A Non-minimally coupled inflation — expansion

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The discussion centers on the role of the Ricci scalar (R) in the context of non-minimally coupled inflation. It clarifies that R does not measure the expansion of space but rather indicates the curvature of spacetime. The formula presented involves the inflaton field (Φ) and its interaction with the curvature, represented by the coupling constant (ξ). This distinction is crucial for understanding the dynamics of inflationary models in cosmology. Overall, the Ricci scalar is essential for describing spacetime geometry rather than expansion directly.
svenz706
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Hello,

In the Wikipedia article on "Inflaton" there appears the following formula:
##S=\int d^{4}x \sqrt{-g}[ \frac{1}{2}m^2_{P}R-\frac{1}{2}\partial^\mu\Phi\partial_{ \mu }\Phi-V(\Phi)-\frac{ 1 }{ 2}\xi R \Phi^]##

with
##\xi## representing the strength of the interaction between
R and ##\phi## which respectively relate to the curvature of space and the magnitude of the inflaton field.

Does ##R##, the Ricci scalar, represent a measure of the expansion of space?

https://arxiv.org/abs/1002.2995
 
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No. The Ricci scalar is a measure of the curvature of spacetime.
 
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