Cosmological Perturbations in Non-Commutative Inflation

We compute the spectrum of cosmological perturbations in a scenario in which inflation is driven by radiation in a non-commutative space-time. In this scenario, the non-commutativity of space and time leads to a modified dispersion relation for radiation with two branches, which allows for inflation. The initial conditions for the cosmological fluctuations are thermal. This is to be contrasted with the situation in models of inflation in which the accelerated expansion of space is driven by the potential energy of a scalar field, and in which the fluctuations are of quantum vacuum type. We find that, in the limit that the expansion of space is almost exponential, the spectrum of fluctuations is scale-invariant with a slight red tilt. The magnitude of the tilt is different from what is obtained in a usual inflationary model with the same expansion rate during the period of inflation. The amplitude also differs, and can easily be adjusted to agree with observations.Comment: 7 pages, 1 figur

The Measure for the Multiverse and the Probability for Inflation

We investigate the measure problem in the framework of inflationary cosmology. The measure of the history space is constructed and applied to inflation models. Using this measure, it is shown that the probability for the generalized single field slow roll inflation to last for $N$ e-folds is suppressed by a factor $\exp(-3N)$, and the probability for the generalized $n$-field slow roll inflation is suppressed by a much larger factor $\exp(-3nN)$. Some non-inflationary models such as the cyclic model do not suffer from this difficulty.Comment: 16 page

Noncommutative field gas driven inflation

We investigate early time inflationary scenarios in an Universe filled with a dilute noncommutative bosonic gas at high temperature. A noncommutative bosonic gas is a gas composed of bosonic scalar field with noncommutative field space on a commutative spacetime. Such noncommutative field theories was recently introduced as a generalization of quantum mechanics on a noncommutative spacetime. As key features of these theories are Lorentz invariance violation and CPT violation. In the present study we use a noncommutative bosonic field theory that besides the noncommutative parameter $\theta$ shows up a further parameter $\sigma$. This parameter $\sigma$ controls the range of the noncommutativity and acts as a regulator for the theory. Both parameters play a key role in the modified dispersion relations of the noncommutative bosonic field, leading to possible striking consequences for phenomenology. In this work we obtain an equation of state $p=\omega(\sigma,\theta;\beta)\rho$ for the noncommutative bosonic gas relating pressure $p$ and energy density $\rho$, in the limit of high temperature. We analyse possible behaviours for this gas parameters $\sigma$, $\theta$ and $\beta$, so that $-1\leq\omega<-1/3$, which is the region where the Universe enters an accelerated phase.Comment: Reference added. Version to appear in Journal of Cosmology and Astroparticle Physics - JCA

Is Noncommutative Eternal Inflation Possible?

We investigate the condition for eternal inflation to take place in the noncommutative spacetime. We find that the possibility for eternal inflation's happening is greatly suppressed in this case. If eternal inflation cannot happen in the low energy region where the noncommutativity is very weak (the UV region), it will never happen during the whole inflationary history. Based on these conclusions, we argue that an initial condition for eternal inflation is available from the property of spacetime noncommutativity.Comment: 14 pages, 2 figures, accepted by JCA

Hawking-Moss Tunneling in Noncommutative Eternal Inflation

The quantum behavior of noncommutative eternal inflation is quite different from the usual knowledge. Unlike the usual eternal inflation, the quantum fluctuation of noncommutative eternal inflation is suppressed by the Hubble parameter. Due to this, we need to reconsider many conceptions of eternal inflation. In this paper we study the Hawking-Moss tunneling in noncommutative eternal inflation using the stochastic approach. We obtain a brand-new form of the tunneling probability for this process and find that the Hawking-Moss tunneling is more unlikely to take place in the noncommutative case than in the usual one. We also conclude that the lifetime of a metastable de-Sitter (dS) vacuum in the noncommutative spacetime is longer than that in the commutative case.Comment: 12 pages, 1 figure, accepted by JCA

Perturbative instabilities in Horava gravity

We investigate the scalar and tensor perturbations in Horava gravity, with and without detailed balance, around a flat background. Once both types of perturbations are taken into account, it is revealed that the theory is plagued by ghost-like scalar instabilities in the range of parameters which would render it power-counting renormalizable, that cannot be overcome by simple tricks such as analytic continuation. Implementing a consistent flow between the UV and IR limits seems thus more challenging than initially presumed, regardless of whether the theory approaches General Relativity at low energies or not. Even in the phenomenologically viable parameter space, the tensor sector leads to additional potential problems, such as fine-tunings and super-luminal propagation.Comment: 21 pages, version published at Class. Quant. Gra