Sign of Expansion Scalar in Expanding FLRW Universe

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Thread starter Onyx
Start date Sep 16, 2022
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Cosmology Expanding Expansion General relativity Metric tensor Scalar Sign Tensor calculus Universe

In summary: More precisely, the expansion scalar associated with the congruence of worldlines of comoving observers measures the rate of change of the volume of a ball of matter that contains a fixed number of comoving observers, with respect to those observers' proper time.But that's not what the trace of the extrinsic curvature is?No. The trace of the extrinsic curvature is the trace of the extrinsic curvature tensor of a spacelike surface of constant comoving coordinate time. The specific extrinsic curvature tensor in question will depend on the specific FRW model being used. The case ##a(t) = t## corresponds to the Milne universe, which is an

Sep 19, 2022

Onyx

PeterDonis said:

There is no "the" extrinsic curvature tensor. There are different ones for different choices of spacelike hypersurfaces. Typically defining a frame also defines a choice of spacelike hypersurfaces, but the hypersurfaces don't necessarily look very simple or have any direct physical meaning.

Oh. That's true there, there would be different ones.

<h2>1. What is the Sign of Expansion Scalar in an Expanding FLRW Universe?</h2><p>The expansion scalar, denoted as θ, is a measure of the rate at which the universe is expanding. In an expanding FLRW (Friedmann-Lemaître-Robertson-Walker) universe, the sign of the expansion scalar is positive, indicating that the universe is expanding. This is a key feature of the FLRW model, which is used to describe the large-scale structure of the universe.</p><h2>2. How is the Expansion Scalar Calculated?</h2><p>The expansion scalar is calculated using the Hubble parameter, denoted as H, which is a measure of the rate at which the universe is expanding at a particular point in time. The expansion scalar is given by the equation θ = 3H, where 3 is a constant value in the FLRW model.</p><h2>3. What Causes the Expansion Scalar to Change?</h2><p>The expansion scalar is affected by the density of matter and energy in the universe. As the universe expands, the density of matter and energy decreases, leading to a decrease in the expansion scalar. Additionally, the presence of dark energy, which is thought to be responsible for the accelerating expansion of the universe, also affects the value of the expansion scalar.</p><h2>4. How Does the Sign of the Expansion Scalar Relate to the Fate of the Universe?</h2><p>The sign of the expansion scalar is closely linked to the ultimate fate of the universe. A positive expansion scalar indicates that the universe is expanding, and if this expansion continues, the universe will continue to expand indefinitely. On the other hand, a negative expansion scalar would indicate that the universe is contracting, potentially leading to a collapse known as the "Big Crunch."</p><h2>5. Can the Expansion Scalar Be Measured?</h2><p>Yes, the expansion scalar can be measured using various observational techniques, such as measuring the redshift of distant galaxies and the cosmic microwave background radiation. These measurements can help scientists better understand the expansion rate and overall structure of the universe.</p>

1. What is the Sign of Expansion Scalar in an Expanding FLRW Universe?

The expansion scalar, denoted as θ, is a measure of the rate at which the universe is expanding. In an expanding FLRW (Friedmann-Lemaître-Robertson-Walker) universe, the sign of the expansion scalar is positive, indicating that the universe is expanding. This is a key feature of the FLRW model, which is used to describe the large-scale structure of the universe.

2. How is the Expansion Scalar Calculated?

The expansion scalar is calculated using the Hubble parameter, denoted as H, which is a measure of the rate at which the universe is expanding at a particular point in time. The expansion scalar is given by the equation θ = 3H, where 3 is a constant value in the FLRW model.

3. What Causes the Expansion Scalar to Change?

The expansion scalar is affected by the density of matter and energy in the universe. As the universe expands, the density of matter and energy decreases, leading to a decrease in the expansion scalar. Additionally, the presence of dark energy, which is thought to be responsible for the accelerating expansion of the universe, also affects the value of the expansion scalar.

4. How Does the Sign of the Expansion Scalar Relate to the Fate of the Universe?

The sign of the expansion scalar is closely linked to the ultimate fate of the universe. A positive expansion scalar indicates that the universe is expanding, and if this expansion continues, the universe will continue to expand indefinitely. On the other hand, a negative expansion scalar would indicate that the universe is contracting, potentially leading to a collapse known as the "Big Crunch."

5. Can the Expansion Scalar Be Measured?

Yes, the expansion scalar can be measured using various observational techniques, such as measuring the redshift of distant galaxies and the cosmic microwave background radiation. These measurements can help scientists better understand the expansion rate and overall structure of the universe.