Cosmology and Gravitation

The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since. Still it is interesting to ask whether that basic structure can be altered or generalized. In the last decade Bender et al have shown that one of the fundamental assumptions of quantum mechanics, that operators are represented by Hermitian matrices, can to an extent be relaxed. In this theory, the parity (P) and time-reversal (T) operators play a role analogous to the Hermitian conjugate. Recently we have extended the realm of `PT quantum mechanics' to include systems that are odd under time-reversal (T^2 = - 1), in the interest of constructing the PT-analogue of the Dirac equation. We find that the fundamental representation of the Dirac equation, which describes relativistic fermions, remains unchanged in the generalization to the non-Hermitian theory. Higher dimensional representations, which ordinarily decouple into pairs of Dirac fermions in Hermitian quantum mechanics, here describe new types of particles with extremely compelling properties. Most notably we have constructed a toy model representing two generations of massless neutrinos that nonetheless undergo flavor oscillations; furthermore this model is Lorentz invariant and unitary in time. The Standard Model requires that the neutrino be massive in order to accomodate the observed flavor oscillations, thus this toy model represents a significant departure from Standard Model physics.

It is a prime interest to understand gravitational physics and to develop cosmological applications exploiting the next generation of surveys, scheduled to be launched in the near future, such as SDSS3, DES, XCS, JDEM or EUCLID. The future precision surveys are promising to resolve outstanding problems in modern physics. With the level of precision available in future surveys, we can use the high resolution maps expected to be gained from next-generation surveys to test the foundations of gravity and particle physics. The gravity known to us at solar system scales (GR: general relativity) is possibly challenged at cosmological scales. The measured cosmic acceleration that we have ascribed to the presence of dark energy (DE) could be a signal that GR is broken in some way.

Although the observational evidence for cosmological inflation is growing, the physical mechanism behind it is still unknown. In part this is because inflation probably occurred at energy scales many orders of magnitude higher than that at man-made or astrophysical particle accelerators. So how can we learn about inflation? How does it constrain microphysical theory? One approach to answering these questions is primarily theoretical: attempting to embed inflation in fundamental theories of quantum gravity, such as string theory. Another approach is primarily observational: looking for signatures left by light fields that existed during inflation, such as isocurvature fluctuations from the QCD-axion. In this talk I discuss work on these two approaches.

The problem of the quantum backreaction in expanding spaces is an old, as yet unresolved, question. In this talk I will consider the one-loop backreaction of a massless scalar which couples to the Ricci scalar in an expanding space with constant deceleration. I will show that the infrared divergences, which generically plague the one loop stress energy, can be removed by matching onto an earlier radiation era. An insignificant backreaction occurs, unless the coupling to the Ricci scalar is negative. Similar results hold for the graviton backreaction.

I will discuss the qualitative differences between the single-field and multifield cyclic universes, in particular the resulting global "phoenix" structure and its relation to dark energy. The multifield cyclic universe arises naturally from embedding the cyclic universe in supergravity and leads to distinct observational predictions regarding non-gaussian signatures in the CMB. I will present a simplified derivation of these predictions.

Thanks to the ongoing Planck mission, a new window will be opened on the properties of the primordial density field, the cosmological parameters, and the physics of reionization. Much of Planck's new leverage on these quantities will come from temperature measurements at small angular scales and from polarization measurements. These both depend on the details of cosmological hydrogen recombination; use of the CMB as a probe of energies greater than 10^16 GeV compels us to get the ~eV scale atomic physics right. One question that remains is how high in hydrogen principle quantum number we have to go to make sufficiently accurate predictions for Planck. Using sparse matrix methods to beat computational difficulties, I have modeled the influence of very high (up to and including n=200) excitation states of atomic hydrogen on the recombination history of the primordial plasma, resolving all angular momentum sub-states separately and including, for the first time, the effect of hydrogen quadrupole transitions. I will review the basic physics, explain the resulting plasma properties, discuss recombination histories, and close by discussing the effects on CMB observables.

Two possible explanations for the type SNe Ia supernovae observations are a nonlinear, underdense void embedded in a matter dominated Einstein-de Sitter spacetime or dark energy in the ?CDM model. Both of these alternatives are faced with Copernican fine-tuning problems. A case is made for the void scenario that avoids introducing undetected dark energy.

Underlying the standard cosmological model is the assumption that it is possible to coarse-grain the energy density of the Universe, and that the dynamical and optical properies of space-time should be well modelled by the result. However, even if the average coarse-grained geometry does have the same dynamical properties as the fine-grained system it is intended to imitate, there are good reasons to suspect that the optical properties may be different. To investigate this we consider a simple model of the Universe in which the matter content is in the form of uniformly distributed discrete islands, rather than a continuous fluid. It is found that in the appropriate limits the resulting large-scale dynamics of the model approach those of an FRW universe, while the optical properties do not. We find the angular diameter distance, luminosity distance and redshifts that would be measured by observers inside such a space-time, and use preliminary results to show that the effect on estimates of the cosmological constant can be of the order of 10%.

Weak gravitational lensing is a powerful probe of modifications of General Relativity on cosmological scales, since such modifications can affect both how matter produces gravitational potential wells and how photons move within these wells. I will discuss alternative theories of gravitation and how we may constrain such theories using weak lensing observables, including those that could be obtained with the balloon-borne High Altitude Lensing Observatory (HALO). I will also discuss the "parametrized-post-Friedmannian" approach for obtaining model-independent constraints, in which new parameters are introduced to characterize the departure from General Relativity on large scales.

Near the Planckian scales, quantum gravity is expected to drastically change the structure of spacetime, one feature of which may be noncomutativity of the coordinates. Based on the recent advances in quantum field theories on such noncommutative spaces, I will consider the fluctuations of inflaton and look for possible noncommutative corrections in the CMB. Anisotropy and non-gaussianity are the result. The resultant distribution is then compared with ACBAR, CBI and WMAP data to constrain the scale of noncommutativity parameter.