Cosmological Timeline · Bounce to SPHEREx
The Cosmic Timeline
From the parent universe to SPHEREx: what bounce cosmology predicts at every stage.
This page traces the history of a bouncing universe from beginning to experimental verdict. Each epoch shows what happens physically, what the theory predicts, and where key equations enter. Read it like a museum exhibit: top to bottom, past to future.
The Parent Universe
A massive star in a parent universe collapses into a rotating black hole. Inside the event horizon, matter density increases relentlessly toward the Planck scale (\(\rho_{\rm Pl} \approx 5.16 \times 10^{96}\;\text{kg/m}^3\)). In standard general relativity, this collapse ends in a singularity — a point of infinite density where physics breaks down.
But in loop quantum cosmology (LQC), quantum geometry effects become important before the singularity forms. The interior of the black hole is about to become a new universe.
Matter-Dominated Contraction
The contracting phase is dominated by dust-like matter with equation of state \(w \approx 0\). This is the key prediction engine. During this phase, perturbations grow as \(|\eta|^{-3}\) on superhorizon scales, dramatically amplifying any primordial fluctuations.
The Maldacena cubic action evaluated in this matter-dominated background, with slow-roll parameter \(\varepsilon = 3/2\), produces a specific, parameter-free non-Gaussianity:
This value is 300 times larger than what standard slow-roll inflation predicts (\(f_{\rm NL}^{\rm local} \sim 0.01\)) and opposite in sign. It depends only on the contraction being matter-dominated — no free parameters, no model tuning.
The Bounce
At the critical density, quantum gravity effects (LQC holonomy corrections) replace the singularity with a smooth transition. The Hubble parameter \(H\) passes through zero and reverses sign: contraction becomes expansion. No singularity occurs.
The correction factor \((1 - \rho/\rho_{\rm crit})\) is the entire mechanism: when \(\rho \to \rho_{\rm crit}\), the right-hand side vanishes, forcing \(H = 0\). For \(\rho > \rho_{\rm crit}/2\), gravity effectively becomes repulsive. A new expanding region — a baby universe — begins. It inherits angular momentum from the parent black hole's rotation.
Perturbation Transmission
Do the perturbations from the contracting phase survive the bounce? At linear order (the power spectrum), the answer is yes — verified by Wilson-Ewing (2012). Perturbations transmit faithfully through the LQC bounce.
At cubic order (the bispectrum, where the \(f_{\rm NL}\) prediction lives), this has not yet been verified. This is a key assumption of the program. If the bounce disrupts the bispectrum, the \(f_{\rm NL} = -35/8\) prediction would be modified or destroyed.
This is one of the honest gaps we document. See Paper 2 for the full discussion.
Inflation
After the bounce, slow-roll inflation proceeds normally. This phase solves the standard problems of cosmology — flatness, horizon, monopole — exactly as in the conventional picture.
Here is a crucial fact: the bounce adds nothing observable during this phase. This is the "perturbation transparency" result. The bounce mechanism (holonomy corrections, torsion, etc.) is invisible at energy scales below \(\rho_{\rm crit}\). All memory of the bounce geometry is erased except for the primordial perturbation spectrum established during contraction, which is now frozen into the expanding universe.
This is why we found 14 structural barriers when trying to connect the bounce to dark energy — the two problems are separated by the transparency wall.
Recombination & the CMB
The universe cools enough for neutral atoms to form. CMB photons stream freely for the first time — the oldest light we can observe.
Two signatures are encoded in this light:
1. Bispectrum. The \(f_{\rm NL} = -35/8\) signal from contraction is imprinted in the three-point correlation function of CMB temperature fluctuations. Planck has measured \(f_{\rm NL}^{\rm local} = -0.9 \pm 5.1\), which is consistent with our prediction but not precise enough to confirm or exclude it.
2. Birefringence. If a Planck-scale axion-like particle (ALP) with decay constant \(f_a \sim M_{\rm Pl}\) exists, its field begins evolving after recombination, rotating the polarization plane of CMB photons:
This prediction uses only natural parameter values: \(f_a \sim M_{\rm Pl}\), \(\Delta a \sim f_a\). No tuning required.
Structure Formation
As galaxies form, the \(f_{\rm NL}\) signature imprints on their spatial distribution through scale-dependent bias:
The key feature: the effect scales as \(1/k^2\), so it is strongest on the largest observable scales. With \(f_{\rm NL} = -4.375\) (versus the inflationary prediction of ~0.01), the bounce signal is enormously amplified. Galaxy surveys targeting these large scales are the most powerful tool for detecting it.
Today
Current observational status:
Our MCMC verification (424,000+ posterior samples) confirms: \(H_0 = 67.68\;\text{km/s/Mpc}\), \(\Delta N_{\rm eff} \approx 0\). The spin-torsion coupling does not shift standard cosmological parameters. This is consistent with the perturbation-transparency result.
We have cataloged 14 structural barriers that close all minimal routes from the bounce to dark energy. The bounce and late-time acceleration are independent problems. But the two predictions above — \(f_{\rm NL}\) and \(\beta\) — survive, because they depend on contraction dynamics and natural ALP scales, not on the bounce mechanism itself.
SPHEREx
NASA's SPHEREx mission will survey 450 million galaxies in the near-infrared, measuring \(f_{\rm NL}^{\rm local}\) to a precision of \(\sigma(f_{\rm NL}) \approx 0.8\text{–}1.0\).
At that precision, the bounce prediction \(f_{\rm NL} = -4.375\) would be detected at ~5.5σ significance (template-corrected).
Bayes factor ~8-17:1 (prior-dependent) in favor of the matter bounce over tuned multifield competitors. The strongest evidence yet that the universe bounced.
The quasi-dust matter bounce is ruled out at >4σ. The model is falsified cleanly. No wiggle room.
LiteBIRD
JAXA's LiteBIRD satellite (JFY2032) will map CMB polarization across the full sky with unprecedented precision, measuring the birefringence angle \(\beta\) to \(\sigma(\beta) \approx 0.03°\).
At that precision, the ALP prediction \(\beta = 0.27°\) would be confirmed at ~9σ significance — a decisive result.
If confirmed, this establishes the existence of a Planck-scale ALP with precisely the properties expected from quantum gravity. While the birefringence prediction is bounce-independent (it works in any cosmology with this ALP), its confirmation would strongly motivate the broader framework.
The Verdict
Within five years, we will know if the universe bounced.
SPHEREx tests the bounce-specific prediction (\(f_{\rm NL} = -35/8\)). LiteBIRD tests the ALP prediction (\(\beta = 0.27°\)). Both are sharp, parameter-free, and falsifiable. Both use missions that are already funded and scheduled.
This is not a "maybe someday" situation. The data is coming. The predictions are on the record. The theory either survives or it doesn't.