Beyond Inflation: A Cyclic Universe Scenario

Inflation has been the leading early universe scenario for two decades, and has become an accepted element of the successful `cosmic concordance' model. However, there are many puzzling features of the resulting theory. It requires both high energy and low energy inflation, with energy densities differing by a hundred orders of magnitude. The questions of why the universe started out undergoing high energy inflation, and why it will end up in low energy inflation, are unanswered. Rather than resort to anthropic arguments, we have developed an alternative cosmology, the Cyclic universe, in which the universe exists in a very long-lived attractor state determined by the laws of physics. The model shares inflation's phenomenological successes without requiring an epoch of high energy inflation. Instead, the universe is made homogeneous and flat, and scale-invariant adiabatic perturbations are generated during an epoch of low energy acceleration like that seen today, but preceding the last big bang. Unlike inflation, the model requires low energy acceleration in order for a periodic attractor state to exist. The key challenge facing the scenario is that of passing through the cosmic singularity at t=0. Substantial progress has been made at the level of linearised gravity, which is reviewed here. The challenge of extending this to nonlinear gravity and string theory remains.Comment: 27 pages, 6 figures, talk given at the Nobel Symposium `String Theory and Cosmology', 2003. To appear, Physica Script

A Cyclic Model of the Universe

We propose a cosmological model in which the universe undergoes an endless sequence of cosmic epochs each beginning with a `bang' and ending in a `crunch.' The temperature and density are finite at each transition from crunch to bang. Instead of having an inflationary epoch, each cycle includes a period of slow accelerated expansion (as recently observed) followed by slow contraction. The combination produces the homogeneity, flatness, density fluctuations and energy needed to begin the next cycle.Comment: 15 pages, 1 figure, revisions as publishe

Channel Trading and Imperfect Competition: Good Trades and Bad Trades

We investigate the potential economic effects of spectrum trading amongst firms who require spectrum licences as part of their activities. Trading takes place within the technical interference constraints enforced by a regulator. The model accommodates a variety of markets and firms, as well as both chan- nel exchange and channel re-use (i.e. sharing across different markets). Our most detailed analytical results have focused on trade amongst oligopolists in a given (geographical) market. In this context, our results suggest that trade can enhance productive efficiency by placing licences in the hands of firms who value them most (i.e. low-cost firms). These are the ‘good trades’. However, there is a danger that this process may cause higher consumer prices which, in turn, could offset the welfare effects of lower cost production, the ‘bad trades’. An important outcome of our modelling is to make clear a role played by licences: they provide credible commitment mechanisms to restrict output.radio spectrum, spectrum trading, imperfect competition

Price Regulation, Investment and the Commitment Problem

We consider a dynamic model of price regulation with asymmetric information where strategic delegation is available to the regulator. Firms can sink non-contractible, cost-reducing investment but regulators cannot commit to future price levels. We fully characterise the perfect Bayesian equilibrium and show that, with incentive contracts and no delegation, under-investment occurs. We then show that delegation to a suitable regulator can both improve investment incentives and ameliorate the ratchet effect by credibly offering the firm future rent. Simulations indicate significant welfare gains from these two effects and that a wide range of regulatory preferences can achieve this result.under-investment, commitment, price regulation

Optimal Administered Incentive Pricing of Spectrum

Administered Incentive Pricing (AIP) of radio spectrum as advocated by Smith/NERA (1996) and recently assessed by Indepen (2003) envisages an incremental path towards e±cient pricing, with revealed and stated prefer- ence methods being used to reveal opportunity costs. We build on the latter to develop and optimal pricing scheme that allows for consumer surplus, in- terference constraints and their implications for productive e±ciency, revenue implications and market structure. We demonstrate the subtle relationship between the interference constraints and the pricing and channel use decisions of network operators. We proceed to show that the optimal AIP is higher in sectors where spectrum can be shared and that it acts as Ramsey tax across sectors of the economy, i.e., is inversely related to the elasticity of demand. As a special case of our model we examine optimal pricing where the regula- tor is constrained to ignore the revenue implications. Then optimal spectrum prices are lower and the relationship between prices and the ability to share spectrum is reversed.radio spectrum, spectrum pricing, administered incentive pricing