Cosmic Microwave Background Anisotropies Research Articles

Lensing convergence and anisotropic dark energy in galaxy redshift surveys

Analyses of upcoming galaxy surveys will require careful modelling of relevant observables such as the power spectrum of galaxy counts in harmonic space Cℓ(z,z′). We investigate the impact of disregarding relevant relativistic effects by considering a model of dark energy including constant sound speed ceff2, constant equation of state w, and anisotropic stress sourced by matter perturbations π. Cosmological constraints were computed using cosmic microwave background anisotropies, baryon acoustic oscillations, supernovae type Ia, and redshift space distortions. Our results are consistent with w=−1, ceff2=1, and π=0. Then, a forecast for the performance of an Euclid-like galaxy survey was carried out also adding information from other probes. Here we show that, regardless of the galaxy survey configuration, neglecting the effect of lensing convergence will lead to substantial shifts in the galaxy bias b0 and the neutrino mass ∑mν. Shifts in the dark energy sound speed and anisotropic stress also appear, but they depend on the survey configuration and hence lack robustness. While neglecting lensing convergence also leads to a Hubble constant H0 moving downwards, the significance of the shift is not big enough to play a relevant part in the current H0 tension.

Testing CCC+TL Cosmology with Observed Baryon Acoustic Oscillation Features

The primary purpose of this paper is to see how well a recently proposed new model fits (a) the position of the baryon acoustic oscillation (BAO) features observed in the large-scale distribution of galaxies and (b) the angular size measured for the sound horizon due to BAO imprinted in the cosmic microwave background (CMB) anisotropy. The new model is a hybrid model that combines the tired light (TL) theory with a variant of the ΛCDM model in which the cosmological constant is replaced with a covarying coupling constants’ (CCC) parameter α. This model, dubbed the CCC+TL model, can fit the Type Ia supernovae Pantheon+ data as accurately as the ΛCDM model, and also fit the angular size of cosmic dawn galaxies observed by the James Webb Space Telescope, which is in tension with the ΛCDM model. The results we obtained are 151.0 (±5.1) Mpc for the absolute BAO scale at the current epoch, and the angular size of the sound horizon θ sh = 0.°60, matching Planck’s observations at the surface of the last scattering when the baryon density is set to 100% of the matter density and ∣α∣ is increased by 5.6%. It remains to be seen if the new model is consistent with the CMB power spectrum, the Big Bang nucleosynthesis of light elements, and other critical observations.

The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters

We present cosmological constraints from a gravitational lensing mass map covering 9400 deg2 reconstructed from measurements of the cosmic microwave background (CMB) made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with measurements of baryon acoustic oscillations and big bang nucleosynthesis, we obtain the clustering amplitude σ 8 = 0.819 ± 0.015 at 1.8% precision, S8≡σ8(Ωm/0.3)0.5=0.840±0.028 , and the Hubble constant H 0 = (68.3 ± 1.1) km s−1 Mpc−1 at 1.6% precision. A joint constraint with Planck CMB lensing yields σ 8 = 0.812 ± 0.013, S8≡σ8(Ωm/0.3)0.5=0.831±0.023 , and H 0 = (68.1 ± 1.0) km s−1 Mpc−1. These measurements agree with ΛCDM extrapolations from the CMB anisotropies measured by Planck. We revisit constraints from the KiDS, DES, and HSC galaxy surveys with a uniform set of assumptions and find that S 8 from all three are lower than that from ACT+Planck lensing by levels ranging from 1.7σ to 2.1σ. This motivates further measurements and comparison, not just between the CMB anisotropies and galaxy lensing but also between CMB lensing probing z ∼ 0.5–5 on mostly linear scales and galaxy lensing at z ∼ 0.5 on smaller scales. We combine with CMB anisotropies to constrain extensions of ΛCDM, limiting neutrino masses to ∑m ν < 0.13 eV (95% c.l.), for example. We describe the mass map and related data products that will enable a wide array of cross-correlation science. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the ΛCDM model, while paving a promising path for neutrino physics with lensing from upcoming ground-based CMB surveys.

The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and Its Implications for Structure Growth

We present new measurements of cosmic microwave background (CMB) lensing over 9400 deg2 of the sky. These lensing measurements are derived from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB data set, which consists of five seasons of ACT CMB temperature and polarization observations. We determine the amplitude of the CMB lensing power spectrum at 2.3% precision (43σ significance) using a novel pipeline that minimizes sensitivity to foregrounds and to noise properties. To ensure that our results are robust, we analyze an extensive set of null tests, consistency tests, and systematic error estimates and employ a blinded analysis framework. Our CMB lensing power spectrum measurement provides constraints on the amplitude of cosmic structure that do not depend on Planck or galaxy survey data, thus giving independent information about large-scale structure growth and potential tensions in structure measurements. The baseline spectrum is well fit by a lensing amplitude of A lens = 1.013 ± 0.023 relative to the Planck 2018 CMB power spectra best-fit ΛCDM model and A lens = 1.005 ± 0.023 relative to the ACT DR4 + WMAP best-fit model. From our lensing power spectrum measurement, we derive constraints on the parameter combination S8CMBL≡σ8Ωm/0.30.25 of S8CMBL=0.818±0.022 from ACT DR6 CMB lensing alone and S8CMBL=0.813±0.018 when combining ACT DR6 and Planck NPIPE CMB lensing power spectra. These results are in excellent agreement with ΛCDM model constraints from Planck or ACT DR4 + WMAP CMB power spectrum measurements. Our lensing measurements from redshifts z ∼ 0.5–5 are thus fully consistent with ΛCDM structure growth predictions based on CMB anisotropies probing primarily z ∼ 1100. We find no evidence for a suppression of the amplitude of cosmic structure at low redshifts.

A new precise determination of the primordial abundance of deuterium: measurement in the metal-poor sub-DLA system at z = 3.42 towards quasar J 1332+0052

ABSTRACT The theory of Big Bang nucleosynthesis, coupled with an estimate of the primordial deuterium abundance (D/H)pr, offers insights into the baryon density of the Universe. Independently, the baryon density can be constrained during a different cosmological era through the analysis of cosmic microwave background anisotropy. The comparison of these estimates serves as a rigorous test for the self-consistency of the standard cosmological model and stands as a potent tool in the quest for new physics beyond the standard model of particle physics. For a meaningful comparison, a clear understanding of the various systematic errors affecting deuterium measurements is crucial. Given the limited number of D/H measurements, each new estimate carries significant weight. This study presents the detection of D i absorption lines in a metal-poor sub-Damped Lyman-α system ($\rm [O/H]=-1.71\pm 0.02$, log N(H i) = 19.304 ± 0.004) at zabs = 3.42 towards the quasar SDSS J133254.51+005250.6. Through simultaneous fitting of H i and D i Lyman-series lines, as well as low-ionization metal lines, observed at high spectral resolution and high signal-to-noise using VLT/UVES and Keck/HIRES, we derive log (D i/H i) = −4.622 ± 0.014, accounting for statistical and systematic uncertainties of 0.008dex and 0.012 dex, respectively. Thanks to negligible ionization corrections and minimal deuterium astration at low metallicity, this D/H ratio provides a robust measurement of the primordial deuterium abundance, consistent and competitive with previous works. Incorporating all prior measurements, the best estimate of the primordial deuterium abundance is constrained as: (D/H)pr = (2.533 ± 0.024) × 10−5. This represents a 5 per cent improvement in precision over previous studies and reveals a moderate tension with the expectation from the standard model (≈2.2σ). This discrepancy underscores the importance of further measurements in the pursuit of new physics.

Patchy screening of the CMB from dark photons

We study anisotropic (patchy) screening induced by the resonant conversion of cosmic microwave background (CMB) photons into dark-sector massive vector bosons (dark photons) as they cross non-linear large scale structure (LSS). Resonant conversion takes place through the kinetic mixing of the photon with the dark photon, one of the simplest low energy extensions to the Standard Model. In the early Universe, resonant conversion can occur when the photon plasma mass, obtained as the photon propagates through the ionized interstellar and intergalactic media, matches the dark photon mass. After the epoch of reionization, resonant conversion occurs mainly in the ionized gas that occupies virialized dark matter halos, for a range of dark photon masses between 10-13 eV ≲ m A' ≲ 10-11 eV. This leads to new CMB anisotropies that are correlated with LSS, which we refer to as patchy dark screening, in analogy with anisotropies from Thomson screening. Its unique frequency dependence allows it to be distinguished from the blackbody CMB. In this paper, we use a halo model approach to predict the imprint of dark screening on the CMB temperature and polarization anisotropies, as well as their correlation with LSS. We then examine the two- and three-point correlation functions of the dark-screened CMB, as well as correlation functions between CMB and LSS observables, to project the sensitivity of future measurements to the kinetic mixing parameter and dark photon mass. We demonstrate that an analysis with existing CMB data can improve upon current constraints on the kinetic mixing parameter by two orders of magnitude with the two-point correlation functions, while data from upcoming CMB experiments and LSS surveys can further improve the reach by another order of magnitude with two- and three-point correlation functions.

Minkowski Functionals in 𝖲𝖮(3) for the spin-2 CMB polarisation field

The study of the angular power spectrum of Cosmic Microwave Background (CMB) anisotropies, both in intensity and in polarisation, has led to the tightest constraints on cosmological parameters. However, this statistical quantity is not sensitive to any deviation from Gaussianity and statistical isotropy in the CMB data. Minkowski Functionals (MFs) have been adopted as one of the most powerful statistical tools to study such deviations, since they characterise the topology and geometry of the field of interest. In this paper, we extend the application of MFs to CMB polarisation data by introducing a new formalism, where we lift the spin 2 polarisation field to a scalar function in a higher-dimensional manifold: the group of rotations of the sphere, SO(3). Such a function is defined as f = Q cos(2ζ) - U sin(2ζ). We analytically obtain the expected values for the MFs of f in the case of Gaussian isotropic polarisation maps. Furthermore, we present a new pipeline which estimates these MFs from input HEALPix polarisation maps. We apply it to CMB simulations in order to validate the theoretical results and the methodology. The pipeline is to be included in the publicly available Python package Pynkowski .

Cosmological constraints from the tomography of DES-Y3 galaxies with CMB lensing from ACT DR4

We present a measurement of the cross-correlation between the MagLim galaxies selected from the Dark Energy Survey (DES) first three years of observations (Y3) and cosmic microwave background (CMB) lensing from the Atacama Cosmology Telescope (ACT) Data Release 4 (DR4), reconstructed over ∼ 436 deg2 of the sky. Our galaxy sample, which covers ∼ 4143 deg2, is divided into six redshift bins spanning the redshift range of 0.20<z<1.05. We adopt a blinding procedure until passing all consistency and systematics tests. After imposing scale cuts for the cross-power spectrum measurement, we reject the null hypothesis of no correlation at 9.1σ. We constrain cosmological parameters from a joint analysis of galaxy and CMB lensing-galaxy power spectra considering a flat ΛCDM model, marginalized over 23 astrophysical and systematic nuisance parameters. We find the clustering amplitude S 8 ≡ σ 8(Ω m /0.3)0.5 = 0.75+0.04 -0.05. In addition, we constrain the linear growth of cosmic structure as a function of redshift. Our results are consistent with recent DES Y3 analyses and suggest a preference for a lower S 8 compared to results from measurements of CMB anisotropies by the Planck satellite, although at a mild level (< 2σ) of statistical significance.

Non-minimal unimodular inflation

We study an extension of the unimodular cosmological inflation in the context of the non-minimal coupling of a generic scalar field with gravitational sector. We consider the non-minimal coupling of the scalar field and gravity as the only source of energy–momentum tensor in this setup. Without introducing new particles other than those already existing in electroweak theory, the generic scalar field’s non-minimal coupling is responsible for the generation of the seeds of perturbations for structure formation and the observed Cosmic Microwave Background anisotropies in this scenario. We calculate inflation parameters in both the Jordan and Einstein frames, and then we study primordial spectral indices for slow-roll parameters in Einstein’s frame at the first and second orders. The numerical results of this model are consistent with the Planck2018 and BICEP/Keck joint data sets in some subspaces of the model parameters space. By considering a sufficient amount of inflation, we estimate the strength of the non-minimal coupling parameter, ξ, to find appropriate new constraints on the values of this parameter. By comparing the numerical values of the inflation observables in two frames and also with observation, we comment on the issue of frames in this framework.

Tracking the multifield dynamics with cosmological data: a Monte Carlo approach

We introduce a numerical method specifically designed for investigating generic multifield models of inflation where a number of scalar fields ϕ K are minimally coupled to gravity and live in a field space with a non-trivial metric 𝒢> IJ (ϕ K ). Our algorithm consists of three main parts. Firstly, we solve the field equations through the entire inflationary period, deriving predictions for observable quantities such as the spectrum of scalar perturbations, primordial gravitational waves, and isocurvature modes. We also incorporate the transfer matrix formalism to track the behavior of adiabatic and isocurvature modes on super-horizon scales and the transfer of entropy to scalar modes after the horizon crossing. Secondly, we interface our algorithm with Boltzmann integrator codes to compute the subsequent full cosmology, including the cosmic microwave background anisotropies and polarization angular power spectra. Finally, we develop a novel sampling algorithm able to efficiently explore a large volume of the parameter space and identify a sub-region where theoretical predictions agree with observations. In this way, sampling over the initial conditions of the fields and the free parameters of the models, we enable Monte Carlo analysis of multifield scenarios. We test all the features of our approach by analyzing a specific model and deriving constraints on its free parameters. Our methodology provides a robust framework for studying multifield inflation, opening new avenues for future research in the field.

Disentangling patchy reionization signatures from primordial gravitational waves using CMB E-mode and B-mode polarization

ABSTRACT The detection of large angular scale B mode in the cosmic microwave background (CMB) polarization signal will open a direct window into not only the primary CMB anisotropies caused by the primordial gravitational waves (PGW) originating in the epoch of inflation, but also the secondary anisotropies imprinted during the epoch of cosmic reionization. The existence of patchiness in the electron density during reionization produces a unique distortion in the CMB B-mode polarization, which can be distinguished from the PGW signal with the aid of spatial frequency modes. In this work, we employ an EB estimator by combining E-mode and B-mode polarization for the τ power spectrum signal generated in a photon-conserving seminumerical reionization model called SCRIPT. We developed a Bayesian framework for the joint detection of the PGW and reionization signal from CMB observations and show the efficacy of this technique for upcoming CMB experiments. We find that, for our model, the τ power spectrum signal effectively tracks the inhomogeneous electron density field, allowing for robust constraints on the patchy B-mode signal. Further, our results indicate that employing the EB estimator for the τ signal will facilitate ground-based CMB-S4 to detect the patchy B-mode signal at approximately ≥2σ confidence level, while observations with space-based PICO will improve this detection to ≥3σ going as high as ≥7σ for extreme reionization models. These findings not only highlight the future potential of these experiments to provide an improved picture of the reionization process but also have important implications towards an unbiased measurement of r.

Minkowski functionals of CMB polarization intensity with pynkowski: theory and application to Planck and future data

ABSTRACT The angular power spectrum of the cosmic microwave background (CMB) anisotropies is a key tool to study the Universe. However, it is blind to the presence of non-Gaussianities and deviations from statistical isotropy, which can be detected with other statistics such as Minkowski functionals (MFs). These tools have been applied to CMB temperature and E-mode anisotropies with no detection of deviations from Gaussianity and isotropy. In this work, we extend the MF formalism to the CMB polarization intensity, P2 = Q2 + U2. We use the Gaussian kinematic formula to derive the theoretical predictions of MFs for Gaussian isotropic fields. We develop a software that computes MFs on P2healpix maps and apply it to simulations to verify the robustness of both theory and methodology. We then estimate MFs of P2 maps from Planck, both in pixel space and needlet domain, comparing them with realistic simulations that include CMB and instrumental noise residuals. We find no significant deviations from Gaussianity or isotropy in Planck CMB polarization intensity. However, MFs could play an important role in the analysis of CMB polarization measurements from upcoming experiments with improved sensitivity. Therefore, we forecast the ability of MFs applied to P2 maps to detect much fainter non-Gaussian anisotropic signals than with Planck data for two future complementary experiments: the LiteBIRD satellite and the ground-based Simons Observatory. We publicly release the software to compute MFs in arbitrary scalar healpix maps as a fully documented python package called pynkowski.

GW_CLASS: Cosmological Gravitational Wave Background in the cosmic linear anisotropy solving system

The anisotropies of the Cosmological Gravitational Wave Background (CGWB) retain information about the primordial mechanisms that source the gravitational waves and about the geometry and the particle content of the universe at early times. In this work, we discuss in detail the computation of the angular power spectra of CGWB anisotropies and of their cross correlation with Cosmic Microwave Background (CMB) anisotropies, assuming different processes for the generation of these primordial signals. We present an efficient implementation of our results in a modified version of CLASS which will be publicly available. By combining our new code GW_CLASS with MontePython, we forecast the combined sensitivity of future gravitational wave interferometers and CMB experiments to the cosmological parameters that characterize the cosmological gravitational wave background.

Conditions for the absence of infrared sensitivity in cosmological probes in any gravity theories

Large-scale surveys allow us to construct cosmological probes such as galaxy clustering, weak gravitational lensing, the luminosity distance, and cosmic microwave background anisotropies. The gauge-invariant descriptions of these cosmological probes reveal the presence of numerous relativistic effects in the cosmological probes, and they are sensitive (or even divergent) to the long wave-length fluctuations in the initial conditions. In the standard ΛCDM model, this infrared sensitivity is absent due to subtle cancellations among the relativistic contributions, once the Einstein equation is used. Here we derive the most general conditions for the absence of infrared sensitivity in the cosmological probes without committing to general relativity. We discuss the implications of our results for gravity theories beyond general relativity.

A bias using the ages of the oldest astrophysical objects to address the Hubble tension

Recently different cosmological measurements have shown a tension in the value of the Hubble constant, H_0. Assuming the Lambda CDM model, the Planck satellite mission has inferred the Hubble constant from the cosmic microwave background (CMB) anisotropies to be H_0 = 67.4 pm 0.5 , text {km} , text {s}^{-1} , text {Mpc}^{-1}. On the other hand, low redshift measurements such as those using Cepheid variables and supernovae Type Ia (SNIa) have obtained a significantly larger value. For instance, Riess et al. reported H_0 = 73.04 pm 1.04 , text {km} , text {s}^{-1} , text {Mpc}^{-1}, which is 5sigma apart of the prediction from Planck observations. This tension is a major problem in cosmology nowadays, and it is not clear yet if it comes from systematic effects or new physics. The use of new methods to infer the Hubble constant is therefore essential to shed light on this matter. In this paper, we discuss using the ages of the oldest astrophysical objects (OAO) to probe the Hubble tension. We show that, although this data can provide additional information, the method can also artificially introduce a tension. Reanalyzing the ages of 114 OAO, we obtain that the constraint in the Hubble constant goes from slightly disfavoring local measurements to favoring them.

Cosmic Microwave Background Radiation (CMB), the Observable and Non-Observable Universes, and Their Respective Distances

Guided by the monumental Big Bang theory, this research paper embarks on a captivating exploration of cosmic vistas, delving into the enigmatic origins of the universe, the enigmatic cosmic microwave background radiation (CMBR), and the intricate interplay between observable and non- observable universes. Intricately woven into this cosmic fabric are the pioneering observations of the Cosmic Background Explorer (COBE), the Wilkinson Microwave Anisotropy Probe (WMAP), and the Planck satellite. These scientific sentinels have charted the CMBR's temperature fluctuations, offering windows into the universe's earliest epochs. COBE's revelation of temperature variations in 1992 solidified the Big Bang theory. WMAP, launched in 2001, delved deeper, unraveling the CMBR's anisotropies and refining cosmic parameter measurements. The Planck satellite, soaring into space in 2009, etched precision onto the cosmic canvas, encapsulating the universe's age, composition, and evolutionary trajectory. This narrative unfolds the epic tale of emergence from a minuscule singularity and the subsequent grand cosmic inflation. At the heart of this cosmic odyssey lies the CMBR, a whispered echo from the universe's primordial dawn that unfolds the saga of its early epochs and the daring journey of the first light. The tapestry of time itself is probed, unveiling the temporal intricacies of these realms shaped by phenomena like redshift and the relentless cosmic expansion. Across a 13.8-billion-year narrative, our observational prowess extends to reveal galaxies within a 46.5 billion light-year radius—43% visible, 57% veiled. Anchored by elegant mathematical frameworks like Hubble's Law, this journey through cosmic mechanics nurtures the growth of understanding and discovery. An expedition both poetic and scientific, this paper unearths the blueprint of the universe, resonating with themes of curiosity and evolution that span unfathomable eons.

A Cross-internal Linear Combination Approach to Probe the Secondary CMB Anisotropies: Kinematic Sunyaev–Zel’dovich Effect and CMB Lensing

We propose a cross-internal linear combination (cross-ILC) approach to measure the small-scale cosmic microwave background (CMB) anisotropies robustly against the contamination from astrophysical signals. In particular, we focus on the mitigation of systematics from cosmic infrared background (CIB) and thermal Sunyaev–Zel’dovich (tSZ) signals in kinematic Sunyaev–Zel’dovich (kSZ) power spectrum and CMB lensing. We show the cross-spectrum measurement between two CMB maps created by nulling the contributions from CIB (CIB-free map) and tSZ (tSZ-free map) to be robust for kSZ, as the approach significantly suppresses the total contribution of CIB and tSZ signals. Similarly, for CMB lensing, we use the approach introduced by Madhavacheril & Hill but with a slight modification by using the tSZ-free and CIB-free maps in the two legs of the quadratic estimator. By cross-correlating the CMB lensing map created using this technique with galaxy surveys, we show that the biases from both CIB and tSZ are negligible. We also compute the impact of unmodeled CIB/tSZ residuals on kSZ and cosmological parameters, finding the kSZ measured using the standard ILC to be significantly biased. The kSZ estimate from the cross-ILC remains less affected by CIB/tSZ, making it crucial for current and upcoming CMB surveys such as the South Pole Telescope (SPT), Simons Observatory (SO), and CMB-S4. With the cross-ILC approach, we find that the total kSZ power spectrum can be measured at very high significance in the coming years: 35σ by SPT, 22σ by SO, and 80σ by CMB-S4. Finally, we forecast constraints on the epoch of reionization using the kSZ power spectrum and find that the duration of reionization, currently unconstrained by Planck, can be constrained to = 1.5 or 0.5 depending on the choice of the prior on the optical depth to reionization. The data products and the associated codes can be downloaded from this link (https://github.com/sriniraghunathan/cross_ilc_methods_paper).

Tomographic Alcock–Paczyński Test with Redshift-space Correlation Function: Evidence for the Dark Energy Equation-of-state Parameter w > −1

The apparent shape of galaxy clustering depends on the adopted cosmology used to convert observed redshift to comoving distance, the r(z) relation, as it changes the line elements along and across the line of sight differently. The Alcock–Paczyński (AP) test exploits this property to constrain the expansion history of the universe. We present an extensive review of past studies on the AP test. We adopt an extended AP test method introduced by Park et al., which uses the full shape of redshift-space two-point correlation function (CF) as the standard shape, and apply it to the Sloan Digital Sky Survey DR7, BOSS, and eBOSS LRG samples covering the redshift range up to z = 0.8. We calibrate the test against the nonlinear cosmology-dependent systematic evolution of the CF shape using Multiverse simulations. We focus on examining whether or not the flat Lambda cold dark matter (ΛCDM) concordance model is consistent with observation. We constrain the flat wCDM model to have and from our AP test alone, which is significantly tighter than the constraints from the BAO or SNe Ia methods by a factor of 3–6. When the AP test result is combined with the recent BAO and SNe Ia results, we obtain and . This puts a strong tension with the flat ΛCDM model with w = −1 at the 4.2σ level. Consistency with w = −1 is obtained only when the Planck cosmic microwave background (CMB) observation is combined. It remains to be seen whether this tension between observations of galaxy distribution at low redshifts and CMB anisotropy at the decoupling epoch becomes greater in future studies and leads us to a new paradigm of cosmology.

Primordial black holes from single-field inflation: a fine-tuning audit

All single-field inflationary models invoke varying degrees of tuning in order to account for cosmological observations. Mechanisms that generate primordial black holes (PBHs) from enhancement of primordial power at small scales posit inflationary potentials that transiently break scale invariance and possibly adiabaticity over a range of modes. This requires additional tuning on top of that required to account for observations at scales probed by cosmic microwave background (CMB) anisotropies. In this paper we study the parametric dependence of various single-field models of inflation that enhance power at small scales and quantify the degree to which coefficients in the model construction have to be tuned in order for certain observables to lie within specified ranges. We find significant tuning: changing the parameters of the potentials by between one part in a hundred and one part in 108 (depending on the model) is enough to change the power spectrum peak amplitude by an order one factor. The fine-tuning of the PBH abundance is larger still by 1–2 orders of magnitude. We highlight the challenges imposed by this tuning on any given model construction. Furthermore, polynomial potentials appear to require significant additional fine-tuning to also match the CMB observations.

Angular correlations on causally-coherent inflationary horizons

We develop a model for correlations of cosmic microwave background (CMB) anisotropy on the largest angular scales, based on standard causal geometrical relationships in slow-roll inflation. Unlike standard models based on quantized field modes, it describes perturbations with nonlocal directional coherence on spherical boundaries of causal diamonds. Causal constraints reduce the number of independent degrees of freedom, impose new angular symmetries, and eliminate cosmic variance for purely angular 2-point correlations. Distortions of causal structure from vacuum fluctuations are modeled as gravitational memory from randomly oriented outgoing and incoming gravitational null shocks, with nonlocally coherent directional displacements on curved surfaces of causal diamonds formed by standard inflationary horizons. The angular distribution is determined by axially symmetric shock displacements on circular intersections of the comoving sphere that represents the CMB photosphere with other inflationary horizons—those centered on it, and those that pass through an observer’s world line. Displacements on thin spheres at the end of inflation have a unique angular power spectrum that approximates the standard expectation on small angular scales, but differs substantially at large angular scales due to horizon curvature. For a thin sphere, the model predicts a universal angular correlation function with an exact ‘causal shadow’ symmetry, , and significant large-angle parity violation. We apply a rank statistic to compare models with WMAP and Planck satellite data, and find that a causally-coherent model with no shape parameters or cosmic variance agrees with the measured better than a large fraction () of standard model realizations. Model-independent tests of holographic causal symmetries are proposed.