Synchronizing the Consistency Relation

[2304.10559] Synchronizing the Consistency Relation Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Astrophysics > Cosmology and Nongalactic Astrophysics arXiv:2304.10559 (astro-ph) [Submitted on 20 Apr 2023 ( v1 ), last revised 16 Aug 2026 (this version, v3)] Title: Synchronizing the Consistency Relation Authors: Keisuke Inomata , Hayden Lee , Wayne Hu View a PDF of the paper titled Synchronizing the Consistency Relation, by Keisuke Inomata and 2 other authors View PDF HTML (experimental) Abstract: We study the $N$-point function of the density contrast to quadratic order in the squeezed limit during the matter-dominated (MD) and radiation-dominated (RD) eras in synchronous gauge. Since synchronous gauge follows the free-fall frame of observers, the equivalence principle dictates that in the gradient approximation for the long-wavelength mode there is only a single, manifestly time-independent consistency relation for the $N$-point function. This simple form is dictated by the initial mapping between synchronous and local coordinates, unlike Newtonian gauge and its correspondingly separate dilation and Newtonian consistency relations. Dynamical effects only appear at quadratic order in the squeezed limit and are again characterized by a change in the local background, also known as the separate universe approach. We show that for the 3-point function the compatibility between these squeezed-limit relations and second-order perturbation theory requires both the initial and dynamical contributions to match, as they do in single-field inflation. This clarifies the role of evolution or late-time projection effects in establishing the consistency relation for observable bispectra, which is especially important for radiation acoustic oscillations and for establishing consistency below the matter-radiation equality scale in the MD era. Defining an appropriate angle and time average of these oscillations is also important for making separate universe predictions of spatially varying local observables during the RD era, which can be useful for a wider range of cosmological predictions beyond $N$-point functions. Comments: 66 pages, 1 figure, v3: corrected many typos that do not change the conclusion Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) ; General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2304.10559 [astro-ph.CO] (or arXiv:2304.10559v3 [astro-ph.CO] for this version) https://doi.org/10.48550/arXiv.2304.10559 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Keisuke Inomata [ view email ] [v1] Thu, 20 Apr 2023 18:00:00 UTC (405 KB) [v2] Fri, 18 Aug 2023 01:03:03 UTC (405 KB) [v3] Sun, 16 Aug 2026 09:39:08 UTC (406 KB) Full-text links: Access Paper: View a PDF of the paper titled Synchronizing the Consistency Relation, by Keisuke Inomata and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: astro-ph.CO < prev | next > new | recent | 2023-04 Change to browse by: astro-ph gr-qc hep-ph hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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