Hubble Constant and Hubble Law

The constant of proportionality between the speed of a galaxy and its distance from us, as described by the Hubble Law. It measures the rate at which the universe is expanding.

The present-day value of the Hubble parameter. It measures the current rate of expansion of the universe.

A dimensionless parameter representing the uncertainty in the measured value of the Hubble constant. It ranges from 0.6 to 1, and it's used to express a range of possible values for cosmological parameters.

The relationship between the speed of a galaxy and its distance from us. It shows that galaxies are moving away from us, and the further away they are, the faster they're moving.

The distance to an object beyond which we cannot see any signal originating from it. This is because light from these objects would never reach us due to the expansion of the universe.

The maximum distance from which light emitted today can reach us in the future. It represents the observable universe.

The distance between two objects in a static universe, as measured at a specific moment in time. It's analogous to the distance between two points on a flat map.

The distance to an object as measured by its apparent luminosity. It can be different from proper distance due to the expansion of the universe.

The velocity of a galaxy can be described as the sum of its recession velocity due to the expansion of the universe and its peculiar velocity caused by its own motion relative to other galaxies.

For galaxies at very large distances (greater than 10 Mpc), the peculiar velocity becomes negligible compared to the recession velocity.

Measuring the distance to celestial objects is challenging, especially for galaxies beyond 1 Mpc. Standard candles, objects with known intrinsic brightness, are used to estimate distances.

Standard candles, like Cepheid variables and Type 1a supernovae, are used to determine distances in astronomy. However, they provide relative distances, not absolute values.

To determine the absolute distance to an object, the Hubble constant (H0) is needed. This constant relates a galaxy's recession velocity to its distance.

The Hubble law states that a galaxy's recession velocity is proportional to its distance. This relationship, however, doesn't provide the absolute value of the Hubble constant. It's like knowing the distance is proportional to speed, but not the exact speed.

The cosmic distance ladder is a method used to determine absolute distances in the Universe by using a chain of standard candles with known intrinsic brightness. It starts with nearby objects and gradually reaches out to more distant objects.

The Hubble constant, H0, is used to determine the age of the Universe. However, the age estimate is a rough one, as the exact value of the Hubble constant is still actively researched.

The age of the universe, calculated using the integral of the inverse of the Hubble parameter over time, from the initial moment to the present.

A universe that is not dominated by matter but has a significant contribution from a cosmological constant. This constant represents an anti-gravity component that causes the universe to expand at an accelerating rate.

A universe that is dominated by matter, meaning that the gravitational pull of matter is the primary factor in determining the rate of expansion.

A universe where the sum of the density parameters of matter and dark energy equals 1. This implies a flat geometry, where the influence of gravity is balanced by the expansion rate.

A universe where the curvature of spacetime is negative, implying that the expansion rate is faster than that of a flat universe. This leads to an open, unbounded geometry.

A universe where the curvature of spacetime is positive, indicating that the expansion rate is slower than that of a flat universe. This leads to a closed, bounded geometry.

The maximum distance that light could have travelled from the Big Bang to reach us today. It represents the edge of the observable universe.

The Robertson-Walker metric describes the expansion of the universe, and we can use it to derive the redshift of radiation properly.

Light emitted from a galaxy at a specific time (t1) will be redshifted when it reaches us at a later time (t2) due to the expansion of the universe. This redshift is a measure of the expansion between the two times.

The time interval (dte) between the emission of light from a galaxy and the reception of that light at a later time (dtr) is influenced by the expansion of the universe. This affects the redshift measurement.

The integral of the Robertson-Walker metric over time can be used to calculate the redshift of light, considering the expansion of the universe over the course of the journey.

The expression for the redshift can be written as the ratio of the time intervals (dte and dtr) divided by the scale factor (a).

The Robertson-Walker metric is a fundamental tool for understanding the expansion of the universe and its implications for the redshift of light.

Light from distant galaxies travels through an expanding universe, which stretches the wavelength of the light and causes it to appear redder. This redshift depends on the distance of the galaxy.

The redshift of radiation provides astronomers with valuable insights into the expansion of the universe, the distances to galaxies, and the age of the universe.

The distance a celestial object appears to be based on its luminosity, assuming the inverse square law holds.

The luminosity distance is directly proportional to the actual distance (r0) and the redshift (z). Distant objects appear further away due to the redshift, which reduces their apparent luminosity.

In a flat universe, the luminosity distance is equal to the proper distance multiplied by (1 + z). For nearby objects, the redshift is very small, so the luminosity distance is approximately equal to the proper distance.

In a closed universe, the luminosity distance is given by the equation: 1+z/√ksin(√kdp). This equation reflects how the curvature of space affects the apparent distance of objects.

In an open universe, distant objects appear closer than they actually are. This is the opposite effect of a closed universe.

Standard candles are celestial objects with known intrinsic brightness, allowing astronomers to estimate distances. However, they provide relative distances, not absolute values.

The Hubble constant (H0) relates a galaxy's recession velocity to its distance and is crucial for determining absolute distances in the universe.

The cosmic distance ladder is a method for calculating accurate distances in the universe. It uses a chain of standard candles with known intrinsic brightness, starting with nearby objects and gradually extending to more distant ones.

For objects very close to us (z << 1), the luminosity distance (dlum) is approximately equal to the physical separation (dp) between the observer and the object, multiplied by a factor that depends on the cosmological constant (k). This approximation is also valid for an open universe.

The angular diameter distance (ddiam) is the distance an object with a known physical size appears to be at, assuming Euclidean geometry. It tells us how big an object appears from our perspective, considering the expansion of the universe.

The angular diameter distance is calculated by dividing the object's physical extent (l) by the angle (dθ) it subtends in the sky.

For objects very close to us (z << 1), the angular diameter distance is roughly equal to the object's real distance (r0). In a flat universe, the angular diameter distance is similar to the luminosity distance.

Standard candles are objects with known intrinsic brightness, such as Type Ia supernovae. These celestial objects help us measure distances in the universe, as their brightness is independent of their location.

The luminosity distance can be used to measure cosmological parameters, such as the Hubble constant and the deceleration parameter, by comparing the observed brightness of standard candles with their intrinsic brightness.

Type Ia supernovae, a type of stellar explosion with a consistent peak brightness, serve as excellent standard candles in cosmology. Their brightness allows us to measure distances to very distant galaxies and study the expansion of the universe.

The expansion of the universe affects the way we perceive the size and brightness of distant objects. To accurately understand these effects, we need to consider the concept of luminosity distance and angular diameter distance.