Gauge-invariant Cosmological Perturbation Theory Research Articles

Gauge invariant perturbation theory via homotopy transfer

We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.

Manifestly gauge-invariant cosmological perturbation theory from full loop quantum gravity

We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the new cosmological perturbation theory of LQG, and various power spectrums are studied for scalar mode and tensor mode perturbations. Comparing these power spectrums with predictions from the classical theory demonstrate corrections in the ultra-long wavelength regime. These corrections are results from the lattice discretization in LQG. In addition, tensor mode perturbations at late time demonstrate the emergence of spin-2 gravitons as low energy excitations from LQG. The graviton has a modified dispersion relation and reduces to the standard graviton in the long wavelength limit.

Second-order cosmological perturbation theory and initial conditions forN-body simulations

We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the synchronous-comoving gauge, allows us to go beyond the Newtonian predictions and to calculate relativistic corrections to it. We use an Einstein--de Sitter model, including both growing and decaying modes in our solutions. The impact of our results should be assessed through the implementation of the featured displacement in cosmological $N$-body simulations.

Effects of non-linearities on magnetic field generation

Magnetic fields are present on all scales in the Universe. While we understand the processes which amplify the fields fairly well, we do not have a ``natural'' mechanism to generate the small initial seed fields. By using fully relativistic cosmological perturbation theory and going beyond the usual confines of linear theory we show analytically how magnetic fields are generated. This is the first analytical calculation of the magnetic field at second order, using gauge-invariant cosmological perturbation theory, and including all the source terms. To this end, we have rederived the full set of governing equations independently. Our results suggest that magnetic fields of the order of 10-30- 10-27 G can be generated (although this depends on the small scale cut-off of the integral), which is largely in agreement with previous results that relied upon numerical calculations. These fields are likely too small to act as the primordial seed fields for dynamo mechanisms.

Perturbations of matter fields in the second-order gauge-invariant cosmological perturbation theory

To show that the general framework of the second-order gauge-invariant perturbation theory developed by K. Nakamura [Prog. Theor. Phys. 110, 723 (2003); Prog. Theor. Phys. 113, 481 (2005)] is applicable to a wide class of cosmological situations, some formulas for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe, which is developed in Prog. Theor. Phys. 117, 17 (2007). We derive the formulas for the perturbations of the energy-momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a single scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing. Through these formulas, we may say that the decomposition formulas for the perturbations of any tensor field into gauge-invariant and gauge-variant parts, which are proposed in the above papers, are universal.

Gauge-invariant cosmological perturbation theory

The linear perturbation theory of Friedman universes is treated in a gauge-invariant manner (i.e., invariant under linearized coordinate transformations). After presenting some mathematical tools in Chapter 1, the perturbation equations are derived with the help of the 3+1 formalism of general relativity in Chapter 2. Bardeens perturbation theory [4] is thereby extended to the treatment of collisionless matter. In Chapter 3 we solve the perturbation equations for perfect fuids explicitely. The results are applied to the discussion of the Sachs-Wolfe effet and of the traditional baryonic scenario of galaxy formation. In Chapter 4 numerical solutions of the gauge invariant perturbation equations are presented for a universe consisting of collisionless particles of mass mx ≠ 0, massless neutrinos and radiation. In this scenarios the masses of the first objects to collapse are of the order of m³pl/m²x. Within the gauge-invariant treatment, the perturbation amplitudes exhibit no growth on scales which are larger than the present horison size.

Gauge-invariant cosmological perturbation theory with seeds.

Gauge-invariant cosmological perturbation theory is extended to handle perturbations induced by seeds. A calculation of the Sachs-Wolfe effect is presented. A second-order differential equation for the growth of density perturbations is derived and the perturbation of Liouville's equation for collisionless particles is also given. The results are illustrated by a simple analytic example of a single texture knot, where we calculate the induced perturbations of the energy of microwave photons, of baryonic matter, and of collisionless particles.