Cosmological Cuts: Techniques & Implications

• Cosmological cuts are methods that extract discontinuities in primordial observables and factorize internal channels into lower-point building blocks.
• They employ techniques ranging from unitarity-based cutting rules and geometric residue bases to renormalization-group cutoffs, bridging theoretical analysis and data inference.
• This framework underpins applications in cosmological collider physics, branch-cut cosmology, and the regulation of multiverse and EFT models.

Searching arXiv for recent and foundational papers on cosmological cuts and related cosmological cutting rules. Cosmological cuts are a family of constructions rather than a single standardized notion. In the literature on primordial observables, the term usually denotes discontinuity relations for wavefunction coefficients or in-in correlators, derived from unitarity, causality, and the analytic structure implied by Bunch–Davies initial conditions; in this sense, a cut isolates an internal channel and factorizes it into lower-point building blocks glued by power spectra, Wightman functions, or polarization sums (Goodhew et al., 2020, Melville et al., 2021, Goodhew et al., 2021). In other parts of cosmology, related terminology refers to renormalization-group cutoff identification in FLRW backgrounds (Chen et al., 2024), cutoff measures in eternal inflation (Noorbala et al., 2010, Vilenkin et al., 2019, Bousso et al., 2010), scale cuts in EFT-based data analysis (Chudaykin et al., 2024, Truttero et al., 9 Jun 2026), and branch-cut cosmology in a topological and thermodynamic sense (Pacheco et al., 2022).

1. Terminological scope

The literature uses the language of cuts, cutoffs, and branch cuts in several technically distinct ways.

Usage	Core object	Representative papers
Cosmological cutting rules	Discontinuities of wavefunction coefficients or correlators	(Melville et al., 2021, Goodhew et al., 2021, Agui-Salcedo et al., 2023, Ema et al., 2024)
Cut basis / cut geometry	Residues, cut tubings, relative twisted cohomology, GKZ reductions	(De et al., 2024, Glew et al., 15 Aug 2025, Grimm et al., 7 Mar 2025)
RG cutoff identification	Mapping $k$ to FLRW scales with running $G(k)$, $\Lambda(k)$	(Chen et al., 2024)
Multiverse cutoff measures	Regulating eternal inflation and assigning probabilities	(Noorbala et al., 2010, Vilenkin et al., 2019, Bousso et al., 2010)
Scale cuts in inference	Maximum wavenumber $k_{\max}$ in EFT-based surveys	(Chudaykin et al., 2024, Truttero et al., 9 Jun 2026)
Branch-cut cosmology	Topological transition replacing a singular beginning	(Pacheco et al., 2022)

A useful organizing distinction is between discontinuity cuts, which extract analytic information from cosmological observables, and regulating cutoffs, which define a scale, measure, or data domain. The same vocabulary appears across these settings, but the underlying mathematical objects are different.

2. Unitarity cuts for the wavefunction of the universe

In the wavefunction-based literature, the starting point is the late-time wavefunction expanded as

$\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$

or, equivalently, as an expansion in wavefunction coefficients $\psi_n$ that encode primordial correlators (Goodhew et al., 2021, Goodhew et al., 2020). The key claim is that unitary time evolution constrains the analytic structure of these coefficients in close analogy with the optical theorem for flat-space amplitudes.

The first systematic statement was the Cosmological Optical Theorem. For contact diagrams, it yields a Hermitian-analyticity relation of the form

$$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$

and for four-point exchange diagrams it relates $\psi_4$ to products of lower-point $\psi_3$ data sewn by the internal power spectrum $P_\sigma(s)$ (Goodhew et al., 2020). The same work also gives the relation between total-energy poles of cosmological correlators and flat-space amplitudes, and shows, for example, that any correlator with an odd number of conformally-coupled scalar fields and any number of massless scalar fields must vanish (Goodhew et al., 2020).

This framework was generalized into full cosmological cutting rules, where the discontinuity of a diagram is written as a sum over cuts of its internal lines. In the formulation of (Melville et al., 2021), the bulk-to-bulk propagator differs from the usual Feynman propagator by a boundary term,

$G(k)$0

and a cut internal line is replaced schematically by

$G(k)$1

This yields a master rule in which the discontinuity of a connected diagram is a sum over all nonempty cut sets, with each cut line turned into two external legs and a power-spectrum factor (Melville et al., 2021). The stated scope is broad: arbitrary interactions of fields of any mass and any spin, and a very general class of FLRW spacetimes with a Bunch–Davies vacuum (Melville et al., 2021).

3. Tree-level single cuts, loop decomposition, and collider signals

A more refined tree-level structure is the single-cut rule. Instead of summing over all cuts, one chooses a specific internal line and studies the discontinuity in that channel. The central relation derived in (Goodhew et al., 2021) is

$G(k)$2

with the cut line pushed to the boundary and converted into two external insertions. The derivation relies on Hermitian analyticity of bulk-to-boundary and bulk-to-bulk propagators and on the factorization

$G(k)$3

The result is stated for fields with a linear dispersion relation, any mass, any integer spin, arbitrary local interactions with any number of derivatives, and general FLRW backgrounds admitting a Bunch–Davies vacuum, including de Sitter, slow-roll inflation, power-law cosmologies, and resonant axion monodromy (Goodhew et al., 2021).

Loop-level factorization is organized by the Cosmological Tree Theorem. There, any Feynman-Witten loop diagram can be rewritten as a sum of tree-level diagrams with only momentum integrals over cut lines,

$G(k)$4

and the derivation uses the vanishing of a closed product of retarded propagators,

$G(k)$5

Within the same framework, equal-time correlators exhibit a KLN-like cancellation: total-energy branch points produced in the wavefunction by loop integration do not appear in the corresponding equal-time correlation functions (Agui-Salcedo et al., 2023).

At the level of equal-time in-in correlators in the Keldysh $G(k)$6 basis, the cutting rule takes a different but complementary form. Each diagram decomposes into fully retarded functions on either side of the cut and cut-propagators built purely from Wightman functions, with the proof relying on unitarity, locality, the causal structure of the in-in formalism, and microcausality (Ema et al., 2024). A major application is cosmological collider physics: under microcausality, the fully retarded subdiagrams are analytic in momenta, so non-local cosmological collider signals arise solely from cut-propagators. A practical consequence is that the conformal-time integrals factorize because the cut-propagators do not contain time-ordering $G(k)$7-functions (Ema et al., 2024).

A distinct but related collider-oriented formulation is the bulk-evolution cutting rule of (Tong et al., 2021). There the leading signal is extracted by rewriting a time-ordered integral as a factorized cut contribution plus a commutator remainder, then discarding the commutator piece at leading order because it carries no cosmological collider signal in the relevant momentum regime. This approach classifies collider signals into local and nonlocal pieces with different physical origins: the nonlocal part is tied to gravitational pair production and depends on $G(k)$8, while the local part is momentum-analytic and tied to resonant production and decay (Tong et al., 2021).

4. Correlator-level, non-Bunch–Davies, and spinning generalizations

The Bunch–Davies assumption is not the end of the story. For Bogoliubov initial states, the cutting rules persist but the discontinuity operation must be modified. For a Bogoliubov mode function

$G(k)$9

the massive case requires a shifted continuation,

$\Lambda(k)$0

which leads to the new discontinuity prescriptions $\Lambda(k)$1 and $\Lambda(k)$2 (Ghosh et al., 8 Feb 2025). The same paper states that the extension to arbitrary spin follows helicity by helicity, since each helicity mode obeys a scalar-like mode equation with its own sound speed. It also discusses far-past convergence of time integrals and introduces an adiabatic regulator $\Lambda(k)$3 to define the analytic continuation (Ghosh et al., 8 Feb 2025).

A second extension acts directly on Schwinger–Keldysh observables, rather than on wavefunction coefficients. In (Colipí-Marchant et al., 27 Dec 2025), the discontinuity of a cosmological correlator across an internal energy channel factorizes into lower-point correlators, but only after introducing barred correlators, special linear combinations of SK diagrams that are not themselves standalone observables. This is the correlator-level counterpart of the cosmological optical theorem. The paper verifies the resulting rules for cubic exchange, spatial derivative interactions, temporal derivative interactions, general tree chains, and a one-loop example in $\Lambda(k)$4 theory (Colipí-Marchant et al., 27 Dec 2025).

A third route lifts flat-space unitarity cuts into dS/EAdS by cosmological dressing. In that representation, the flat-space Cutkosky delta function

$\Lambda(k)$5

maps directly to a cosmological $\Lambda(k)$6 operation in the exchanged energy variable, yielding tree-level and one-loop cutting identities for conformally coupled scalars (Ansari et al., 13 Jan 2026). This gives a diagram-by-diagram explanation of why cosmological discontinuities mirror flat-space unitarity cuts after analytic continuation and dressing (Ansari et al., 13 Jan 2026).

For spinning observables, the Yang–Mills construction in de Sitter space makes the factorization especially explicit. A cut in channel $\Lambda(k)$7 obeys

$\Lambda(k)$8

with

$\Lambda(k)$9

For ray-like trees and one-loop $k_{\max}$0-gons, the maximal cuts reduce to scalar $k_{\max}$1 discontinuities dressed by ordered Yang–Mills numerators built from local gluing maps. Reconstruction through six points then splits the answer into a cut-detectable part from gluing and a cut-invisible completion fixed by current conservation and the flat-space limit (He et al., 24 Jun 2026).

5. Geometric, cohomological, and algorithmic cut bases

Another line of work treats cosmological cuts as a geometric organization of FRW integrals. In power-law FRW spacetime, wavefunction coefficients are written as twisted integrals over hyperplane arrangements. The full twisted cohomology is then larger than the space needed for physical differential equations. The paper (De et al., 2024) argues that the appropriate smaller space is the physical subspace selected by compatible sequential residues, and that the dual relative twisted cohomology is automatically organized by cuts: $k_{\max}$2 At tree level, the physical subspace is populated by forms associated to cuts whose residues factorize the integrand entirely into flat-space amplitudes (De et al., 2024). Concrete reductions are stated explicitly: for the 3-site chain, the full cohomology has $k_{\max}$3, but only a 16-dimensional physical subspace survives; the 4-site chain and 4-site star reduce from 213 and 312 classes to physical bases of dimension 64; the 1-loop 3-gon reduces from 99 to 50 (De et al., 2024).

The cut-basis construction of (Glew et al., 15 Aug 2025) sharpens this picture by labeling independent cuts with acyclic minors, equivalently decorated graphs with solid, broken, and oriented edges. Each basis element $k_{\max}$4 is a logarithmic form associated with a positive geometry $k_{\max}$5, and the residues of the physical FRW-form become canonical forms of graphical zonotopes,

$k_{\max}$6

The resulting differential equations are derived by relative twisted cohomology and intersection theory, with a diagonal intersection matrix for the cut basis. The paper’s central slogan is that the combinatorics of kinematic flow is the reverse of the flow of cuts, and that the differential equations decouple into $k_{\max}$7 sectors, one for each subset of broken edges (Glew et al., 15 Aug 2025).

A more algebraic reduction program recasts tree-level cosmological correlators as solutions of GKZ systems. When the GKZ system is reducible, one obtains reduction operators that generate algebraic relations between tubings. These include cut relations, factorization relations, and contraction relations, and substantially reduce the number of independent functions required to represent a correlator (Grimm et al., 7 Mar 2025). In this formulation, the correlator associated to a graph $k_{\max}$8 is written as a sum over complete tubings,

$k_{\max}$9

and the reduction operators act by removing a tube from a tubing and replacing it with derivatives on simpler sub-tubings (Grimm et al., 7 Mar 2025). This suggests that “cosmological cuts” can also be understood as an algebraic reduction principle, not only as a discontinuity operation.

6. Cutoffs as physical scales and measures

A different use of cut language appears in asymptotically safe FLRW cosmology. There the issue is how to identify the renormalization-group momentum cutoff $\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$0 with a cosmological scale when the couplings run,

$\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$1

and the modified Friedmann equation becomes

$\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$2

The criterion for a suitable identification is that it respect FLRW symmetry, satisfy the Bianchi consistency condition, reproduce the classical limit, and avoid spurious scales (Chen et al., 2024). The stated result is sharply conditional: for vanishing classical cosmological constant, $\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$3 is suitable; for non-vanishing classical cosmological constant, $\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$4 fails because $\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$5 introduces an independent scale $\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$6, so the cutoff must instead track the full scale content of the solution, schematically $\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$7 (Chen et al., 2024). The same work emphasizes that the choice $\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$8 breaks time-translation invariance and thereby introduces a new physical scale (Chen et al., 2024).

In eternal inflation, cutoff language refers to regulating infinities and defining probabilities. One critique holds that most global time cutoff measures violate basic probability identities for repeated local experiments because the relevant probabilities are computed on different sample spaces: past boundaries $\Psi [ \phi ] \propto \exp \left[ -\sum_{n=2}^{\infty} \int_{\bfk_1,..,\bfk_n}\frac{1}{n!} \psi_{ \bfk_1 ... \bfk_n } \phi_{\bfk_1} ... \phi_{\bfk_n} \right],$9, whole regions $\psi_n$0, and conditioned regions (Noorbala et al., 2010). The proposed alternative is “geocentric cosmology,” where the observer’s accessible region is finite and the measure problem is reformulated as an initial-state distribution $\psi_n$1 on the past boundary; if a spatial Markov property holds, this distribution is equivalent to a 3-dimensional Euclidean Lagrangian (Noorbala et al., 2010).

A constructive alternative is the 4-volume cutoff measure, defined by the 4-volume swept out per unit initial comoving volume,

$\psi_n$2

in locally FRW regions (Vilenkin et al., 2019). This measure is introduced because it remains monotonic even in contracting regions with $\psi_n$3, where the scale-factor cutoff is not well defined. Its predicted distribution for $\psi_n$4 is numerically close to the scale-factor result, with total probability for $\psi_n$5 about 8% instead of about 3%, and its curvature distribution is described as almost indistinguishable from the scale-factor prediction (Vilenkin et al., 2019).

A related literature studies geometric cutoff regions such as the causal patch, fat geodesic, and apparent horizon cutoff. For positive cosmological constant vacua, these measures are reported to favor the “double coincidence”

$\psi_n$6

with the characteristic scale related to the number of vacua in the landscape through $\psi_n$7 (Bousso et al., 2010). For negative cosmological constant vacua, the same work states that none of the three measures is successful at the stated level of generality (Bousso et al., 2010).

7. Scale cuts in inference and branch-cut cosmology

In large-scale-structure inference, scale cuts mean truncating the data vector at a maximum wavenumber $\psi_n$8 beyond which the EFT model is not trusted. This use of cut language is operational rather than analytic. The central warning of (Chudaykin et al., 2024) is that priors and scale cuts are not interchangeable: prior-volume effects can distort marginalized posteriors, but overoptimistic scale cuts create a genuine systematic bias from omitted two-loop corrections that does not vanish with larger data volume or better priors. The paper states a rough scaling

$\psi_n$9

and reports that a WC/D’Amico-style setup can overestimate $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$0 by over 5%, whereas the CLASS-PT-like EC3 setup gives a negligible or $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$1 bias in best-fit cosmological recovery (Chudaykin et al., 2024).

The same issue appears in forecast work for LSST $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$2pt analyses. There, a linear bias model is reported to remain unbiased for $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$3 and $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$4 only up to

$$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$5

while HEFT and a minimal-bias variant can be pushed to $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$6 for $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$7CDM parameters in the tested scenarios (Truttero et al., 9 Jun 2026). The same study emphasizes that higher-order bias can mimic baryonic suppression, but baryons cannot reproduce the full range of higher-order bias behaviour, and that a detection of $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$8 requires access to $$\psi_n'(k_a,\hat{k}_a\!\cdot\!\hat{k}_b) + \left[\psi_n'(-k_a-i\epsilon,\hat{k}_a\!\cdot\!\hat{k}_b)\right]^* =0,$$9 under the assumptions adopted იქ (Truttero et al., 9 Jun 2026). This use of scale cuts is therefore conceptually distinct from cosmological cutting rules: it regulates model validity in data analysis rather than factorizing singularities.

A final, wholly different usage is branch-cut cosmology. Here the branch cut is an analogy with complex analysis and Riemann sheets, used to describe a non-singular transition between contraction and expansion. The proposal is constrained by the Bekenstein bound,

$\psi_4$0

or, for the branch region,

$\psi_4$1

The branch-cut picture interprets the transition as a topological leap, wormhole-like region, or helix-shaped path around a branch point, and suggests a non-temporal beginning described through a Wick rotation in which the imaginary-time component is replaced by temperature (Pacheco et al., 2022). This suggests a radically different meaning of “cosmological cuts”: not a discontinuity operation and not a regulator, but a topological model of the primordial transition.

Across these literatures, “cosmological cuts” therefore names a set of non-equivalent but structurally related ideas: discontinuity and factorization rules for primordial observables, geometric residue bases for FRW integrals, RG and multiverse cutoffs, data-analysis scale cuts, and branch-cut models of cosmic origin. The dominant modern meaning is the unitarity-based factorization of cosmological wavefunctions and correlators, but the broader terminology remains heterogeneous.