Cosmological Dressing Rules (2503.10598v1)

Abstract: The basic observables in cosmology are known as in-in correlators. Recent calculations have revealed that in-in correlators in four dimensional de Sitter space exhibit hidden simplicity stemming from a close relation to scattering amplitudes in flat space. In this paper we explain how to make this property manifest by dressing flat space Feynman diagrams with certain auxiliary propagators. These dressing rules hold for any order in perturbation theory and can be derived for a broad range of scalar theories, including those with infrared divergences. In the latter case we show that they reproduce the same infrared divergences predicted by the Schwinger-Keldysh formalism.

Cosmological Dressing Rules: An Analysis

In the field of theoretical cosmology, understanding the fundamental observables is crucial for delineating the universe's blueprint during its early stages, particularly during inflation. Of particular interest are in-in correlators within de Sitter (dS) space—termed due to their basis as initial state correlation functions that do not rely on asymptotic state definitions. The intricate paper titled "Cosmological Dressing Rules" endeavors to simplify the computation of these correlators by leveraging an intriguing relation to scattering amplitudes in flat space.

Methodology and Framework

The paper begins by highlighting the complexity of calculating correlation functions in curved spacetimes like dS due to the lack of Poincaré invariance—a linchpin for computation simplifications in flat space. Despite sharing the isometries with Minkowski space, dS spacetimes do not afford the straightforward momentum conservation seen in their flat space counterparts, primarily due to dS's non-conserved energies. This complexity necessitates a departure from conventional computation techniques.

In tackling these challenges, the researchers introduce dressing rules wherein flat-space Feynman diagrams are supplemented with auxiliary propagators, effectively bridging the gap between flat and curved space computations. These dressing rules, formulated at the integrand level, allow for the computation of in-in correlators to all perturbative orders and for scalar field theories with arbitrary polynomial interactions, including those grappling with infrared (IR) divergences.

Technical Insights

A salient feature of the dressing rules is their derivation from the shadow formalism—a method that reformulates cosmological correlators in Euclidean Anti-de Sitter (EAdS) space by introducing shadow fields. For conformally coupled $\phi^4$ theories, individual Feynman diagrams are endowed with auxiliary propagators described by an expression $\frac{k_{\rm ext}}{p^{2}+k_{\rm ext}^{2}}$, where $k_{\rm ext}$ and $p$ pertain to external and internal energies, respectively. Such constructs elucidate the newfound symmetries in the analytic structure of these correlators, contrary to their naive cosmological origin.

Intriguingly, this mechanism echoes similar attempts aimed at bootstrapping wavefunction coefficients via amplitude-inspired ideas. A key highlight involves tree-level correlators in conformally coupled $\phi^3$ theories which provide simpler expressions when mapped via these dressing rules as opposed to customary computations directly via the Schwinger-Keldysh formalism, often highlighted by dilogarithmic structures.

On the Massless Case

A significant portion addresses massless scalar theories, known for challenging IR divergence management. Rather than relying solely on standalone cutoffs, the paper posits the use of dimensional regularization to introduce a nuanced regularization scheme for extracting correlators systematically. Remarkably, these adjustments maintain a fidelity to the underlying de Sitter symmetry, propelling a coherent framework for extracting renormalized cosmological correlators.

Implications and Future Directions

The implications of this research are multifaceted. Practically, it opens up new avenues for computational simplifications for cosmological correlators, which play a vital role in interpreting the cosmic microwave background's nuanced perturbations. Theoretically, the paper suggests novel relations between cosmological wavefunctions and scattering amplitudes, potentially fostering a deeper understanding of the universe's initial conditions.

Such developments hint at further exploration into unifying cosmological correlators with established amplitude methodologies, such as the double-copy formalism or unitarity methods, which might benefit from these newfound symmetries. Moreover, the application of similar rules to spinning fields merits an exploration to advance our comprehension beyond scalar interactions.

In conclusion, "Cosmological Dressing Rules" presents a landmark step towards elucidating de Sitter cosmological correlators by capitalizing on their analogies with flat space dynamics, highlighted by methodological rigor and theoretical innovation. Going forward, the potential for these dressing rules to inform larger paradigms—be it inflationary theory or quantum gravity—remains a tantalizing prospect.