The 'Participatory Horizon': Causal Limits and the CMB Low Power Anomaly

The ‘Participatory Horizon’: Causal Limits and the CMB Low Power Anomaly Gregory O’Grady December 16, 2025 Disclaimer: This Measureverse module is shared solely for conceptual exploration and discussion. The analysis and interpretations have not yet been independently reproduced or peer reviewed by domain experts. Portions of the manuscript and the associated computational workflow were produced with assistance from generative AI tools under close human oversight and there may be errors. Abstract Standard ΛCDM cosmology generally provides an excellent fit to the observed Cosmic Microwave Background (CMB), yet anomalies persist at the largest angular scales. One of the most persistent is the near vanishing of the two-point correlation function of CMB temperature fluctuations for angular separations θ≳60◦, as captured by the S1/2statistic. Curiously, the angular scale at which the correlation function crosses zero corresponds, in comoving units, approximately to the size of the present observable universe. Motivated by Wheeler’s ‘participatory universe’, this work explores a conceptual shift in which the CMB is treated not only as a fossil record, but also as a relational record conditioned by the detector that registers it. Adopting a strict definition of measurement as ‘irreversible amplification’, distinct from environmental decoherence, we take as an explicit assumption that decoherence alone may be insufficient, on its own, to select a unique realised history for modes that do not terminate in an accessible macroscopic record. Within this interpretive stance, we hypothesize that the low power anomaly could reflect an apparent loss of realised long range correlations because the largest scale modes remain effectively unmeasured relative to the detector, lying beyond a detector dependent ‘participatory horizon’. As an initial phenomenological proof of principle, this hypothesis is implemented by modelling the local causal horizon as an effective information aperture that suppresses sensitivity to modes with wavelengths comparable to, or larger than, the present conformal horizon. This is encoded as a smooth, scale dependent filter applied to the primordial scalar power spectrum. Using Planck 2018 temperature data and a simplified low multipole χ2diagnostic (with baseline ΛCDM parameters held fixed), the model favours a cutoff parameter near α≃1.5, corresponding to a suppression scale of order the observer’s horizon. In this diagnostic, the filtered spectrum improves the 1 fit to the lowest multipole temperature anisotropies (∆χ2≃ −5) and reduces the S1/2 statistic by approximately 80% relative to the Planck ΛCDM best fit, moving it toward the value reconstructed from the measured sky. If the filter acts at the level of primordial scalar perturbations (rather than as a temperature only selection effect), it should also imply a correlated suppression in the largest scale E-mode polarization pattern, offering a prospective observational test for future missions such as LiteBIRD. 1 Introduction The standard ΛCDM model provides a robust account of the Cosmic Microwave Background (CMB) and the large-scale distribution of matter [1,2]. However, a cluster of anomalies have persisted at the largest angular scales. The most prominent of these is a deficit of large angle temperature correlations compared to concordance predictions, referred to as the low power anomaly. In real space, the two point correlation function C(θ) of the CMB is observed to be anomalously suppressed, effectively vanishing for separations θ≳60◦. This behaviour is captured in the S1/2statistic, which integrates the squared correlation function over these large angular separations [3,4,5]. Simulated CMB skies from the standard ΛCDM ensemble exhibit substantially higher correlation on these angular scales, with the probability of obtaining an S1/2value as low as that measured by Planck being estimated to be of order 10−3 or lower [3,6]. Although this is often dismissed as a statistical fluctuation in the face of large cosmic variance, the persistence of this feature across sequential mission releases leaves open the possibility that it signals a genuine breakdown of standard assumptions at the largest observable scales. Curiously, the angular scale at which the correlation function crosses zero corresponds, when projected to the present epoch in comoving units, to a physical distance comparable to the radius of the observable universe. Beyond the power spectrum, other large-scale anomalies persist, most notably the socalled ‘Axis of Evil’—an unexplained alignment of the quadrupole and octopole phases with one another and with the geometry of the Solar System [7,8,9,5]. Furthermore, tensions have emerged between the CMB kinematic dipole and the cosmic matter rest frame inferred from radio galaxy counts and related tracers [10,11]. Individually, each feature might be attributed to chance, residual foreground contamination, or the look-elsewhere effect associated with a posteriori choices of statistics [12,13,14]. But two striking themes motivate an ongoing search for plausible physical solutions: they predominantly involve the very largest angular scales, and they all hint at a possible non-trivial relationship to the specific context of the observer. Proposed resolutions to the low power anomaly typically focus on modifying the dynamics or initial conditions of the very early universe. Leading scenarios include pre inflationary phases, departures from slow roll inflation, or tuned initial conditions that selectively suppress the longest wavelength modes in the primordial spectrum [15,16,17,6]. Alternatively, the cutoff may arise from non trivial spatial topology or compact spatial sections, where a restricted set of allowed wavelengths naturally generates an infrared cutoff [18,19,20,17]. Phenomenological templates employing smooth exponential or hyperbolic tangent cutoffs 2 have also been explored [e.g. 17,6], as have horizon scale truncations tied to Planck scale physics or alternative background evolutions [21]. While several of these constructions improve one or more low ℓdiagnostics, many require some degree of tuning or non standard physics, and no single explanation has achieved broad consensus. This paper evaluates an alternative line of enquiry. In contrast to the dynamical proposals discussed above, we explore a longstanding line of thought arising from quantum mechanics in which the observer and the act of measurement are not treated as external to the description, but as central. John Archibald Wheeler championed this perspective in his participatory universe’ program. Although his model remained incomplete, Wheeler offered probing enquiries in several directions, famously utilizing ‘visual thinking’ to illustrate how the quantum principle might extend to the cosmos scale (Figure 1). Three of Wheeler’s concepts are most relevant here. First, he conceptualised the universe as a kind of ‘self-excited circuit’, in which acts of observation, including those performed on the earliest light, play a necessary part in ‘bringing that universe into being’ [22,23] (Figure 1A). Second, he viewed environmental decoherence as insufficient alone for creating classical records, insisting that “no elementary phenomenon is a phenomenon until it is a registered phenomenon. ..brought to a close by an irreversible act of amplification” [22,23]. This motivated his description of the unmeasured past as consisting of ‘great clouds of probability’ or superposition states, a concept he famously labelled the ‘great smoky dragon’ (Figure 1B). Third, motivated by delayed-choice experiments, he insisted that any act of measurement in the universe’s history has an inescapable effect on what one can ultimately say about the past (Figure 1C).[24] In this view, the observer is not separated from reality by a plate of glass, but is critically involved in defining what is measurable. Importantly, he used the term ‘observer’ in a minimal sense, denoting anything that preserves an irreversible record, a usage continued here. While Wheeler’s program is typically viewed as philosophically profound yet scientifically elusive, a recent conceptual framework, termed the ‘Measureverse’, proposes to both extend this vision and operationalise it in the context of current cosmological anomalies [25]. Within this framework, the ‘self-excited circuit’ is treated as the central physical architecture. Measurements performed today are modeled not as retrocausal influences, but as late-time boundary conditions that actualize specific histories from the prior quantum superposition. This stance motivates a radical conceptual hypothesis regarding the nature of the CMB. Instead of treating it as a fixed fossil record’ or absolute rest frame, it is proposed to be a ‘relative reference frame’ dynamically coupled to any participating detector. To justify this stance in the face of standard decoherence arguments, a strict Bohr and Wheeler-inspired notion of measurement as irreversible amplification’ is employed. Measurement is thus treated as distinct from environmental decoherence; while decoherence explains the emergence of robust pointer states, it does not by itself select a single realised history in the absence of a terminating record. The further hypothesis is then advanced that the low-power anomaly is anticipated, because in this stance correlations on the very largest scales must remain in an unmeasured superposition from the perspective of the present detector, effectively filtered out because they link regions lying beyond its ‘participatory horizon’. The present paper advances this line of enquiry toward an initial quantitative realisation, with the aim of offering a complementary perspective to ΛCDM; a participatory overlay 3 Figure 1: Visual thinking diagrams used by Wheeler to illustrate the participatory role of the observer. (A) Wheeler’s ‘U’ diagram: posing the universe as a kind self-excited circuit, intended to ‘inspire thought’ regarding how observation imparts tangible reality to the early universe [26]. (B) The Great Smoky Dragon: A metaphor for the quantum phenomenon between emission and detection. The tail (entry) and mouth (detection) are sharp, but “about what the dragon does or looks like in between we have no right to speak” [27]. In the present framework, the unmeasured large scale CMB is treated as such a superposition. (C) Smashing the Glass: The classical view (left) assumes the observer watches the universe safely behind a slab of plate glass. Wheeler’s quantum-first view (right) reminds us that to observe even a photon, we must ‘smash the glass and install equipment, making the observer willy nilly a participator’ with an inescapable effect on the resulting measured history [22]. that reframes the low power anomaly as a natural consequence of observation. The central hypothesis is that the local causal horizon acts as an intrinsic ‘information aperture’ for the observer, strictly limiting the resolution at which long wavelength modes can be collapsed into distinct classical records. Consequently, only a finite amount of large scale structure can be written into the observer’s macroscopic record; modes at scales comparable to, or larger than, the horizon remain largely in an unmeasured superposition (‘the smoky dragon’). For any realised sky map, suppression is therefore anticipated for the very largest scale correlations, while the small scale acoustic structure, which lies well within the horizon and is fully decohered, remains essentially unchanged. These principles are demonstrated phenomenologically as follows. The standard ΛCDM background is retained without modifying inflationary dynamics. The participatory horizon is then encoded as a smooth, scale dependent filter applied to the primordial scalar power spectrum. While this filter belongs to the broad class of infrared cutoffs explored in previous studies, in the present context its characteristic scale is specifically tied to the present day horizon radius, motivated as an information based limitation rather than a freely tunable length. The resulting modified spectrum is then propagated through a standard numerical pipeline to obtain the angular power spectrum Cℓ, the real space correlation function C(θ), and the associated S1/2statistic. This analysis serves as a quantitative feasibility test of whether a simple, physically motivated participatory horizon model can bring the large angle correlations of the observed sky into closer agreement with expectation while preserving the success of ΛCDM on smaller scales. 4 2 Conceptual framework: the participatory horizon Scope and limitations. This paper is intended as an exploratory, phenomenological study. The horizon filter F(k) is a template motivated by an interpretive stance, not a derivation from a microscopic theory of measurement. The statistical comparison is intentionally simplified: Planck 2018 TT bandpowers and quoted errors are used with the baseline ΛCDM parameters held fixed, rather than a full Planck likelihood analysis with masks, covariances, and joint parameter inference. The reported ∆χ2values and parameter ranges should therefore be read as indicative diagnostics, not as definitive evidence for model preference. In the standard cosmological treatment, the role of the observer is effectively passive. One specifies a primordial curvature power spectrum, evolves it through recombination using linear perturbation theory, and projects the result onto the sky. The observer enters only through a choice of rest frame and practical constraints such as sky masks. The fundamental assumption is that the large scale modes of the metric and radiation fields exist as well defined classical degrees of freedom, irrespective of any particular observation. This view implicitly assumes that early environmental decoherence rendered all alternative histories negligible and stored redundant information about them in the environment long before any detector existed. As above, the Measureverse framework [25], in operationalising Wheeler’s philosophy [22,23], adopts a different starting point. It posits that macroscopic records of quantum events play the central ontological role, including in CMB measurements. A physical event is not simply a value of a field at a spacetime point, but a realised, effectively irreversible record that is physically stored as information. Following Wheeler’s view that no elementary phenomenon is a phenomenon until it is a registered phenomenon. .. brought to a close by an irreversible act of amplification” [22,23], this framework treats the relevant degrees of freedom before measurement as structured potential (‘a cloud of probability’), rather than as a fixed classical history. Crucially, this approach distinguishes between environmental decoherence and true measurement. While decoherence suppresses interference, it does not by itself constitute the irreversible act of amplification required to actualise a unique record in the Measureverse view. Within this ontology, following Wheeler, the status of the past is not fixed, but is fundamentally relative to the measurements made in the ‘here and now’. Figure 2contrasts this participatory view with the standard passive picture. Panel (a) shows a conventional conformal spacetime diagram where photon trajectories exist independently of the observer. Panel (b) replaces these trajectories with a quantum probability distribution inside the observer’s causal diamond. Definite records are associated only with the causal aperture (the detector) at the apex. The region below the horizon is not a fully written classical history, but an unresolved domain that is accessed only through the records formed at the aperture. The key conceptual step in this paper is to treat that finite causal domain as an information aperture that mediates the link between the primordial spectrum and the actually registered sky. At leading order, this aperture behaves like a smooth, horizon scale filter. It suppresses sensitivity to modes whose wavelengths are significantly larger than the observer’s horizon, while leaving smaller scale modes essentially unchanged. This filter is not introduced as an ad hoc modification of early universe dynamics; rather, it is interpreted 5 as an effective description of how a finite, participatory horizon limits the number of long wavelength degrees of freedom that can be realised as distinct records. 2.1 Causal diamonds and information bounds For a single timelike worldline in an expanding universe, one can associate a causal diamond defined by the intersection of the past and future light cones. In this model the observer is idealised as comoving, with the diamond’s spatial section at the present time approximating a ball of radius η0(the conformal time today), which is of order the comoving horizon radius RH. In the numerical implementation below, η0is computed using camb from a standard ΛCDM background. Theoretical results in gravitational thermodynamics and holography suggest that a region with a finite bounding area cannot support an arbitrarily large number of independent degrees of freedom [28,29]. While specific models vary [e.g. 30,31,32], only the weak assumption is adopted here that there is an effective upper limit on the independent information that can be encoded within a causal diamond. In a participatory ontology this bound applies to the number of distinct records that can be realised. Long wavelength perturbations pose a special case in this setting. A mode with comoving wavenumber kmuch smaller than the horizon scale π/η0varies so slowly across the causal diamond that it is effectively indistinguishable from a uniform offset or a very shallow gradient. Within the finite domain of the observer such modes carry very little independent information. In information theoretic terms they are highly compressed into a few coarse degrees of freedom, for example an overall monopole or dipole, which are conventionally removed from CMB maps. The finer grained information needed to distinguish different long wavelength configurations therefore remains unresolved at the level of macroscopic records. The practical consequence is that the observer does not inherit the full variance of the primordial spectrum P(k) at these scales. The finite causal aperture acts as an effective high-pass filter, such that an observer does not sample these modes as independent random variables. Instead, they experience a restricted, coarse grained version conditioned by the finite capacity of their own horizon. 2.2 Application of a k-space filter To model this effect quantitatively, the situation is treated as analogous to observing a spatial field through a finite window. If δT(x) denotes the temperature fluctuation field and W(x) represents an effective window function (unity inside the diamond, zero outside), the registered field is schematically δTobs(x)=W(x)δT(x).(1) In Fourier space this multiplication becomes a convolution. For a window of size ∼η0, this convolution strongly suppresses power for modes k≪π/η0. While a fully geometric treatment would involve applying a 3D window function to the perturbations, a simpler initial phenomenological approach is adopted here, whereby the aperture’s effect is modeled by directly modulating the isotropic primordial power spectrum. 6 Figure 2: Passive and participatory views of the CMB on a conformal spacetime diagram. (a) In the standard passive picture, classical photon trajectories propagate from a fixed last scattering surface to the observer. (b) In the participatory picture, the interior of the light cone is treated as an unresolved quantum probability distribution. Definite records are actualised only at the detector (causal aperture), with the horizon radius RHacting as an information boundary. The net effect of the aperture is represented by an isotropic transfer function F(k) acting directly on the primordial scalar power spectrum: Peff (k) = PΛCDM(k)F2(k).(2) where F(k)→0 as k→0 and F(k)→1 for k≫kcut. This function acts as an effective information filter, encoding the limit on realisable long wavelength modes. This specific transfer function is not derived from any microscopic theory of measurement; instead we treat it as a phenomenological template that captures the expected suppression of modes whose wavelengths significantly exceed the causal horizon. This places the model in the same phenomenological class as earlier studies using infrared cutoffs [e.g. 17,6], but with a distinct physical interpretation. Here, the cutoff scale is not tied to any exotic early-universe dynamics, but specifically to the size of the observer’s causal diamond, parameterised by η0(or equivalently RH). To implement this without introducing sharp, unphysical artefacts, F(k) is chosen to be a smooth high pass function: F(k;α, p)=1−exp−k kcut p, kcut =απ η0 ,(3) where αis a free, dimensionless parameter that sets the cutoff scale. The exponent pis chosen to be large enough that F(k) behaves as a soft step function while remaining smooth; it is treated as part of the model definition rather than as a tuned parameter. Figure 3provides a schematic view of this construction. Panel (a) shows the idealised real space window, panel (b) the corresponding transfer function in wavenumber space, and panel (c) the qualitative impact on the angular power spectrum: a reduction in low-ℓpower while leaving the acoustic structure at higher ℓintact. 7 Figure 3: Schematic of the horizon scale information filter. (a) The real space information aperture W(r) tapers to zero beyond the horizon radius RH. (b) The corresponding transfer function F2(k) suppresses modes with k≲kcut. (c) The qualitative impact is a reduction of low-ℓpower (affecting the S1/2statistic) while leaving the high-ℓacoustic structure unchanged. 3 Phenomenological model and numerical methods This section details how the horizon scale information filter is implemented at the level of the primordial power spectrum and propagated to observable CMB quantities. To strictly isolate the effects of the participatory horizon, the standard flat ΛCDM background and linear perturbation theory are retained, with the filter treated as a single parameter phenomenological extension constrained by CMB temperature data. 3.1 Baseline cosmology and primordial spectrum The analysis adopts the Planck 2018 best fit parameters for a spatially flat ΛCDM model [2]. The Hubble parameter, physical baryon and cold dark matter densities, and optical depth to reionisation are fixed to their Planck values. The standard primordial curvature spectrum is modelled as a power law: PΛCDM(k) = Ask kpns−1 ,(4) with pivot scale kp= 0.05 Mpc−1, and amplitude Asand spectral index nsfixed to the baseline model. By holding the standard cosmological parameters constant, this treatment focuses exclusively on the impact of the horizon filter on the largest scales. It is acknowledged that this approach does not constitute a full parameter inference; however, the horizon filter induces a specific scale dependent suppression that mainly affects modes with wavenumbers comparable to the cutoff (multipoles ℓ<30). This spectral shape change is distinct from uniform rescalings. While a definitive assessment of statistical preference would require a joint variation of αand the baseline parameters, the present method serves as a robust initial test of consistency, designed to isolate the spectral signature of the horizon filter from other degrees of freedom. 8 The conformal time today, η0, which sets the geometric horizon scale and hence kcut in the filter equation, is computed consistently with these parameters using the Boltzmann code camb. For the Planck baseline cosmology this yields η0≈1.4×104Mpc,(5) placing the fundamental scale π/η0at k≈2.2×10−4Mpc−1. 3.2 Horizon filtered primordial power spectrum The phenomenological horizon filter is implemented by constructing a modified primordial spectrum: Peff (k;α, p)=PΛCDM(k)F2(k;α, p),(6) where F(k;α, p) is the transfer function defined previously. The exponent pcontrols the sharpness of the transition between the suppressed and unsuppressed regimes. Preliminary testing confirmed that the large angle observables are insensitive to the precise value of p, provided the transition is reasonably steep. Accordingly, pis fixed to 8 for this analysis. This choice approximates a soft step function, steep enough to represent a definite horizon scale, but smooth enough to avoid the ringing artefacts associated with sharp cutoffs in k space. It functions as part of the template definition rather than as a free parameter tuned to the data. The dimensionless parameter αis thus treated as the single free parameter of the model, scaling the cutoff wavenumber via kcut =απ η0 .(7) The modified spectrum is supplied to camb using the SplinedInitialPower interface, tabulating Peff (k) on a logarithmic grid spanning kfrom 10−5to 1 Mpc−1. This range comfortably covers the modes relevant for multipoles ℓbetween 2 and 2500. As an internal consistency check, setting α= 0 returns the filter to unity (up to the irrelevant k= 0 mode), reproducing the standard ΛCDM predictions. Lensing and nonlinear corrections are disabled when computing the low multipoles, as these effects are negligible at the angular scales of interest. 3.3 Computation of Cℓ,C(θ)and S1/2 For varying values of α, the temperature angular power spectrum Cℓis computed using camb. Following standard convention Dℓ=ℓ(ℓ+ 1) 2πCℓ,(8) both for comparison with Planck bandpower data and for visualisation. This paper restricts attention to the temperature auto spectrum (TT). A joint analysis including polarisation (TE and EE), and specifically the predicted impact of the horizon filter on the reionisation bump, is reserved for future work. 9 as a vanishing point in information: a limit where the projection of the realised past exhausts all records available in the present. 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