Chaotic Inflation with Time-Variable Space Dimensions

Assuming the space dimension is not constant but decreases during the expansion of the Universe, we study chaotic inflation with the potential $m^2\phi^2/2$. Our investigations are based on a model Universe with variable space dimensions. We write down field equations in the slow-roll approximation, and define slow-roll parameters by assuming the number of space dimensions decreases continuously as the Universe expands. The dynamical character of the space dimension shifts the initial and final value of the inflaton field to larger values. We obtain an upper limit for the space dimension at the Planck length. This result is in agreement with previous works for the effective time variation of the Newtonian gravitational constant in a model Universe with variable space dimensions.Comment: 19 pages, To be published in Int.J.Mod.Phys.D. Minor changes to match accepted versio

The Strong Multifield Slowroll Condition and Spiral Inflation

We point out the existing confusions about the slowroll parameters and conditions for multifield inflation. If one requires the fields to roll down the gradient flow, we find that only articles adopting the Hubble slowroll expansion are on the right track, and a correct condition can be found in a recent book by Liddle and Lyth. We further analyze this condition and show that the gradient flow requirement is stronger than just asking for a slowly changing, quasi-de Sitter solution. Therefore it is possible to have a multifield slowroll model that does not follow the gradient flow. Consequently, it no longer requires the gradient to be small. It even bypasses the first slowroll condition and some related no-go theorems from string theory. We provide the "spiral inflation" as a generic blueprint of such inflation model and show that it relies on a monodromy locus---a common structure in string theory effective potentials.Comment: 12 pages, version 4, cosmetic changes recommended by referee, resubmitting to PR

Probability of Slowroll Inflation in the Multiverse

Slowroll after tunneling is a crucial step in one popular framework of the multiverse---false vacuum eternal inflation (FVEI). In a landscape with a large number of fields, we provide a heuristic estimation for its probability. We find that the chance to slowroll is exponentially suppressed, where the exponent comes from the number of fields. However, the relative probability to have more e-foldings is only mildly suppressed as $N_e^{-\alpha}$ with $\alpha\sim3$. Base on these two properties, we show that the FVEI picture is still self-consistent and may have a strong preference between different slowroll models.Comment: version 3, 21 pages, resubmit to PRD recommanded by refere

Observational constraints on the spectral index of the cosmological curvature perturbation

We evaluate the observational constraints on the spectral index $n$, in the context of the $\Lambda$CDM hypothesis which represents the simplest viable cosmology. We first take $n$ to be practically scale-independent. Ignoring reionization, we find at a nominal 2-$\sigma$ level $n\simeq 1.0 \pm 0.1$. If we make the more realisitic assumption that reionization occurs when a fraction $f\sim 10^{-5}$ to 1 of the matter has collapsed, the 2-$\sigma$ lower bound is unchanged while the 1-$\sigma$ bound rises slightly. These constraints are compared with the prediction of various inflation models. Then we investigate the two-parameter scale-dependent spectral index, predicted by running-mass inflation models, and find that present data allow significant scale-dependence of $n$, which occurs in a physically reasonable regime of parameter space.Comment: ReVTeX, 15 pages, 5 figures and 3 tables, uses epsf.sty Improved treatment of reionization and small bug fixed in the constant n case; more convenient parameterization and better treatment of the n dependence in the CMB anisotropy for the running mass case; conclusions basically unchanged; references adde

Generating the curvature perturbation at the end of inflation

The dominant contribution to the primordial curvature perturbation may be generated at the end of inflation. Taking the end of inflation to be sudden, formulas are presented for the spectrum, spectral tilt and non-gaussianity. They are evaluated for a minimal extension of the original hybrid inflation model.Comment: 5 pages. v3: as it will appear in JCA

Cosmological consequences of particle creation during inflation

Particle creation during inflation is considered. It could be important for species whose interaction is of gravitational strength or weaker. A complete but economical formalism is given for spin-zero and spin-half particles, and the particle abundance is estimated on the assumption that the particle mass in the early universe is of order the Hubble parameter $H$. It is roughly the same for both spins, and it is argued that the same estimate should hold for higher spin particles in particular the gravitino. The abundance is bigger than that from the usual particle collision mechanism if the inflationary energy scale is of order $10^{16} GeV$, but not if it is much lower.Comment: 17 pages, no Figure