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DOE OSTI2025

Kinematic flow for cosmological loop integrands

Recently, an interesting pattern was found in the differential equations satisfied by the Feynman integrals describing tree-level correlators of conformally coupled scalars in a power-law FRW cosmology [1, 2]. It was proven that simple and universal graphical rules predict the equations for arbitrary graphs as a flow in kinematic space. In this note, we show that the same rules — with one small addition — also determine the differential equations for loop integrands. We explain that both the basis of master integrals and the singularities of the differential equations can be represented by tubings of marked graphs. An important novelty in the case of loops is that some basis functions can vanish, and we present a graphical rule to identify these vanishing functions. Taking this into account, we then demonstrate that the kinematic flow correctly predicts the differential equations for all loop integrands.

Cosmological models↗

DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗

DOE OSTI2025

Grand unification at the cosmological collider with chemical potential

We introduce a tree-level chemical potential mechanism for spin-1 particles within cosmological collider physics, allowing them to be detected in primordial non-Gaussianities for masses above the inflationary Hubble scale. We apply this mechanism to orbifold grand unification and the massive unification partners of the standard model gauge bosons. Our mechanism requires at least a pair of massive vector fields which are singlets of the standard model, a condition which is satisfied in the classic “trinification” scenario. Assuming that the gauge hierarchy problem is solved by supersymmetry, gauge coupling running points to unification partners at ~ 10$^{15}$ GeV. We show that, within high-scale inflation, chemical potential enhancement can lead to observably strong signals for trinification partners in future cosmological surveys.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

The no boundary density matrix

We discuss a no-boundary proposal for a subregion of the universe. In the classical approximation, this density matrix involves finding a specific classical solution of the equations of motion with no boundary. Beyond the usual no boundary condition at early times, we also have another no boundary condition in the region we trace out. We can find the prescription by starting from the usual Hartle-Hawking proposal for the wavefunction on a full slice and tracing out the unobserved region in the classical approximation. We discuss some specific subregions and compute the corresponding solutions. These geometries lead to phenomenologically unacceptable probabilities, as expected.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Physical instabilities and the phase of the Euclidean path integral

We compute the phase of the Euclidean gravity partition function on manifolds of the form S p × M q . We find that the total phase is equal to the phase in pure gravity on S p times an extra phase that arises from negative mass squared fields that we obtain when we perform a Kaluza-Klein reduction to S p . The latter can be matched to the phase expected for physical negative modes seen by a static path observer in dS p . In the case of S p × S q the answer can be interpreted in terms of a computation in the static patch of dS p or dS q . We also provide the phase when we have a product of many spheres. We clarify the procedure for determining the precise phase factor. We discuss some aspects of the interpretation of this phase.

Models of Quantum Gravity↗

DOE OSTI2025

The wavefunction of a quantum S 1 × S 2 universe

We study quantum gravity corrections to the no-boundary wavefunction describing a universe with spatial topology S 1 × S 2 . It has been suggested that quantum effects become increasingly important when the size of the circle is large relative to the sphere. In this paper, we confirm this claim by an explicit four-dimensional one-loop calculation of the gravitational path integral preparing such a state. In the process, we clarify some aspects of the gravitational path integral on complex spacetimes. These quantum corrections play a crucial role in ensuring that the norm of the wavefunction is naturally expressed in terms of a path integral over S 2 × S 2 at the classical level. We extend some of the analysis to more general spatial topologies, as well as to the inclusion of fermions.

cosmological models↗

DOE OSTI2025

Cosmohedra

It has been a long-standing challenge to find a geometric object underlying the cosmological wavefunction for Tr(ϕ 3 ) theory, generalizing associahedra and surfacehedra for scattering amplitudes. In this note, we describe a new class of polytopes — “cosmohedra” — that provide a natural solution to this problem. The faces of associahedra capture the combinatorics of non-overlapping chords of the momentum polygon, reflecting all partial factorizations of amplitudes. Cosmohedra are far richer — instead of non-overlapping chords, their faces capture the “russian doll” structure of non-overlapping subpolygons that determine the wavefunction. We show that cosmohedra are intimately related to associahedra, obtained by “blowing up” faces of the associahedron in a simple way. We give a full combinatorial description of cosmohedron faces and their factorization properties, and provide an explicit realization in terms of facet inequalities that further “shave” the facet inequalities of the associahedron. We also discuss a novel way for computing the wavefunction from cosmohedron geometry that extends the usual connection with polytope canonical forms. We illustrate cosmohedra with examples at tree-level and one loop; the close connection to surfacehedra suggests the generalization to all loop orders. Moving beyond the wavefunction, we briefly describe “cosmological correlahedra” for full correlators, which are one higher-dimensional polytopes, interpolating between associahedra and cosmohedra on opposite facets in an extra direction associated with the total energy. We speculate on how the existence of cosmohedra might suggest a “stringy” formulation for the cosmological wavefunction/correlators, generalizing the way in which the Minkowski sum decomposition of associahedra naturally extend particle to string amplitudes.

Scattering Amplitudes↗

DOE OSTI2024

Reviving QFT in ( 2 + 1 )-dimensional de Sitter spacetime

We consider a conformally coupled scalar quantum field theory (QFT) on ( 2 + 1 )-dimensional static Einstein universe R × S 2 and write down the free theory Hilbert space. We explain that this theory is secretly a QFT in ( 2 + 1 )-dimensional de Sitter space because all the quantum observables experience “quantum revivals,” which naturally restricts the timelike R to the appropriate de Sitter time range. Our construction circumvents the causal obstruction to formulating QFT in de Sitter due to event horizons. There are not any in static Einstein. The “unitary gauge” description of the theory is realized by the zonal harmonics P ℓ ( n ^ · n ^ ′ ) . We verify that interactions with conformally invariant external sources are mediated only by these modes. Hence these modes comprise the complete basis of the “bulk” theory. When the theory is cut off in the UV, the basis dimension scales as the Bekenstein-Hawking formula. Published by the American Physical Society 2024

D’Amico, Guido (ORCID:0000000281831214)↗

DOE OSTI2026

Causal horizons, geodesic completeness and stability in slow contraction cosmology

We show that cosmological models with a semi-infinite phase of slow contraction (ekpyrosis) possess a combination of properties that can address several fundamental problems in cosmology, otherwise faced in contracting de Sitter phases or standard big bang expansion. In particular, flat or open slow contraction admits a stable past attractor that asymptotes to Minkowski space and is past geodesically complete, as well as a stable, flat, homogeneous, and isotropic future attractor with negligible Weyl curvature (and, therefore, negligible gravitational entropy). In bouncing cosmologies, this contracting attractor is terminated by a smooth, non-singular bounce that transforms the attractor properties at the end of contraction into the initial conditions for the subsequent expanding phase. Cosmologies incorporating a slow contraction phase have no particle horizon and therefore avoid the causal horizon problem. The past Minkowski attractor also generates an initial spectrum of vacuum-like quantum fluctuations on all wavelengths. Moreover, because the averaged expansion rate along past-directed geodesics is non-positive, models incorporating a semi-infinite phase of slow contraction also evade the Borde–Guth–Vilenkin theorem. By contrast, contracting de Sitter space possesses a finite particle horizon and becomes unstable in the presence of scalar fields, matter, or radiation.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗

DOE OSTI2025

Overlapping qubits from non-isometric maps and de Sitter tensor networks

The emergence of a local effective theory from a more fundamental theory of quantum gravity with seemingly fewer degrees of freedom is a major puzzle of theoretical physics. A recent approach to this problem is to consider general features of the Hilbert space maps relating these theories. In this work, we construct approximately local observables, or overlapping qubits, from such non-isometric maps. We show that local processes in effective theories can be spoofed with a quantum system with fewer degrees of freedom, with deviations from actual locality identifiable as features of quantum gravity. For a concrete example, we construct two tensor network models of de Sitter space-time, demonstrating how exponential expansion and local physics can be spoofed for a long period before breaking down. Our results highlight the connection between overlapping qubits, Hilbert space dimension verification, degree-of-freedom counting in black holes, holography, and approximate locality in quantum gravity.

Quantum information↗

NASA NTRS1967

Differentiating unit orthogonal vectors in a Riemannian space that admits and N-tuply orthogonal system of hypersurfaces.

In a normal coordinate system { y 𝑎 } , the identity 𝜕 2 𝑥 𝑝 /∂y 𝑛 ∂y 𝑚 = ∂ 2 𝑥 𝑝 /∂y 𝑚 ∂y 𝑛 is used to obtain expressions, involving the components of the metric tensor in this coordinate system, for the derivatives of the unit tangent vectors to the parametric curves. An example is given for a normal coordinate system in the De Sitter universe.

Riemann space↗

DOE OSTI2025

The phase of the gravitational path integral

The gravitational path integral on S 2 × S 2 can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial S 1 × S 2 topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular S 2 × S D−2 , finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.

AdS-CFT correspondence↗

DOE OSTI2025

Dynamical dark energy from lattice quantum gravity

We study the behavior of the vacuum in Euclidean dynamical triangulations (EDT). Algorithmic improvements and better lattice spacing determinations allow us to test the properties of the emergent de Sitter geometries of our simulations to higher precision than previously possible. Although the agreement with de Sitter is good, the improved precision reveals deviations that can be interpreted as nontrivial vacuum dynamics, well described by a cosmological constant that runs with scale. The simulations show that the dominant running is quadratic and that the scale can be identified with the Hubble rate. Several key cross-checks support this picture, including consistent results across multiple lattice spacings and the fact that the null energy condition is not violated. The parameters of the running are fully determined by simulations, enabling predictions when extrapolated to the scales relevant for our Universe. This leads to a model for dark energy that is compatible with current observations, but which predicts deviations from the Standard Model of cosmology at the 𝒪⁡(10 −3 ) level in observables that could be tested with future improvements in precision measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1977

de Sitter's theory flattens Jupiter

The discrepancy between values of Jupiter's dynamic oblateness as measured by space probes and via 1971 beta Sco occultations is re-examined. The indicated correction to the Io ephemeris is compared to corrections proposed by Aksnes and Franklin (1975, 1976). It is found that the latter corrections reduce the above discrepancy to a marginal level.

Hubbard, W. B.↗

DOE OSTI2025

A microscopic realization of dS$_3$

We propose a precise duality between pure de Sitter quantum gravity in 2+1 2 + 1 dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arrive at a novel proposal for the quantum state of the universe at future infinity. We compute cosmological correlators of massive particles in the universe specified by this wavefunction. Integrating these correlators over the metric at future infinity yields gauge-invariant observables, which are identified with the string amplitudes of the complex Liouville string [S. Collier et al., arXiv: 2409.17246]. This establishes a direct connection between integrated cosmological correlators and the resolvents of the matrix integral dual to the complex Liouville string, thereby demonstrating one aspect of the dS _3 3 /matrix integral duality. The second aspect concerns the cosmological horizon of the dS static patch and the Gibbons-Hawking entropy it is conjectured to encode. We show that this entropy can be reproduced exactly by counting the entries of the matrix.

Collier, Scott (ORCID:0000000286476653)↗

NASA NTRS1978

On the formation and evolution of clumps of galaxies in an expanding universe

Results are derived for the development of phase-space clumps of mass points in a background spectrum of gravitational-potential fluctuations. The Vlasov equation and the pair correlation equation (in the weak coupling limit) are solved exactly in an Einstein-de Sitter cosmology, and the plasma-clumping theory is used to identify terms that yield important collective effects. Various astrophysical implications are discussed, including the formation of large-scale inhomogeneity and the enhanced generation of correlations in the distribution of galaxies.

Norman, C. A.↗

DOE OSTI2025

A species scale-driven breakdown of effective field theory in time-dependent string backgrounds

We present a novel way in which effective field theory (EFT) can break down in cosmological string backgrounds depending on the behavior of the quantum gravity cutoff in infinite distance limits, known as the species scale $Λ_s$. Namely, EFT can break down if the species scale $Λ_s$ falls off so rapidly as the Friedmann-Robertson-Walker (FRW) scale factor grows from some initial value $a_i$ to some final value $a_f$ that the physical momentum of an initial Hubble-sized perturbation $\sim H_i^{-1}$ grows to exceed the species scale. For EFT to remain valid, a new condition $H_i \frac{a_i}{a_f} \ll Λ_{s,f}$ must hold, which is distinct from Trans-Planckian conditions discussed in the literature. Using the universal relation $\frac{\nabla m}{m} \cdot \frac{\nabla Λ_s}{Λ_s} = \frac{1}{d-2}$ in the infinite distance limits of moduli space where $m$ is the mass scale of the lightest tower and $\nabla$ measures variations with respect to the canonical metric on moduli space, we show that spatially flat FRW solutions in the string landscape violate this condition or at best marginally satisfy it. However, we find that sufficiently large negative spatial curvature always avoids a breakdown. To avoid EFT breakdown, we derive an upper bound on the duration of quasi-de Sitter expansion that classically evolves to decelerated expansion. Our bound is proportional to the Trans-Planckian Censorship Conjecture (TCC) bound, with the advantage that it applies to any FRW solution in the string landscape. Finally, we distinguish EFT breakdown from TCC violation, the latter being a quantum gravity constraint rather than an EFT limitation. Perhaps our most surprising finding is that in any flat FRW solution that develops a weakly coupled string at future infinity the EFT inevitably breaks down.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗

DOE OSTI2025

Holographic Constraints on the String Landscape

We show that holography imposes strong and general constraints on scalar field potentials in the string landscape, determined by the asymptotic structure of the underlying spacetime. Applying these holographic consistency conditions, we identify broad classes of scalar potentials that are incompatible with a well-defined dual description. These include potentials with extended plateaus, excessively steep or shallow asymptotics, certain zero crossings, and specific alignments of stable AdS minima in moduli space. In particular, making the standard assumption that the CFT dual to a stable AdS vacuum must be realized as a worldvolume theory of a brane in string theory, we show that the brane selects an infinite-distance limit in moduli space where parametric scale separation is forbidden. Furthermore, the steepness and positivity of the potential are restricted in that infinite distance direction. We also find that requiring the validity of the effective theory in the future vacuum, a natural holographic criterion, automatically enforces the Trans-Planckian Censorship Conjecture (TCC) for classical cosmological solutions with positive potentials. Taken together, these constraints exclude the leading proposals to realize scale-separated AdS vacua and metastable de Sitter vacua in the string theory landscape such as DGKT and KKLT.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗