On super-exponential inflation in a higher-dimensional theory of gravity with higher-derivative terms

Details On super-exponential inflation in a higher-dimensional theory of gravity with higher-derivative terms On super-exponential inflation in a higher-dimensional theory of gravity with higher-derivative terms

Nov 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988nuphb.309..513p&link_type=abstract

Nuclear Physics B, Volume 309, Issue 3, p. 513-532.

Physics

Nuclear Physics

17

Scientific paper

We consider super-exponential inflation in the early universe, for which H2/Hdot ≡ q >> 1, with particular reference to the higher-dimensional theory of Shafi and Wetterich, which is discussed in further detail. The Hubble parameter H is given by H2 ~ (8π/3mp2)V(φ), where the `inflaton' field φ is related to the radius of the internal space, and obeys the equation of motion 3Hφdot ~ -∂W/∂φ. The spectrum of density perturbations is given by δϱ/ϱ = (M/M0)-s, where s-1 ~ 3(q + 1); and X ≡ (-∂V/∂φ)/(∂W/∂φ). The parameters q and X are both positive constants, hence the need for two distinct potentials, which can be met in a higher-dimensional theory with higher-derivative terms R2 ≡ α1R2 + α2RABRAB + α3RABCDRABCD. Some fine-tuning of the parameters αi and/or of the cosmological constant Λ is always necessary in order to have super-exponential inflation. It is possible to obtain a spectrum of density perturbations with s >~ 1/20, which helps to give agreement with observations of the cosmic microwave background radiation at very large scales ~ 1000 Mpc. When R2 is proportional to the Euler number density, making the four-dimensional theory free of ghosts, then super-exponential inflation is impossible, but a phase of inflation with Hdot < 0 can still occur.

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