Towards a holographic theory of cosmology -- threads in a tapestry

In this Essay we address several fundamental issues in cosmology: What is the nature of dark energy and dark matter? Why is the dark sector so different from ordinary matter? Why is the effective cosmological constant non-zero but so incredibly small? What is the reason behind the emergence of a critical acceleration parameter of magnitude $10^{-8} cm/sec^2$ in galactic dynamics? We suggest that the holographic principle is the linchpin in a unified scheme to understand these various issues.Comment: 8 pages, LaTeX; This Essay, dedicated to the memory of Hendrik van Dam, received Honorable Mention in the 2013 Essay Competition of the Gravity Research Foundatio

Gravitational Theory with a Dynamical Time

A gravitational theory involving a vector field $\chi^{\mu}$, whose zero component has the properties of a dynamical time, is studied. The variation of the action with respect to $\chi^{\mu}$ gives the covariant conservation of an energy momentum tensor $T^{\mu \nu}_{(\chi)}$. Studying the theory in a background which has killing vectors and killing tensors we find appropriate shift symmetries of the field $\chi^{\mu}$ which lead to conservation laws. The energy momentum that is the source of gravity $T^{\mu \nu}_{(G)}$ is different but related to $T^{\mu \nu}_{(\chi)}$ and the covariant conservation of $T^{\mu \nu}_{(G)}$ determines in general the vector field $\chi^{\mu}$. When $T^{\mu \nu}_{(\chi)}$ is chosen to be proportional to the metric, the theory coincides with the Two Measures Theory, which has been studied before in relation to the Cosmological Constant Problem. When the matter model consists of point particles, or strings, the form of $T^{\mu \nu}_{(G)}$, solutions for $\chi^{\mu}$ are found. For the case of a string gas cosmology, we find that the Milne Universe can be a solution, where the gas of strings does not curve the spacetime since although $T^{\mu \nu}_{(\chi)} \neq 0$, $T^{\mu \nu}_{(G)}= 0$, as a model for the early universe, this solution is also free of the horizon problem. There may be also an application to the "time problem" of quantum cosmology.Comment: 21 pages, discussions extended, some more explicit proofs included, more references include