Challenges for String Cosmology

We critically assess the twin prospects of describing the observed universe in string theory, and using cosmological experiments to probe string theory. For the purposes of this short review, we focus on the limitations imposed by our incomplete understanding of string theory. After presenting an array of significant obstacles, we indicate a few areas that may admit theoretical progress in the near future.Comment: 18 pages; contribution to a focus issue on string cosmology for Classical and Quantum Gravit

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

Cosmology with clusters of galaxies

In this Chapter I review the role that galaxy clusters play as tools to constrain cosmological parameters. I will concentrate mostly on the application of the mass function of galaxy clusters, while other methods, such as that based on the baryon fraction, are covered by other Chapters of the book. Since most of the cosmological applications of galaxy clusters rely on precise measurements of their masses, a substantial part of my Lectures concentrates on the different methods that have been applied so far to weight galaxy clusters. I provide in Section 2 a short introduction to the basics of cosmic structure formation. In Section 3 I describe the Press--Schechter (PS) formalism to derive the cosmological mass function, then discussing extensions of the PS approach and the most recent calibrations from N--body simulations. In Section 4 I review the methods to build samples of galaxy clusters at different wavelengths. Section 5 is devoted to the discussion of different methods to derive cluster masses. In Section 6 I describe the cosmological constraints, which have been obtained so far by tracing the cluster mass function with a variety of methods. Finally, I describe in Section 7 the future perspectives for cosmology with galaxy clusters and the challenges for clusters to keep playing an important role in the era of precision cosmology.Comment: 49 pages, 19 figures, Lectures for 2005 Guillermo Haro Summer School on Clusters, to appear in "Lecture notes in Physics" (Springer