Open Access Library Journal How to cite this paper: Sofi, A.H., Akhoon, S.A., Rather, A.A. and Maini, A. (2015) Perturbative Quantum Gravity on de Sit- ter Spacetime. Open Access Library Journal, 2: e1422. http://dx.doi.org/10.4236/oalib.1101422 Perturbative Quantum Gravity on de Sitter Spacetime Ashaq Hussain Sofi 1 , Shabir Ahmad Akhoon 1 , Asloob Ahmad Rather 2 , Anil Maini 3 1 Department of Physics, National Institute of Technology, Srinagar, India 2 Department of Physics, Aligarh Muslim University, Aligarh, India 3 Department of Applied Sciences, College of Engineering and Technology, BGSB University, Rajouri, India Email: shifs237@gmail.com Received 24 March 2015; accepted 9 April 2015; published 13 April 2015 Copyright © 2015 by authors and OALib. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract We will analyse perturbative quantum gravity on de Sitter spacetime. We propose a new type of inner product for modes on de Sitter spacetime. This inner product is used to mode decompose perturbations of the metric on de Sitter spacetime. Using this inner product, it is possible to calcu- late the two-point function for perturbative quantum gravity on de Sitter spacetime. This two- point function will be written in terms of a mode sum for various modes on de Sitter spacetime. Keywords Perturbative Quantum Gravity, de Sitter Spacetime Subject Areas: Applied Physics, Modern Physics 1. Introduction Quantum field theory has been one of the greatest scientific achievements of the last centenary. The perturbative quantum theory has led to many important developments in high energy physics and condensed matter physics. These can include things like ghost condensation which causes the breaking of Lorentz symmetry [1]. It has also been used for analyzing the BRST and anti-BRST symmetries [2]. Most quantum field theories that are used in high energy physics are, gauge theories. Gravity can also be considered as a gauge theory of coordinate trans- formations [3]-[20]. As not all the degrees of freedom, in a theory with gauge symmetry are physical, so it such theories cannot be quantized without fixing a gauge. A gauge is fixed at the quantum level by adding a new term to the original action. This new term is called a gauge fixing term. However, apart from the gauge fixing term, we also need to add a ghost term to the original action. This ensures that the theory unitary to all orders in the perturbation theory. This term is called the ghost term. This term is composed of ghosts fields, which are not physical fields. But it is important to include these fields into the calculation to keep the theory unitarity