Analytical evaluation of cosmological correlation functions

Abstract

Using the Schwinger-Keldysh-formalism, reformulated in [1] as an effective field theory in Euclidean anti-de Sitter, we evaluate the one-loop cosmological four-point function of a conformally coupled interacting scalar field in de Sitter. Recasting the Witten cosmological correlator as flat space Feynman integrals, we evaluate the one-loop cosmological four-point functions in de Sitter space in terms of single-valued multiple polylogarithms. From it we derive anomalous dimensions and OPE coefficients of the dual conformal field theory at space-like, future infinity. In particular, we find an interesting degeneracy in the anomalous dimensions relating operators of neighboring spins.

Bootstrapping one-loop inflation correlators with the spectral decomposition

“…In comparison, general 1-loop massive exchanges remain challenging, and full analytical results are very rare in the literature. 1 Known nontrivial examples include the 1-loop bubble correction to the 2-point function from scalar fields of arbitrary mass in Euclidean dS [88], the 4-point function with 1-loop exchange of conformal scalar (m 2 = 2H 2 , H being the inflationary Hubble scale) in the position space [83]. 2 However, these examples contain no CC signals: the 2-point function is free from any oscillatory signal by the scale symmetry of the problem.…”

The cosmological tree theorem

“…The previous examples in subsection 2.2.1 follow immediately from the general theorem (2.60) with |I| = 1, 2 and 3 internal lines. 28 For instance, for the twovertex loop, we have two internal lines, labelled by I = {1, 2}, and therefore 3 cut diagrams, (where the convention is that q ′ a is the clockwise-most half-edge), In fact, comparing the two tree theorems, we see that,…”

“…On a cosmological (time-dependent) spacetime background, things are even worse: loop diagrams contain potentially divergent integrals both over momenta and over time. Since loop corrections can JHEP12(2023)076 play an important role in a wide variety of cosmological settings -including precise calculations of the primordial power spectrum [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and non-Gaussianity [19][20][21][22][23][24][25][26][27][28][29][30][31]; inflationary features that may seed primordial black holes [32][33][34][35][36][37][38][39][40][41] or produce a stochastic gravitational wave background [42][43][44][45][46]; de Sitter holography …”

On (spinor)-helicity and bosonization in AdS4/CFT3

“…In this case one can consider all the usual renormalizable theories in (A)dS4, e.g. φ 4[30][31][32][33][34] 3. It is a matter of opinion, of course, whether to call these theories simple given the complexity of the action, which is, nevertheless known explicitly thanks to the remarkable efforts in[35,36].…”