## What is Robertson Walker line element?

The Friedmann–Lemaître–Robertson–Walker (FLRW; /ˈfriːdmən ləˈmɛtrə /) metric is an exact solution of Einstein’s field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected.

What is metric in cosmology?

In cosmology, one must first have a definition of space. A metric is a mathematical expression describing points in space. The observation of the sky is done in a spherical geometry; hence a spherical coordinate system shall be used. The distance between two closely spaced points is given by − ds2=dr2+r2θ2+r2sin2θdϕ2.

### What is FRW model?

The Friedmann–Lemaître–Robertson–Walker models (often FRW-models) are class of models in cosmology. These are solutions to Einstein’s equations describing a spatially homogeneous and isotropic expanding or contracting spacetime. Hence these are solutions used as models in cosmology.

What does the cosmological constant represent?

Einstein first proposed the cosmological constant (not to be confused with the Hubble Constant) usually symbolized by the greek letter “lambda” (Λ), as a mathematical fix to the theory of general relativity. In its simplest form, general relativity predicted that the universe must either expand or contract.

## What is de Sitter spacetime?

de Sitter spacetime is the maximally symmetric spacetime of constant positive curva- ture. It is a solution of the vacuum Einstein equations with a positive cosmological constant. It is directly relevant for observation, in two (as fas as we know unrelated!)

How do you find the particle horizon?

The proper distance to the furthest observable point—the particle horizon— at time t is the horizon distance, sh(t). So shor(t)=2ct in the radiation-dominated era and shor(t)=3ct in the matter-dominated era. Notice that these distances are larger than ct, the distance travelled by a photon in time t.

### What causes metric expansion?

The space between objects shrinks or grows as the various geodesics converge or diverge. Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity.

How is luminosity distance calculated?

F = L 4π(a0r1)2(1 + z)2 , thus the luminosity distance to the object is dL = a0r1(1 + z).

## What is the conformal time?

Rather, the conformal time is the amount of time it would take a photon to travel from where we are located to the furthest observable distance, provided the universe ceased expanding.

What was Einstein’s cosmological constant and why did he propose it?

Figure 1: The cosmological constant was originally introduced by Einstein in 1917 as a repulsive force required to keep the Universe in static equilibrium. In modern cosmology it is the leading candidate for dark energy, the cause of the acceleration of the expansion of the universe.

### Do we live in de Sitter space?

And although we do not live in an anti-de Sitter universe (thank goodness for that, as we wouldn’t exist), the work also has implications for our understanding of everything from turbulence to the mysterious connections between theories of gravity and quantum mechanics.