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How does one measure the curvature parameter $k$ in the FLRW metric? $$ds^2=-c^2 \mathrm dt^2+a^2(t)\left(\frac{\mathrm dr^2}{1-kr^2}+r^2 \mathrm d\theta^2+r^2\sin^2\theta \, \mathrm d\phi^2\right)$$ In particular, what is the convenient equation (involving $k$) that is/can be used to measure $k$?

EDIT I'm looking for an answer that will explain the measurement of curvature $k$ with the same clarity as the measurement of spring constant $\kappa$ from the one-dimensional simple harmonic equation $F=-\kappa x$ i.e., having measured the applied force $F$ (can be done with a spring balance may be) and the corresponding displacement $x$ (by a meter rule), one can measure $\kappa$.

How does one measure the curvature parameter $k$ in the FLRW metric? $$ds^2=-c^2dt^2+a^2(t)[\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2\sin^2\theta d\phi^2]$$ In particular, what is the convenient equation (involving $k$) that is/can be used to measure $k$?

EDIT I'm looking for an answer that will explain the measurement of curvature $k$ with the same clarity as the measurement of spring constant $\kappa$ from the one-dimensional simple harmonic equation $F=-\kappa x$ i.e., having measured the applied force $F$ (can be done with a spring balance may be) and the corresponding displacement $x$ (by a meter rule), one can measure $\kappa$. Similarly, if the equation involving curvature $k$ contains non-trivial physical quantities (such as the components of Riemann curvature tensor etc), I would like to know how each of them is measured.

How does one measure the curvature parameter $k$ in the FLRW metric? $$ds^2=-c^2dt^2+a^2(t)[\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2\sin^2\theta d\phi^2]$$ In particular, what is the convenient equation (involving $k$) that is/can be used to measure $k$?

EDIT I'm looking for an answer that will explain the measurement of curvature $k$ with the same clarity as the measurement of spring constant $\kappa$ from the one-dimensional simple harmonic equation $F=-\kappa x$ i.e., having measured the applied force $F$ (can be done with a spring balance may be) and the corresponding displacement $x$ (by a meter rule), one can measure $\kappa$. Similarly, if the equation involving curvature $k$ contains non-trivial physical quantities (such as the components of Riemann curvature tensor etc), I would like to know how each of them is measured.

How does one measure the curvature parameter $k$ in the FLRW metric? $$ds^2=-c^2 \mathrm dt^2+a^2(t)\left(\frac{\mathrm dr^2}{1-kr^2}+r^2 \mathrm d\theta^2+r^2\sin^2\theta \, \mathrm d\phi^2\right)$$ In particular, what is the convenient equation (involving $k$) that is/can be used to measure $k$?

EDIT I'm looking for an answer that will explain the measurement of curvature $k$ with the same clarity as the measurement of spring constant $\kappa$ from the one-dimensional simple harmonic equation $F=-\kappa x$ i.e., having measured the applied force $F$ (can be done with a spring balance may be) and the corresponding displacement $x$ (by a meter rule), one can measure $\kappa$.

How does one measure the curvature parameter $k$ in the FLRW metric? $$ds^2=-c^2dt^2+a^2(t)[\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2\sin^2\theta d\phi^2]$$ In particular, what is the convenient equation (involving $k$) that is/can be used to measure $k$?

EDIT I'm looking for an answer that will explain the measurement of curvature $k$ with the same clarity as the measurement of spring constant $\kappa$ from the one-dimensional simple harmonic equation $F=-\kappa x$ i.e., having measured $F$ and the corresponding displacement $x$, one can measure $\kappa$.

How does one measure the curvature parameter $k$ in the FLRW metric? $$ds^2=-c^2dt^2+a^2(t)[\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2\sin^2\theta d\phi^2]$$ In particular, what is the convenient equation (involving $k$) that is/can be used to measure $k$?

EDIT I'm looking for an answer that will explain the measurement of curvature $k$ with the same clarity as the measurement of spring constant $\kappa$ from the one-dimensional simple harmonic equation $F=-\kappa x$ i.e., having measured the applied force $F$ (can be done with a spring balance may be) and the corresponding displacement $x$ (by a meter rule), one can measure $\kappa$. Similarly, if the equation involving curvature $k$ contains non-trivial physical quantities (such as the components of Riemann curvature tensor etc), I would like to know how each of them is measured.