On loops in inflation

By L. Senatore, M. Zaldarriaga. 2009

280 citations recorded by the source corpus.

We study loop corrections to correlation functions of inflationary perturbations. Previous calculations have found that in certain theories the two-point function can have a logarithmic running of the form log(k/μ), where k is the wavenumber of the perturbation, and μ is the renormalization scale. We highlight that this result would have profound consequences for both eternal inflation and the predictivity of standard inflation. We find a different result in the same cases. We consider two sets of theories: one where the inflaton has a large cubic self-interaction and one where the inflaton interacts gravitationally with N massless spectator scalar fields. We find that there is a logarithmic running but of the form log(H/μ), where H is the Hubble constant during inflation. We find this result in three independent ways: by performing the calculation with a sharp cutoff in frequency-momentum space, in dimensional regularization and by the simple procedure of making the loop integral dimensionless. For the simplest of our theories we explicitly renormalize the correlation function proving that the divergencies can be reabsorbed and that the correlation function for super-horizon modes does not depend on time (once the tadpole terms have been properly taken into account). We prove the time-independence of the super-horizon correlation function in several additional ways: by doing the calculation of the correlation function at finite time using both the regularizations and by developing a formalism which expresses loop corrections directly in terms of renormalized quantities at each time. We find this last formalism particularly helpful to develop intuition which we then use to generalize our results to higher loops and different interactions. In particular we argue correlation functions have no long-term time dependence even if the spectator fields have a potential.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/20662af0736bcffdd9407fed378d0bf4e26aad54

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. L. Senatore
2. D. Baumann
3. M. Zaldarriaga
4. D. Green
5. Rafael A. Porto
6. E. Pajer
7. Yi Wang
8. Valentin Assassi

In Nuclear and High Energy Physics

1. D. Baumann
2. L. Senatore
3. Rafael A. Porto
4. M. Zaldarriaga
5. E. Pajer
6. D. Green
7. D. Seery
8. Valentin Assassi

Citations in the corpus

• Cosmological non-linearities as an effective fluid (2010, background): “In [42] the treatment and inclusion of these kind of terms has been developed in a different, but related context.”
• The effective field theory of cosmological large scale structures (2012, background): “The result is very similar to what is computed in the in-in formalism, for example when computing quantum corrections to inflationary correlation functions [27–29].”
• Infrared effects in inflationary correlation functions (2010, background): “We can regard this as a concrete example of the argument of Senatore and Zaldarriaga [61] discussed just before section 3.”
• The effective field theory of multifield inflation (2010, background): “In this way supersymmetry breaking is transmitted to the sector of the σ fields at leading order only through the effect that the curvature has on the loops [4].”
• The Lagrangian-space Effective Field Theory of large scale structures (2013, background): “See for example [36] for a detailed discussion on the context of Inflation.”
• An infinite set of Ward identities for adiabatic modes in cosmology (2013, background): “In particular, following [38] it would be interesting to generalize the analysis to include correlation functions with time or spatial derivatives acting on the short modes, as this can be useful for loop calculations [63–67].”
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times (2010, background): “” One might at first sight be puzzled by the appearance of large logarithms like we have found, given the analysis of [46], which appears to argue that large logarithms don’t arise in correct calculations, and in particular are forbidden by the symmetry a→ λa, x→ x/λ.”
• Late-time structure of the Bunch-Davies de Sitter wavefunction (2014, background): “See [18–34] for an incomplete list of references on the topic of infrared issues in de Sitter space.”
• The Cosmological Optical Theorem (2020, background): “That is part of the reason for the theoretical efforts made to provide general proofs for the immunity of curvature perturbations to such IR infinities (see [39, 40, 41, 42, 43, 44]).”
• Symmetries and loops in inflation (2012, background): “Essentially, this arises because radiative corrections induce a mass for any unprotected scalars, which then sources superhorizon evolution [8].”