University of Connecticut

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PhD Dissertation Defense

Tuesday, July 12, 2022
10:00am – 12:00pm

Storrs Campus

Graduate Student Asanka Amarasinghe, Department of Physics, University of Connecticut

Cosmological Perturbation Theory in Standard Gravity and Conformal Gravity

Cosmological perturbations play a vital role in the study of the anisotropy of the cosmic microwave background radiation and in large-scale structure formation. The standard procedure for treating these perturbations is to decompose them into scalar (S), vector (V) and tensor (T) components, and assume (the decomposition theorem) that the three sectors independently satisfy the fluctuation equations. Ordinarily, this procedure is carried out in a convenient gauge in a background geometry with vanishing spatial 3-curvature. We have carried out a general SVT decomposition in a cosmology with an arbitrary spatial 3-curvature and expansion radius in a completely gauge invariant way that involves no choice of gauge at all. We have been able to prove the decomposition theorem in this general case, by first manipulating the fluctuation equations so that the various sectors separate out at a higher derivative level; and then finding appropriate boundary conditions under which the solving of these equations leads to the form that is required of the decomposition theorem. With these boundary conditions we thus justify the use of the decomposition theorem in the standard Einstein gravity-based cosmology. In addition, we establish the decomposition theorem in the alternate conformal gravity theory. In addition, using this same SVT decomposition we have derived a closed form expression for the fluctuation in the temperature of the cosmic microwave background for the arbitrary background with arbitrary spatial 3-curvature and arbitrary expansion radius, with the expression that we obtain being completely gauge invariant and with no choice of gauge being made. Interestingly, the expression that we obtain in the non-vanishing spatial 3-curvature case has no explicit dependence on the spatial 3-curvature. This meshes very well with the standard inflationary universe where there is no dependence on the spatial 3-curvature.

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Prof. P. Mannheim

Physics Department (primary), College of Liberal Arts and Sciences, UConn Master Calendar

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