{"id":"dea8468c-7ff6-4326-bdd0-a7824ff5117e","arxiv_id":"2506.16943","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Adding an extra Euclidean boundary to the no-boundary de Sitter path integral defines a family of excited states whose holographic correlators are modified relative to the vacuum.","lead":"This paper proposes a way to define excited states in de Sitter space by adding an extra boundary to the no-boundary Euclidean path integral and fixing Dirichlet data there. It computes correlation functions for a scalar field in dS_{1+1} and shows they match the structure of a holographically dual conformal field theory with a source.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Excited-state construction rests on an unproven assumption that the extra Euclidean boundary defines a state satisfying gravitational constraints; if the Gauss/WdW constraints forbid it, the proposal is empty.","rationale":"The paper is best read as a proposal rather than a theorem. The free-field construction is coherent, and the explicit dS_{1+1} computation is a useful proof of principle. The weakest link is the step from a field-theoretic state on a fixed background to a state of the gravitational theory. Because the holographic dictionary (1.1) is a statement about quantum gravity, the new boundary condition must be legitimate under the gravitational constraints; the paper explicitly defers this to future work in Section 4, naming the Wheeler-DeWitt equation and the gravitational Gauss law. This is an externally valid concern rather than an internal inconsistency, and a concrete linearized-constraint computation would settle it. Therefore the reader's conditional verdict is appropriate, and I recommend no change to that verdict. The concern matches the reader's weakest-assumption identification.","tokens_in":15150,"tokens_out":19844,"duration_ms":219102,"concrete_test":"Evaluate the linearized gravitational constraints on the semiclassical state (2.5) in dS_{d+1}, say d=3: include linearized metric perturbations and the scalar field, compute the on-shell action including Gibbons-Hawking-York boundary terms, and check whether the wave functional is annihilated by the linearized Hamiltonian and momentum constraints for generic phi_b and finite tau_b. In parallel, compute the Brown-York stress tensor on Sigma_b and test the Israel junction conditions at Sigma_0; if the constraints force phi_b=0 or tau_b -> -infinity, the construction is not a valid excited-state family.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is eq. (2.5)-(2.8): the wave functional built from a Euclidean path integral on M^b_E with an extra boundary Sigma_b and Dirichlet data phi_b is declared to equal the CFT generating function. For this to be a state of quantum gravity, not just of a scalar field on a fixed background, the full configuration (metric plus scalar) must satisfy the gravitational constraints. The paper excludes gravity before Section 2.1 ('we exclude gravity from the current study') and fixes the dS metric throughout Section 3, so the computation cannot see whether the new boundary is compatible with the Hamiltonian and momentum constraints or the Gauss law. The authors themselves list the Wheeler-DeWitt equation and gravitational Gauss law as open questions in Section 4. If, as the cited [9,10] suggest, the dS linearized constraints admit only the Bunch-Davies vacuum, then arbitrary boundary data phi_b would be forbidden and the family (2.5) would not define physical states. The free-field dS_{1+1} correlators are self-consistent but do not test this.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a generalization of the Hartle-Hawking no-boundary proposal in de Sitter space. Instead of preparing the vacuum by a Euclidean path integral over a compact geometry with a single boundary, the authors introduce an additional compact boundary Σ_b in the Euclidean region and impose arbitrary Dirichlet data φ_b on it. The resulting wavefunctional Ψ'_φ_b(φ,T) is then identified, via Eq. (2.8), with the CFT generating function Z_CFT(J) on the future boundary, with φ_b playing the role of a source for a dual operator. In Section 2 the authors argue heuristically that this describes excited states, and in Section 3 they carry out an explicit free massive scalar computation in dS_{1+1} in the complementary series, obtaining a nonvanishing one-point function (3.20) and modified two-point function (3.18)-(3.19) in the small-hole limit τ_b → -∞. They also argue in Appendix B that these states are not α-vacua. Gravity is excluded from the analysis, and the gravitational constraints are left for future work.","tokens_in":15402,"tokens_out":6064,"duration_ms":65613,"significance":"If the proposal is correct, it would provide a concrete holographic dictionary for excited states in de Sitter space, extending the dS/CFT correspondence beyond the Euclidean vacuum and giving explicit, computable modifications to late-time cosmological correlators. The free-field computation in Section 3 is careful and self-contained, and the comparison with α-vacua in Appendix B is a useful falsifiable distinction. The main strength is that the paper gives explicit formulas rather than a purely formal proposal. However, the central equality (2.8) is assumed rather than derived, gravity is excluded from the outset, and the physical interpretation relies on a CFT dictionary that is not established independently. These issues are acknowledged by the authors but they are load-bearing for the claim that the construction defines physical excited states of de Sitter quantum gravity.","major_comments":[{"comment":"The central identification Ψ'_φ_b(φ,T) = Z_CFT(J) is posited rather than derived. The consistency check in Section 2.2 is structural: Z_CFT(J) is introduced through the same bulk wavefunctional, so the nonvanishing one-point function (2.14) and the shift J = J_b + δJ restate the ansatz rather than provide independent evidence. To make the dictionary claim load-bearing, the paper should derive this equality from a concrete microscopic construction (such as an explicit CFT computation on S^1 with a source) or at least formulate it as a precise conjecture with a specified domain of validity, rather than presenting it as an immediate consequence of the path integral.","section":"Section 2.1, Eqs. (2.5)-(2.8)"},{"comment":"Gravity is excluded and the de Sitter background metric is fixed, so the additional boundary Σ_b is imposed by hand. The existence of the proposed states depends on Σ_b being a legitimate Euclidean saddle of the full gravitational path integral, but the paper never checks compatibility with the gravitational constraints; the authors themselves list the Wheeler-DeWitt equation and the gravitational Gauss law as open questions in Section 4. This is a load-bearing gap: if linearized gravitational constraints around de Sitter admit only the Bunch-Davies vacuum (as suggested by the cited references [9,10]), then arbitrary boundary data φ_b could be forbidden. A minimal consistency check in minisuperspace or in the linearized theory is needed before the states can be claimed to be states of quantum gravity rather than states of a scalar field on a fixed background.","section":"Section 2 (before Section 2.1) and Section 4"},{"comment":"All explicit results are obtained in the small-hole expansion τ_b → -∞. The two-point correction (3.19) is proportional to e^{2τ_b}, and the one-point kernel (3.21) is also given at leading order in this expansion. The paper motivates this regime as the one closest to the Euclidean vacuum, but the physically interesting excited states are those with finite τ_b, and the current computation does not control that regime. It is also not shown that the expansion is uniform in the mode number n or that the resulting states are normalizable. Without such control, the leading-order results cannot be safely extrapolated to the regime where the excitation is significant.","section":"Section 3, Eqs. (3.18)-(3.21)"},{"comment":"The bulk boundary data φ_b on Σ_b are identified with the CFT source J_b only through the formal equality (2.8). The explicit one-point function (3.20) is a convolution of φ_b with the kernel K_b on S^1, but it is not shown that this response matches a CFT perturbed by a local source J_b(φ) inserted on the future boundary I^+. Without this identification, the phrase 'excited states' describes a bulk construction whose dual CFT interpretation is asserted rather than demonstrated. The paper should clarify the precise map between φ_b and J_b, including whether J_b is an arbitrary local function or is constrained by the bulk dynamics on the Euclidean interval.","section":"Section 2.2 and Section 3, Eqs. (2.14), (3.20)"}],"minor_comments":[{"comment":"There are several typographical errors: 'Schwinger-Kelldysh' (Sections 2 and 2.1), 'pertubately' (Section 3), 'Riemmanian' (Introduction), 'ans' (Appendix A), and 'We must us verify' (Section 2.1). These should be corrected before publication.","section":"Throughout"},{"comment":"In the displayed formula for ⟨ϕ1ϕ2ϕ3⟩_{J_b=0}, the product of the three factors (−2Re ψ̂2(k_i)) appears without an explicit division symbol; the intended expression is presumably 2Re[ψ̂3] δ(...) divided by that product. Please make the notation unambiguous.","section":"Section 2.3, Eq. (2.23)"},{"comment":"The phrase 'terms that are bilinear in ϕ and ϕb respectively' is unclear; it presumably means terms quadratic in ϕ and terms quadratic in ϕ_b, but the sentence should state this explicitly.","section":"Section 2.2, after Eq. (2.13)"},{"comment":"The computation is restricted to the complementary series ∆ ∈ [0,1/2], while the proposal in Section 2 is phrased generally. A brief comment on whether the principal series or the massless case would change the construction would be useful.","section":"Section 3"},{"comment":"The relationship between the left Schwinger-Keldysh contour and the right saddle geometry could be clarified, especially the location of Σ_b and the direction of the Euclidean interval (τ_b, 0).","section":"Figure 2"}],"recommendation":"major_revision","confidential_remarks":"This is a speculative but carefully written proposal with a solid free-field computation. The central dictionary step is an ansatz, and the gravitational consistency of the additional boundary is not addressed. If the journal regularly publishes heuristic holographic proposals with explicit computations, major revision is the right outcome; the authors should either tighten the conjecture, add a constrained-saddle check, or clearly state the domain of validity. The paper is not fatally flawed, but the load-bearing issues need work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Useful take: this is a real computation, not a hand-wave. The authors take the AdS 'extra Euclidean boundary' trick from their earlier work and apply it to the dS no-boundary proposal: put a second boundary Sigma_b in the Euclidean region with Dirichlet data phi_b, and use the resulting wave functional as a CFT generating function. In dS_{1+1} they compute the free scalar on-shell action in the complementary series, extract the one-point kernel K_b and the two-point correction, and show the deformed correlators do not have the antipodal divergences characteristic of alpha-vacua. That last point is a useful physical discriminant.\n\nThe soft spots are named in the text, which I respect. Equation (2.8) is asserted, not derived; the state is defined by the path integral and then declared to equal Z_CFT(J). The extra boundary is imposed by hand, and gravity is switched off before Section 2.1. So the hard question—whether the configuration (metric plus scalar) satisfies the gravitational constraints, or whether the new boundary is a legitimate saddle of the full path integral—is simply not addressed. If the linearized constraints only allow Bunch-Davies, the family (2.5) might be empty. That is a real open issue, but it is one the authors flag in Section 4 (WdW, Gauss law). It does not invalidate the scalar computation or the consistency check with CFT excitations; it just means the holographic interpretation is conditional. Also, the explicit results are only in the tau_b -> -infinity small-hole limit, with '...' terms, so the quantitative reach is limited.\n\nOn the circularity worry: yes, part of the CFT consistency is built into (2.8) by construction. But they do use an external benchmark—the standard dS/CFT dictionary for the vacuum, and the contrast with alpha-vacua—so I would not call it a circular argument, more a structurally defined proposal.\n\nWho it is for: anyone working on dS/CFT, cosmological correlators, or the no-boundary wave function. It deserves a serious referee; I would send it out, with the expectation that the gravitational constraint issue gets pushed in review. I would cite it as a construction with a concrete example, not as an established dictionary.","headline":"A carefully computed proposal for excited dS states via an extra Euclidean boundary; the central map is posited and gravity is left for later, but it deserves a real referee.","tokens_in":15880,"tokens_out":2411,"would_cite":true,"duration_ms":25424,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that adding a second Euclidean boundary with arbitrary Dirichlet data to the no-boundary path integral defines excited states in de Sitter holography, and it computes their correlators.","keywords":["de Sitter holography","no-boundary proposal","excited states","dS/CFT correspondence","holographic correlators","Euclidean path integral","late-time correlators","alpha-vacua"],"falsifier":"Include back-reaction in the $dS_{1+1}$ computation, solve the junction conditions and the Hamiltonian constraint on the two-boundary geometry, and check whether a finite-norm wave functional exists for finite $\\tau_b$ with generic $\\phi_b$; if only $\\phi_b = 0$ or $\\tau_b \\to -\\infty$ survive, the construction fails. A lighter test is to compute the corrected two-point function (3.18)-(3.19) near $\\tau_b \\to 0$, where the small-hole expansion breaks down; a divergence or a failure of the CFT-source interpretation there would signal that the holographic identification does not hold.","tokens_in":14947,"feed_emoji":"🌌","tokens_out":11268,"duration_ms":103573,"temperature":0.7,"pith_summary":"The paper aims to establish that excited states in de Sitter holography (the dS/CFT correspondence) can be built by relaxing the no-boundary proposal: instead of a Euclidean geometry whose only boundary is the Cauchy surface, one considers a Euclidean region with a second compact boundary $\\Sigma_b$ and fixes arbitrary Dirichlet data $\\phi_b$ there. The central claim is that the resulting wave functional $\\Psi'_{\\phi_b}$ equals the CFT generating function with a nonzero source $J_b$, so the dual operator acquires a nonvanishing one-point function and late-time cosmological correlators are modified. This matters because it supplies a concrete holographic dictionary for states other than the Euclidean vacuum in de Sitter holography, a gap highlighted by the paper. The construction is worked out explicitly for a free massive scalar in $dS_{1+1}$, yielding corrected one- and two-point functions and a wave-function renormalization controlled by $\\phi_b$.","feed_headline":"Adding a boundary turns no-boundary de Sitter into excited states","feed_subtitle":"Holographic correlators gain one-point terms and state-dependent corrections, a concrete dS/CFT dictionary beyond vacuum.","key_machinery":"The load-bearing object is the generalized Euclidean path integral with two boundaries, equation (2.5), which prepares the state by evolving from an arbitrary field configuration $\\phi_b$ at Euclidean time $\\tau_b$ to the Cauchy surface. The identity that carries the argument is the generalized holographic prescription $\\Psi'_{\\phi_b} = Z_{\\mathrm{CFT}}(J_b)$, checked by functional differentiation: the linear kernel $K_b(x,y)$ in the on-shell action couples the asymptotic source to the boundary data and produces the one-point function. The explicit computation in $dS_{1+1}$ relies on mode solutions written in terms of associated Legendre functions $P^{|n|}_{\\Delta-1}$ and on splitting the renormalized on-shell action into an asymptotic piece, a $\\Sigma_b$ piece, and a cross term; the asymptotic piece yields the deformed two-point function while the cross term yields the one-point kernel.","core_discovery":"The paper's central claim is that the identity $\\Psi'_{\\phi_b}(\\phi,T) = Z_{\\mathrm{CFT}}(J)$ holds when the initial state is prepared by a Euclidean path integral on a compact manifold with two boundaries, $\\Sigma_0$ and $\\Sigma_b$, with arbitrary Dirichlet data $\\phi_b$ on $\\Sigma_b$. Functional differentiation then identifies wave-functional coefficients with CFT $n$-point functions in the source $J_b$; in particular, the linear term gives $\\langle O(x)\\rangle_{J_b} = \\int_{\\Sigma_b} dy\\, K_b(x,y)\\, \\phi_b(y)$, which is nonzero for generic $\\phi_b$. In the explicit $dS_{1+1}$ example, the late-time two-point function becomes the vacuum correlator times a correction depending only on the boundary position $\\tau_b$, the one-point function is governed by the kernel $K_b$, and the boundary data renormalize the wave function even at zero field. The paper also argues that these states are not $\\alpha$-vacua, since the corrected correlators exhibit no antipodal singularities.","pith_inferences":["Not stated in the paper: the residual $\\tau_b$ dependence at $\\phi_b = 0$ suggests the boundary position acts like a state label interpolating between the vacuum at $\\tau_b \\to -\\infty$ and a maximally deformed state at $\\tau_b \\to 0$; this could be probed by searching for the predicted correction in primordial non-Gaussianity data.","Not stated in the paper: the same two-boundary construction should generalize to higher-dimensional de Sitter and to weakly interacting fields, where the leading $\\psi_1$ correction to the three-point function gives a concrete bispectrum shape; measuring this shape in the CMB would test the proposal.","Not stated in the paper: because no $\\alpha$-vacuum trace appears, the boundary data behave like a single-trace source rather than a double-trace deformation; checking whether a double-trace deformation reproduces the same corrections would clarify the dictionary.","Not stated in the paper: including back-reaction through the junction conditions and imposing the Hamiltonian constraint of quantum gravity may select a discrete family of allowed $\\phi_b$ configurations, which would quantize the space of excited states."],"forward_implications":["If the generalized prescription is correct, late-time de Sitter correlators in an excited state are not vacuum correlators: one-point functions become nonzero and the two-point function picks up the explicit correction of equations (3.18)-(3.19).","Taking $\\phi_b \\to 0$ does not restore the undeformed vacuum; the presence of the boundary at $\\tau_b$ leaves a residual correction, so the geometry itself deforms the state.","The states defined by $(\\Sigma_b, \\phi_b)$ form a family distinct from $\\alpha$-vacua, because their correlators show no antipodal singularities order by order in the small-hole expansion.","The wave functional is renormalized by the boundary data, as in equation (3.22), so normalization of the de Sitter wave function encodes information about the state preparation.","Each excited state has a semiclassical bulk geometry by construction, so the dictionary maps dual CFT excitations to geometries with an extra Euclidean boundary."],"supporting_citations":[{"why":"Defines the no-boundary wave function of the universe as a path integral over compact Euclidean geometries with no extra boundary; this is the object the paper generalizes.","marker":"[1]"},{"why":"Establishes the de Sitter/CFT correspondence by identifying the boundary CFT on the future boundary and matching late-time correlators; this fixes the target of the holographic formula.","marker":"[2]"},{"why":"Provides the standard prescription relating de Sitter wave functions to CFT generating functions and the computation of cosmological correlators that the paper extends.","marker":"[5]"},{"why":"Supplies the lecture-note treatment of cosmological correlators used as the technical basis for the late-time computations.","marker":"[6]"},{"why":"Gives the Euclidean/Lorentzian path-integral construction with Dirichlet boundary data in AdS, the template for the two-boundary Euclidean region and the on-shell action split.","marker":"[17, 18]"},{"why":"Shows how AdS excited states arise from Dirichlet conditions on the asymptotic boundary, motivating the analogous construction in de Sitter.","marker":"[19]"},{"why":"Provides the junction conditions used to glue Euclidean and Lorentzian field configurations, which structure the boundary terms of the on-shell action.","marker":"[21]"},{"why":"Defines the alpha-vacua family in de Sitter, whose correlators the paper computes and contrasts with the boundary-proposal states.","marker":"[11]"},{"why":"Identifies the gravitational constraints that the paper sets aside, marking the main caveat for the existence of the extra boundary.","marker":"[9, 10]"}],"fun_headline_variants":["Extra boundary excites de Sitter holography","Boundary condition turns dS vacuum into excited states","No-boundary gets a boundary: excited states in dS","Excited de Sitter states from a second boundary"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole construction rests on the premise that, once gravity is turned on, a Euclidean geometry with an extra boundary at finite Euclidean time is still a legitimate configuration of the path integral; the paper assumes this by neglecting back-reaction, so if the constraints of quantum gravity forbid such a boundary, the proposed excited states would not exist.","fun_headline_variants_meta":{"raw":{"variants":["Extra boundary excites de Sitter holography","Boundary condition turns dS vacuum into excited states","No-boundary gets a boundary: excited states in dS","Excited de Sitter states from a second boundary"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000213,"raw_usage":{"total_tokens":1471,"prompt_tokens":1042,"completion_tokens":429,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":658,"completion_tokens_details":{"reasoning_tokens":364}},"tokens_in":658,"tokens_out":429,"duration_ms":4806,"temperature":1.0,"reasoning_tokens":364,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:15:45.853428+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Include back-reaction in the $dS_{1+1}$ computation, solve the junction conditions and the Hamiltonian constraint on the two-boundary geometry, and check whether a finite-norm wave functional exists for finite $\\tau_b$ with generic $\\phi_b$; if only $\\phi_b = 0$ or $\\tau_b \\to -\\infty$ survive, the construction fails. A lighter test is to compute the corrected two-point function (3.18)-(3.19) near $\\tau_b \\to 0$, where the small-hole expansion breaks down; a divergence or a failure of the CFT-source interpretation there would signal that the holographic identification does not hold.","supporting_citations":[{"cited_title":"Hartle and S.W.Hawking, Wave function of the universe , Phys","cited_arxiv_id":null,"evidence_quote":"Defines the no-boundary wave function of the universe as a path integral over compact Euclidean geometries with no extra boundary; this is the object the paper generalizes."},{"cited_title":"Lectures on Cosmological Correlations","cited_arxiv_id":null,"evidence_quote":"Supplies the lecture-note treatment of cosmological correlators used as the technical basis for the late-time computations."}],"review_version":2}