Inflation from higher dimensions

Abstract

We derive the scalar potential in four spacetime dimensions from an eight-dimensional $(R+\gamma R^4-2\Lambda-F_4^2)$ gravity model in the presence of the 4-form $F_4$, with the (modified gravity) coupling constant $\gamma$ and the cosmological constant $\Lambda$, by using the flux compactification of four extra dimensions on a 4-sphere with the warp factor. The scalar potential depends upon two scalar fields: the scalaron and the 4-sphere volume modulus. We demonstrate that it gives rise to a viable description of cosmological inflation in the early Universe, with the scalaron playing the role of inflaton and the volume modulus to be (almost) stabilized at its minimum. We also speculate about a possibility of embedding our model in eight dimensions into a modified eight-dimensional supergavity that, in its turn, arises from a modified eleven-dimensional supergravity.Comment: 24 pages, 3 figures, Late

Starobinsky–Bel–Robinson Gravity

“…As was demonstrated in Refs. [4,5], it is only possible when n = D/2 and p = n. In particular, when D = 8, the modulus (radius) of the hidden four-sphere S 4 of extra dimensions can be stabilized, while the modified D = 8 gravity can be embedded into the modified D = 8 (Salam-Sezgin) gauged supergravity [6]. In turn, as was argued in Ref.…”

Starobinsky-Bel-Robinson gravity

“…In turn, as was argued in Ref. [5], the modified D = 8 supergravity may be derived by compactifying the modified 11-dimensional supergravity on a three-sphere S 3 . As a result, the Starobinsky action (1) may be derivable from the 11-dimensional supergravity modified by the term quartic in the scalar curvature and compactified on the product S 4 × S 3 of extra dimensions.…”

Analytic extensions of Starobinsky model of inflation

“…where only the first two terms are essential for the CMB observables [37]. The inflaton potential (3) can therefore be modified as…”