IMPERIAL/TP/2019/TM/03 Scalar correlation functions in de Sitter space from the stochastic spectral expansion Tommi Markkanena;b , Arttu Rajantiea , Stephen Stopyrac and Tommi Tenkanend aDepartment of Physics, Imperial College London, Blackett Laboratory, London, SW7 2AZ, United Kingdom bLaboratory of High Energy and Computational Physics, National Institute of Chemical Physics and Biophysics, R¨avala pst. 10, Tallinn, 10143, Estonia cDepartment of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT, United Kingdom dDepartment of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, United States of America E-mail:
[email protected], tommi.markkanen@kbfi.ee,
[email protected],
[email protected],
[email protected] Abstract. We consider light scalar fields during inflation and show how the stochastic spec- tral expansion method can be used to calculate two-point correlation functions of an arbitrary local function of the field in de Sitter space. In particular, we use this approach for a massive scalar field with quartic self-interactions to calculate the fluctuation spectrum of the density contrast and compare it to other approximations. We find that neither Gaussian nor linear arXiv:1904.11917v2 [gr-qc] 1 Aug 2019 approximations accurately reproduce the power spectrum, and in fact always overestimate it. For example, for a scalar field with only a quartic term in the potential, V = λφ4=4, we find a blue spectrum with spectral index n 1 = 0:579pλ. − Contents 1 Introduction1 2 The stochastic approach2 2.1