Résultats de recherche pour « Cosmological correlators »

In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and useful tools from the qualitative theory of dynamical systems. They provide the theoretical basis for the qualitative study of concrete cosmological models. Chapters 1 and 2 are a review of well-known results. Chapters 3, 4, 5 and 6 are devoted to our main results. In these chapters are extended and settled in a substantially different, more strict mathematical language, several results obtained by one of us in arXiv:0812.1013 [gr-qc]; arXiv:1009.0689 [gr-qc]; arXiv:0904.1577[gr-qc]; and arXiv:0909.3571 [hep-th]. In chapter 6, we provide a different approach to the subject discussed in astro-ph/0503478. Additionally, we perform a Poincaré compactification process allowing to construct a global phase space containing all the cosmological information in both finite and infinite regions for all the models.

We provide a first principle definition of cosmological correlation functions for a large class of scalar toy models in arbitrary FRW cosmologies, in terms of novel geometries we name weighted cosmological polytopes. Each of these geometries encodes a universal rational integrand associated to a given Feynman graph. In this picture, all the possible ways of organising, and computing, cosmological correlators correspond to triangulations and subdivisions of the geometry, containing the in-in representation, the one in terms of wavefunction coefficients and many others. We also provide two novel contour integral representations, one connecting higher and lower loop correlators and the other one expressing any of them in terms of a building block. We study the boundary structure of these geometries allowing us to prove factorisation properties and Steinmann-like relations when single and sequential discontinuities are approached. We also show that correlators must satisfy novel vanishing conditions. As the weighted cosmological polytopes can be obtained as an orientation-changing operation onto a certain subdivision of the cosmological polytopes encoding the wavefunction of the Universe, this picture allows us to sharpen how the properties of cosmological correlators are inherited from the ones of the wavefunction. From a mathematical perspective, we also provide an in-depth characterisation of their adjoint surface.

We investigate cosmological correlators for conformally coupled $φ^4$ theory in four-dimensional de Sitter space. These \textit{in-in} correlators differ from scattering amplitudes for massless particles in flat space due to the spacelike structure of future infinity in de Sitter. They also require a regularization which preserves de Sitter-invariance, which makes the flat space limit subtle to define at loop-level. Nevertheless we find that up to two loops, the \textit{in-in} correlators are structurally simpler than the wave function and have the same transcendentality as flat space amplitudes. Moreover, we show that their loop integrands can be recast in terms of flat space integrands and can be derived from a novel recursion relation.

A bstract Cosmological correlation functions are significantly more complex than their flat-space analogues, such as tree-level scattering amplitudes. While these amplitudes have simple analytic structure and clear factorisation properties, cosmological correlators often feature branch cuts and lack neat expressions. In this paper, we develop off-shell perturbative methods to study and compute cosmological correlators. We show that such approach not only makes the origin of the correlator singularity structure and factorisation manifest, but also renders practical analytical computations more tractable. Using a spectral representation of massive cosmological propagators that encodes particle production through a suitable iϵ prescription, we remove the need to ever perform nested time integrals as they only appear in a factorised form. This approach explicitly shows that complex correlators are constructed by gluing lower-point off-shell correlators, while performing the spectral integral sets the exchanged particles on shell. Notably, in the complex mass plane instead of energy, computing spectral integrals amounts to collecting towers of poles as the simple building blocks are meromorphic functions. We demonstrate this by deriving a new, simple, and partially resummed representation for the four-point function of conformally coupled scalars mediated by tree-level massive scalar exchange in de Sitter. Additionally, we establish cosmological largest-time equations that relate different channels on in-in branches via analytic continuation, analogous to crossing symmetry in flat space. These universal relations provide simple consistency checks and suggest that dispersive methods hold promise for developing cosmological recursion relations, further connecting techniques from modern scattering amplitudes to cosmology.

A bstract Cosmological correlators encode rich information about physics at the Hubble scale and may exhibit characteristic oscillatory signals due to the exchange of massive particles. Although many 1-loop processes, especially those that break de Sitter (dS) boosts, can generate significant leading signals for various particle models in cosmological collider physics, the precise results for these correlators or their full signals remain unknown due to the lack of symmetry. In this work, we apply the method of partial Mellin-Barnes (PMB) representation to the calculation of cosmological correlators at the loop level. As a first step, we use the PMB representation to calculate four-point cosmological correlators with bubble topology. We find that both the nonlocal and local signals arise from the factorized part, validating the cutting rules proposed in previous work, and are free from ultraviolet (UV) divergence. Furthermore, the UV divergence originates solely from the background piece and can be manifestly canceled by introducing the appropriate counterterm, similar to the procedure in flat spacetime. We also demonstrate how to renormalize the 1-loop correlators in Mellin space. After a consistency check with known results for the covariant case, we provide new analytical results for the signals generated from a nontrivial dS-boost-breaking bubble.

We outline the nonlinear transformation in the path integral representation for partition function of O(N) symmetric oscillator systems bringing their duality to certain one-dimensional oscillators with unstable potential shapes. This duality transformation realizes the equivalence between spectra of a Hermitian and a non-Hermitian Hamiltonians. It is exploited to calculate exactly the spectra of quantum rotators . The zero-temperature limit is considered and the dual representation of n-point correlators of coordinate operators is obtained.

A bstract In this paper,we explore the cluster algebras for symbol letters or singularities of cosmological correlators in a conformally coupled scalar field theory. We show that the symbol letters for tree-level n -site ladder cosmological correlators are governed by A 2( n −1) cluster algebras. Additionally, we demonstrate that the symbol letters for one-loop bubble cosmological correlator are an union of two A 3 cluster algebras. The algebras relations of letters will provide an important tool to bootstrap analytic cosmological correlators.

This is the dawning of the age of precision cosmology, when all the important parameters will be established to one significant figure or better, within the cosmological model. In the age of accurate cosmology the model, which nowadays includes general relativity theory and the CDM model for structure formation, will be checked tightly enough to be established as a convincing approximation to reality. I comment on how we might make the transition. We already have some serious tests of gravity physics on the length and time scales of cosmology. The evidence for consistency with general relativity theory is still rough, but impressive, considering the enormous extrapolation from the empirical basis, and these probes of gravity physics will be considerably improved by work in progress on the cosmological tests. The CDM model has some impressive observational successes too, and some challenges, not least of which is that the model is based on a wonderfully optimistic view of the simplicity of physics in the dark sector. I present as a cautionary example a model for dark matter and dark energy that biases interpretations of cosmological observations that assume the CDM model. In short, cosmology has become an empirically rich subject with a well-motivated standard model, but it needs work to be established as generally accurate.

A bstract We propose a Mellin space approach to the evaluation of late-time momentum-space correlation functions of quantum fields in ( d + 1)-dimensional de Sitter space. The Mellin-Barnes representation makes manifest the analytic structure of late-time correlators and, more generally, provides a convenient general d framework for the study of conformal correlators in momentum space. In this work we focus on tree-level correlation functions of general scalars as a prototype, including n -point contact diagrams and 4-point exchanges. For generic scalars, both the contact and exchange diagrams are given by (generalised) Hypergeometric functions, which reduce to existing expressions available in the literature for d = 3 and external scalars which are either simultaneously conformally coupled or massless. This approach can also be used for the perturbative bulk evaluation of momentum space boundary correlators in ( d + 1)-dimensional anti-de Sitter space (Witten diagrams).