Primordial and Cosmological Probes

The early universe can amplify microscopic quantum effects into correlations across the sky, but amplification does not make a signal unique. A primordial feature must be derived from a state and dynamics, propagated through reheating and photon transfer, and compared with conventional inflationary features, foregrounds, and statistical fluctuations in the same likelihood. Present data constrain parameterized spectra and relic populations; they do not identify a quantum-gravity theory.

Required background. Equivalence Principles and Gravitational Measurement supplies the distinction between relational observables and coordinate artifacts in the early universe.

Helpful background. Flat-Spacetime Quantum Field Theory supplies mode functions and correlators; Einstein Equations supplies the background and perturbation constraints; Quantum Information supplies state discrimination; Quantum Gravity supplies microscopic claim boundaries; and Gravitational Radiation and Waveforms supplies stochastic-background inference.

From a microscopic state to a normalized template

Let $\mathcal R$ be the comoving curvature perturbation, with Fourier convention $\mathcal R(\mathbf x)=\int d^3k\,(2\pi)^{-3}e^{i\mathbf k\cdot\mathbf x}\mathcal R_{\mathbf k}$. Use comoving $k$ and normalize today’s scale factor to one. For a homogeneous isotropic state, define the dimensionless scalar spectrum by

$$\langle\mathcal R_{\mathbf k}\mathcal R_{\mathbf k'}\rangle =(2\pi)^3\delta^3(\mathbf k+\mathbf k') \frac{2\pi^2}{k^3}\mathcal P_{\mathcal R}(k).$$

A modified initial state may be written relative to a declared positive-frequency basis as

$$v_k=\alpha_kv_k^{(0)}+\beta_kv_k^{(0)*}, \qquad \lvert\alpha_k\rvert^2-\lvert\beta_k\rvert^2=1.$$

When the reference late-time mode is chosen real, the leading scalar modification is

$$\mathcal P_{\mathcal R}(k) =\mathcal P_{\mathcal R}^{(0)}(k) \lvert\alpha_k+\beta_k\rvert^2.$$

This is not yet a prediction. A model must fix $\beta_k$, its phase, ultraviolet falloff, matching surface, and relation to the same parameters in tensors and higher-point functions. Its excitation energy,

$$\rho_\beta\sim \frac{1}{a^4}\int\frac{d^3k}{(2\pi)^3}\, k\lvert\beta_k\rvert^2,$$

must remain small compared with the background energy density; otherwise the assumed geometry is not self-consistent. Bounce matching, discrete dynamics, or a boundary-state proposal faces the analogous task: derive a dimensionful scale and phase rather than fit an unrestricted oscillation.

Photon transfer turns the primordial template into several observables,

$$C_\ell^{XY} =4\pi\int d\ln k\, \mathcal P_{\mathcal R}(k) \Delta_\ell^X(k)\Delta_\ell^Y(k)+C_{\ell,\mathrm{tensor}}^{XY},$$

with $X,Y\in\{T,E\}$ and a corresponding treatment for $B$ modes and lensing. A credible mechanism predicts a shared pattern in $TT$, $TE$, $EE$, polarization, and—where applicable—the bispectrum or a stochastic gravitational-wave background.

What can be discriminating?

Mechanism-level input	Required cross-observable pattern	Conventional competitor or failure test
Excited or boundary initial state	Phase-related oscillations in scalar spectra and bispectra, with a declared cutoff	A feature in the inflationary potential, non-adiabatic reheating, or flexible foreground residuals
Pre-inflationary high-curvature phase	Linked suppression, oscillation scale, and tensor transfer fixed by one matching history	Cosmic variance, ordinary fast-roll evolution, and dependence on the number of inflationary e-folds
Primordial tensor modification	$B$-mode shape plus tensor tilt or chirality tied to the same operators	Dust, synchrotron, lensing, calibration angle, and non-quantum-gravity parity violation
Relic population or defect network	CMB, lensing, burst, or stochastic-background rates from one abundance and evolution model	Astrophysical populations, network uncertainty, and selection-dependent searches
Primordial non-Gaussian state	A normalized bispectrum or trispectrum whose phase and scale dependence match the two-point feature	Standard multifield dynamics, secondary anisotropies, masks, and estimator look-elsewhere effects

Planck’s standard local, equilateral, and orthogonal bispectrum estimators are consistent with Gaussian initial conditions, but those bounds apply to their named shapes and analysis choices Planck Collaboration 2020, §§5–8. They do not automatically constrain a sharply localized or oscillatory quantum-gravity template. Conversely, an isolated low-multipole residual cannot select a microscopic mechanism.

Data products, calibration, and selections

The pinned large-scale baseline is Planck 2018 Public Release 3 (PR3), using likelihood code COM_Likelihood_Code-v3.0_R3.01 and baseline data COM_Likelihood_Data-baseline_R3.00, together with the released maps, beams, masks, simulations, and lensing products in the official archive European Space Agency 2018–2019, PR3 cosmology record. The baseline likelihood combines high-multipole plikHM $TT$, $TE$, and $EE$, low-multipole temperature and lowE polarization, and lensing when the tested model requires it.

For tensors, the pinned product is BICEP/Keck BK18, the multifrequency analysis through the 2018 observing season. It fits BICEP/Keck, WMAP, and Planck auto- and cross-spectra with lensed $\Lambda$CDM, dust, synchrotron, noise, and $r$; the primary analysis reports $r_{0.05}\lt0.036$ as a 95% posterior upper limit, an upper limit rather than a detection BICEP/Keck Collaboration 2021, pp. 2–7. The collaboration’s 2024 status paper identifies BK18 as the current published constraint while describing later seasons and delensing as ongoing improvements BICEP/Keck Collaboration 2024, §§2–4.

Here $r_{0.05}$ is the tensor-to-scalar primordial power ratio at the comoving pivot $k_*=0.05\,\mathrm{Mpc}^{-1}$, summing both tensor polarizations. The quoted posterior bound conditions on the adopted tensor spectrum, foreground model, and prior $r\ge0$; it is not a model-independent limit on all primordial gravitational waves.

An independent small-scale product available at the cutoff is ACT DR6.02, containing 90, 150, and 220 GHz maps from 2017–2022, beam and passband products, masks, spectra, covariance files, chains, and full and CMB-only likelihoods ACT Collaboration 2025, official DR6.02 product page. Its baseline spectra are well fit by $\Lambda$CDM Louis et al. 2025, §§3–8, but a feature analysis would still require a dedicated trials-calibrated template search.

Selections must declare sky masks, multipole ranges, frequencies, cross-spectra, feature position and width, relic population cuts, and every scan over phase, scale, direction, or shape. Calibration must propagate gain, beams, temperature-to-polarization leakage, polarization efficiency and angle, filtering transfer functions, passbands, foreground covariance, and lensing reconstruction. Cross-survey combinations also require common-sky and calibration covariance rather than multiplying nominally independent likelihoods.

Likelihood, priors, and current evidence

For parameters $\theta$ and nuisance variables $\eta$, the data model is

$$\mathcal L(D\mid\theta,\eta) \propto \exp\!\left[ -\frac12 (\widehat{\mathbf C}-\mathbf C(\theta,\eta))^{T} \mathbf\Sigma^{-1} (\widehat{\mathbf C}-\mathbf C(\theta,\eta)) \right],$$

or the corresponding released non-Gaussian low-multipole likelihood. Priors on oscillation frequency, phase, width, cutoff, reheating history, foregrounds, and calibration determine both posterior volume and look-elsewhere cost. A likelihood-ratio maximum over many templates must be calibrated on simulations passed through the same masks and selection pipeline. A Bayes factor must state the complete prior volume and theory error.

This discussion reflects results available through 2026-08-20. Planck PR3, BK18, and ACT DR6.02 remain consistent with conventional primordial spectra within their tested model spaces; the Planck inflation analysis gives the PR3 model and likelihood scope in Planck Collaboration 2020, §§3–7. PR3 is the pinned reproducible baseline, while Planck PR4/NPIPE CamSpec supplies a current robustness check. A public 2026 preprint finds local improvements up to roughly $\Delta\chi^2=-15$ for some oscillatory templates but no Bayesian support; the largest PR4 global significance is $1.7\sigma$, and several PR3 candidates weaken Raffaelli, Ballardini, and Barbieri 2026, §6, pp. 19–20. This is a quoted cross-check, not an independent rerun.

Product or analysis	Version and statistic	Interpretation boundary
Planck spectra, lensing, and inflation constraints	PR3 likelihood packages named above	Cosmic variance and foreground/likelihood choices dominate some feature scales
Planck feature robustness	PR4/NPIPE CamSpec public preprint analysis	Local improvements lose strength after prior volume and global trials
BICEP/Keck polarization	BK18 through 2018; posterior upper limit on $r_{0.05}$	Constrains tensor amplitude within the foreground and spectral model
ACT temperature and polarization	DR6.02 maps, spectra, covariance, and likelihoods	High-resolution consistency is not a dedicated quantum-gravity feature search

Reproduction status. No Planck, BK18, or ACT likelihood was rerun for this page, and no numerical fit or null injection is claimed. A clean reproduction would record product checksums, exact likelihood commits and environments, masks, parameter files, priors, seeds, chain convergence, nuisance posteriors, and simulated maximum-statistic distributions. Until that work is performed, published statistics remain attributed results.

Exercise

A feature scan tests 80 approximately independent frequencies. Its best local one-sided $p$-value is $2\times10^{-3}$. Estimate the global false-alarm probability and explain why this estimate is not yet the final significance.

Solution

For independent trials,

$$p_{\mathrm{global}} =1-(1-0.002)^{80} \approx0.148.$$

The chance of at least one equally strong fluctuation is about 15%, so the local excess is not compelling. Real feature templates overlap, while nuisance refitting, masks, and boundaries make the trials non-independent. The final global statistic must therefore be calibrated with simulations that repeat the complete search. Even a smaller global probability would support the declared feature template, not quantum gravity generically.

References

• ACT Collaboration (2025), “ACT DR6.02 Data Release,” NASA LAMBDA, official product record.
• BICEP/Keck Collaboration (2021), “BICEP/Keck XIII: Improved Constraints on Primordial Gravitational Waves Using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,” Physical Review Letters 127, 151301, doi:10.1103/PhysRevLett.127.151301, Open PDF.
• BICEP/Keck Collaboration (2024), “Constraining Inflation with the BICEP/Keck CMB Polarization Experiments,” arXiv:2405.19469.
• European Space Agency (2018–2019), “Planck PR3 Cosmology Products,” Planck Legacy Archive, official release record.
• Louis, Thibaut, et al. (2025), “The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters,” Journal of Cosmology and Astroparticle Physics 2025(11), 062, doi:10.1088/1475-7516/2025/11/062.
• Planck Collaboration (2020), “Planck 2018 Results. IX. Constraints on Primordial Non-Gaussianity,” Astronomy & Astrophysics 641, A9, doi:10.1051/0004-6361/201935891, Open PDF.
• Planck Collaboration (2020), “Planck 2018 Results. X. Constraints on Inflation,” Astronomy & Astrophysics 641, A10, doi:10.1051/0004-6361/201833887, Open PDF.
• Raffaelli, Antonio, Mario Ballardini, and Nicola Barbieri (2026), “Signals from the Early Universe: A Comprehensive Search for Primordial Features in Planck CMB Datasets,” preprint, arXiv:2605.30236.