Inflation from $(R+\gamma R^n-2\Lambda)$ Gravity in Higher Dimensions

Understand

We propose a derivation of the inflaton scalar potential from the higher $(D)$ dimensional $(R+\gamma R^n-2\Lambda)$ gravity, with the new coupling constant $\gamma$ and the cosmological constant $\Lambda$.

• We assume that a compactification of extra dimensions happened before inflation, so that the inflaton scalar potential in four spacetime dimensions appears to be dependent upon the parameters $(\gamma,\Lambda ,D,n)$.
• We find that consistency requires $n=D/2$, while the dimension $D$ has to be a multiple of four.
• We calculate the potential for any $D$, and determine the values of $\gamma$ and $\Lambda$ from observations.