Post-Newtonian Lagrangian Perturbation Approach to the Large-Scale Structure Formation

We formulate the Lagrangian perturbation theory to solve the non-linear dynamics of self-gravitating fluid within the framework of the post-Newtonian approximation in general relativity, using the (3+1) formalism. Our formulation coincides with Newtonian Lagrangian perturbation theory developed by Buchert for the scale much smaller than the horizon scale, and with the gauge invariant linearized theory in the longitudinal gauge conditions for the linear regime. These are achieved by using the gauge invariant quantities at the initial time when the linearized theory is valid enough. The post-Newtonian corrections in the solution of the trajectory field of fluid elements are calculated in the explicit forms. Thus our formulation allows us to investigate the evolution of the large-scale fluctuations involving relativistic corrections from the early regime such as the decoupling time of matter and radiation until today. As a result, we are able to show that naive Newtonian cosmology to the structure formation will be a good approximation even for the perturbations with scales not only inside but also beyond the present horizon scale in the longitudinal coordinates. Although the post-Newtonian corrections are small, it is shown that they have a growing transverse mode which is not present in Newtonian theory as well as in the gauge invariant linearized theory. Such post-Newtonian order effects might produce characteristic appearances of the large-scale structure formation, for example, through the observation of anisotropies of the cosmic microwave background radiation (CMB). Furthermore since our approach has a straightforward Newtonian limit, it will be also convenient for numerical implementation based on the presently available Newtonian simulation. ......Comment: 26 pages, accepted for publication in MNRA

Finite Grand Unified Theories and Inflation

A class of finite GUTs in curved spacetime is considered in connection with the cosmological inflation scenario. It is confirmed that the use of the running scalar-gravitational coupling constant in these models helps realizing a successful chaotic inflation. The analyses are made for some different sets of the models.Comment: 10 pages, latex, 4 figures, epic.sty and eepic.sty are use

Geometric Bremsstrahlung in the Early Universe

We discuss photon emission from particles decelerlated by the cosmic expansion. This can be interpretated as a kind of bremsstrahlung induced by the Universe geometry. In the high momentum limit its transition probability does not depend on detailed behavior of the expansion.Comment: 20 pages, No figure

Newtonian and Relativistic Cosmologies

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed, which allows for such nonlinearity at small scales. We propose a relatively straightforward "dictionary"---which is exact at the linearized level---that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our "ordering scheme" to determine the degree to which the resulting metric and matter distribution solve Einstein's equation. We find that Einstein's equation fails to hold at "order 1" at small scales and at "order $\epsilon$" at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein's equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.Comment: 35 pages; minor change