitioning from the matter era to the dark energy era. (The fact that we happen to be living at a "special time" where the Universe is transitioning between two eras, instead of clearly in one or the other, is sometimes called "the coincidence problem.")

Therefore, I would argue that a more refined version of your question would be:

What is the approximate value of the Hubble parameter during the period of transition between the matter and dark energy eras?

In which case, the value of the Hubble constant is a decent approximate answer:

\begin{equation} H_0 \approx 70\ {\rm km\ s^{-1}\ Mpc^{-1}} \end{equation} This number is good to one significant figure. Partly this is because the Hubble parameter will evolve somewhat over the course of the transition. However, additionally there are multiple methods to measure the Hubble constant which achieve more decimal places, but these methods currently disagree with each other given their claimed uncertainties; this is known as the Hubble tension.