Zero-parameter cosmological concordance

from entanglement entropy

We confront the entanglement entropy prediction of the cosmological
constant with the full landscape of modern cosmological data-28
observables spanning the CMB, baryon acoustic oscillations (BAO),
redshift-space distortions, weak gravitational lensing, Type Ia
supernovae, and Hubble parameter measurements-using zero free dark
energy parameters.  The framework predicts
, where 
and  are determined exactly by the Standard Model field content
and the graviton, and the area-law coefficient
 is measured on the lattice to 
precision.  Against Planck 2018, the prediction sits at 
with  for four CMB observables.  Against 15
redshift-space distortion measurements, -better
than the Planck best fit.  Across all 26 data points from five probe
classes, the framework achieves a lower total  (172.65)
than the Planck  best fit (178.02), winning on three of five
probe classes despite having one fewer parameter.  Bayesian model
comparison using the Savage-Dickey density ratio yields a proper
Bayes factor of - in favour of the framework over ,
with the BIC approximation underestimating the true Occam factor
by .  The equation of state is  exactly, a
theorem rather than an assumption; current DESI Y1 CDM
tension () is shown to fail all four diagnostic criteria
for genuine new physics and is Bayes-disfavoured .
The framework predicts kmsMpc
(consistent with Planck,  from SH0ES) and
eV (normal hierarchy minimum).  We provide
pre-registered predictions for DESI Y3 and Euclid, and identify
DESI Y5 as the decisive falsification test.

Introduction
The cosmological constant problem-the -fold mismatch
between the quantum field theory vacuum energy and the observed
dark energy density-has resisted resolution for
decades .  In the standard 
concordance model,  is a free parameter fit to
data .  Companion papers 
 have developed a framework in
which  is instead predicted from the entanglement entropy
of quantum fields across the cosmological horizon, via the
Jacobson-Cai-Kim horizon thermodynamics .
The prediction depends on two UV quantities-the area-law coefficient
 and the logarithmic (trace anomaly) coefficient -summed
over all Standard Model fields and the graviton, with zero adjustable
dark energy parameters.

The purpose of this paper is not to re-derive the prediction but to
test it.  We take the framework's output-a single number,
-and ask how it fares against every major class of
cosmological observation available in 2025.  The answer is surprisingly
good: the zero-parameter prediction fits the data as well as, or
better than, the one-parameter  fit across most probes.

The paper is organised as follows.
Section  summarises the prediction and its inputs.
Section  confronts it with the CMB.
Section  performs a bin-by-bin BAO analysis using DESI DR1.
Section  tests the growth rate .
Section  derives the parameter-free  prediction.
Section  extracts a neutrino mass constraint.
Section  examines the equation of state.
Section  presents the full Bayesian model comparison.
Section  analyses the global tension minimum.
Section  confronts DESI covariance and survival probability.
Section  discusses limitations and pre-registered predictions.
The prediction
The entanglement entropy of a free field across a spherical entangling
surface of radius  takes the form

where  is the area,  the UV cutoff,
 the area-law coefficient, and  the logarithmic
coefficient determined by the conformal trace
anomaly .

The companion derivation  shows that the
Cai-Kim first law applied at the cosmological horizon, combined with
the assumption  ,
yields the self-consistency condition

where  and
 sum over all field species.

Inputs

The prediction requires three classes of input, all determined
independently of cosmological data:

Trace anomaly coefficients .
These are exact, protected by the Adler-Bardeen non-renormalization
theorem:

For the graviton, only the entanglement entropy component contributes
(edge modes are gauge artifacts that do not enter the Clausius
relation ):
Field content.
The Standard Model contains 4 real scalars (Higgs doublet),
45 Weyl fermions, and 12 gauge bosons (vectors).  The graviton adds
one additional species.  The effective scalar degrees of freedom are

where the heat kernel ratios 
and  are confirmed on the lattice
to  , and the graviton screening
fraction  is derived from the Benedetti-Casini and
Christensen-Duff values 
.

Area-law coefficient .
The only quantity requiring numerical computation.
Richardson extrapolation on the Srednicki radial lattice
gives 
confirmed to  precision via double-limit 
extrapolation.

The number

Substituting:

and

This is the single number against which all observational tests
in this paper are performed.  Every other cosmological parameter
follows from  combined with standard physics (flatness,
CMB acoustic peaks, BBN).
CMB concordance
The Planck 2018 constraint on the dark energy
density  is .  The
framework prediction sits at

We derive the remaining cosmological parameters from  via
the standard  relations.  Flatness gives .  The CMB acoustic scale determines
 , yielding
 and hence kmsMpc.
Framework predictions vs. Planck 2018 best fit.
All framework values follow from  plus standard
physics; no parameters are fit to cosmological data.
Table  shows the comparison.  All five parameters
lie within  of the Planck best fit.  The joint CMB
test gives  for three independent observables
(, , ) with zero free parameters:
.  This is a better fit than most
one-parameter models achieve.
Baryon acoustic oscillations
The DESI DR1 BAO measurement  provides 12 data points
(transverse comoving distance  and Hubble distance 
at six effective redshifts).  We compute the framework predictions
using the predicted  and the Planck-calibrated
, with no free parameters.
DESI DR1 BAO bin-by-bin comparison.  Pulls are given
for both the framework () and Planck 
().
Table  presents the results.  Two bins show
tension at : LRG1  at  and LRG2 
at .  These same bins are in tension with Planck 
at comparable levels, indicating the tension is with 
generically, not with the framework specifically.  The framework-Planck
 is only 1.37 across 12 bins; the two models are
observationally indistinguishable at DESI DR1 precision.

Including the full DESI covariance matrix increases 
by  to  (, ).
The BAO-only best-fit dark energy density is , a  pull from the framework.
We return to this tension in Section .
Structure growth:  and 
The growth rate  is measured
via redshift-space distortions (RSD) and provides a test
independent of the distance-redshift relation.  The framework
predicts  and , following from  and the standard linear
growth function.

RSD test

We compare against 15 RSD measurements spanning 
to , including six DESI DR1 data points.  The results are:

The framework gives  per measurement versus
 for Planck-a better fit with one fewer free parameter.
No individual measurement deviates by more than .
The mean pull is , consistent with zero bias.

For DESI-only RSD data:
 per point.

 tension

The framework's  shifts the prediction toward weak
lensing surveys relative to Planck's :
The  tension is reduced by - per survey,
moving in the right direction but not resolving the discrepancy.
The total  against four lensing surveys drops from 31.5
(Planck) to 24.9 (framework), an improvement of .
Hubble parameter prediction
The framework turns  from a free parameter into a derived
quantity.  The chain is:

where the uncertainty comes entirely from 
(CMB acoustic peak spacing).
Framework  compared with measurements.
The prediction uses zero free dark energy parameters.
Table  shows the confrontation.  The framework
agrees with Planck (), DESI+CMB (),
and the CCHP TRGB measurement ().  It disagrees
with SH0ES Cepheid-calibrated supernovae at .  This
tension is not specific to the framework: Planck  disagrees
with SH0ES at .  The framework shifts  upward
by kmsMpc-the correct direction
toward the distance ladder-but covers only  of the gap.

A notable coincidence: if the graviton had only 
transverse-traceless modes (instead of the correct  from
edge mode counting),  would be , giving
kmsMpc-almost exactly the
SH0ES value.  The data require the full covariant count.

An independent route via BBN

A second, fully independent route uses only the predicted
, BBN deuterium (),
and the CMB acoustic scale ():

This pure-prediction route sits  below Planck and
 below SH0ES.  The kmsMpc
gap between routes measures the additional constraining power of
the full CMB power spectrum shape beyond the acoustic peak positions
alone.  Both routes exclude  at .
Neutrino mass constraint
In ,  and  are degenerate: increasing
the neutrino mass raises  at the expense of .
The framework breaks this degeneracy by fixing .  Every
electron-volt of neutrino mass must come from ,
not from .

Using Planck's constraint 
and the framework's :

where the central value coincides exactly with the normal hierarchy
minimum (eV).  The inverted
hierarchy minimum (eV) lies at
.
Neutrino mass and its cosmological impact.
Table  shows the progression.  At the normal
hierarchy minimum, -between Planck's  and the
weak lensing consensus of .  The framework naturally
selects the minimal neutrino mass, consistent with oscillation data
and the recent DESI+Planck bound eV
(95% CL) .
Equation of state:  exactly
The framework predicts  as a theorem, not an
assumption.  The argument is as follows: the trace anomaly coefficient
 is mass-independent for  (verified on the
lattice to  ).  All Standard
Model particles satisfy  to , deep
in the massless regime.  Since  sets , and  is
mass-independent and scale-independent,  does not evolve: 
identically.

This sharply confronts DESI Y1.  Combined with Planck and Type Ia
supernovae, DESI reports  in the CDM
parameterisation- from  .

The systematic case against 

We apply four diagnostic criteria for genuine new physics in the
 signal :

[label=(*)]
Cross-compilation consistency.
  The SN tension varies from  (Pantheon+) to 
  (DESY5).  Fails.
BAO-only evidence.
  BAO data alone prefer .  Fails.
Signal exceeds systematics.
  The maximum distance-modulus signal is 44mmag;
  the host-mass step systematic is 60mmag.  Fails.
Peak redshift independence.
  The signal peaks at -, coinciding with the
  host-mass systematic peak.  Fails.
The signal fails all four criteria (0/4).

Bayesian model selection:  vs 
Model comparison at DESI DR1 BAO.
Table  shows that CDM fits the BAO data
only  better than the framework, while
its two extra parameters incur a BIC penalty of .
The net Bayes factor is  in favour of the framework.

The DESI best-fit CDM requires phantom dark energy
() at , violating the null energy condition.
This is a second reason to doubt the physical reality of the
signal.

Forecast

If the  trend persists, DESI Y4 (2027) is the
crossover point where BIC shifts against the framework.
If the trend is a fluctuation, DESI Y3 will see 
converge toward , with a Bayes factor of 
in the framework's favour.
Bayesian model comparison
The framework replaces one free dark energy parameter
() with a prediction.  The proper Bayesian evidence comparison
requires computing the Occam factor-the ratio of the predictive
prior volume to the posterior volume-which the BIC approximation
dramatically underestimates.

Savage-Dickey density ratio

For a nested model comparison (framework is  restricted to
), the Bayes factor is 
where  is the prior at the predicted value and
 the posterior.
Bayes factors for framework vs. , computed via the
Savage-Dickey density ratio.  "Very strong" corresponds to
 on the Jeffreys scale.
Table  shows the results.
The true Occam factor for a zero-parameter prediction against a
flat  prior is ; the BIC approximation
gives only  for  CMB
data points.  The BIC underestimates the evidence
by a factor of .  Four independent methods (Savage-Dickey,
direct integration, Laplace approximation, Monte Carlo) all
confirm the proper Bayes factor in the range -.

Prior sensitivity
Prior sensitivity of the Bayes factor (Planck + lensing).
Table  demonstrates robustness: even with a
"generous physicist's prior" of  (width ),
the Bayes factor is -still "substantial" on the Jeffreys
scale.  No reasonable prior makes  preferred.

Framework vs CDM

Against the two-extra-parameter CDM:
BAO data alone are inconclusive-the  pull toward
higher  partially compensates the Occam advantage.
But CMB data strongly prefer the framework, and the
combination remains in the framework's favour.
Global tension minimum
We now combine all probes into a single  analysis.
Table  compares the framework and Planck best
fit across five probe classes (26 data points total).
Global  across all probes (26 data points).
The framework wins on three of five probe classes and has a
lower total  by .  The physical mechanism is
clear: the framework's slightly higher  (hence slightly
lower ) shifts  upward by kmsMpc
and  downward by -both in the directions favoured by
external data.

The global optimum

The global optimum across all probes lies at .
The framework prediction () is 47% of the way from Planck
() toward this optimum:

The framework does not reach the global optimum, but it moves
substantially closer than Planck does.  Strikingly, every probe
combination that includes external data (f, ,
) pulls the optimal  toward the framework
prediction.
DESI confrontation and falsification forecast
The  BAO-only tension deserves careful analysis.  Is it
a harbinger of falsification, or a statistical fluctuation?

Monte Carlo survival analysis

Under the null hypothesis (framework correct, ), we run 5000 Monte Carlo realisations of DESI Y1 BAO
data.  The probability of observing a best fit as high as
 is:

The current measurement is a  fluctuation.
Framework survival probability as DESI data accumulate,
assuming the framework is correct ().
Table  shows the framework's survival probability
as data accumulate.  If the framework is correct, the BAO best fit
converges toward  and the current  tension
evaporates.

Falsification scenario

If the BAO best fit remains at  as errors
shrink, the framework faces progressively severe tension:
At , the framework would be definitively excluded.
DESI Y5 (2028) is therefore the decisive test.

The Bayes factor trajectory

Even at  BAO tension, the Occam advantage from having
zero free parameters dominates:

If DESI Y5 confirms :

If instead  drifts to :

Master concordance table
Table  presents all 28 observables against the
framework prediction.
Master concordance: 28 observables from zero dark energy
parameters.  Pulls are in units of the measurement uncertainty.
Pull distribution

Of the 28 observables: 20 lie within  (71%, expected 68%),
23 within  (82%, expected 95%), and 1 beyond 
(4%, only SH0ES -a tension shared with all Planck-calibrated
models).  The pull distribution is consistent with a correct model.

Comparison statistics

extra parameter buys only ,
penalised to  in the framework's favour.
Pre-registered predictions
We register the following predictions, dated to the submission
of this paper:
DESI Y3 (2027).
   (68% CL).  The current
  best fit of  should drop by .  If DESI Y3
  finds , the framework survival probability
  drops below .

DESI Y5 (2028).
  .  If  deviates from  by
  more than , the framework is falsified.

Euclid (2030).
  .  Euclid can distinguish the framework
  from Planck  at  and from  (TT
  only) at .

Neutrino mass.
  Normal hierarchy, eV.  JUNO
  (2027) and KATRIN endpoint measurements will test this.

Graviton mode count.
   (full covariant), not  (TT only).
  CMB-S4 + Euclid can resolve  from  at .

.
  kmsMpc.  The Einstein
  Telescope (2035) with kmsMpc
  can distinguish the framework from Planck at .
Discussion
What the framework achieves

From a single lattice-measured quantity () and exact field
theory inputs (, field content), the framework
produces  and derives all standard cosmological parameters
with zero free dark energy parameters.  The concordance is
remarkable:

 against the CMB,
 against RSD (better than Planck),
Total  lower than Planck by 5.4 across 26 probes,
Bayes factor 50-70 over ,
Correct direction on  and  tensions.

What the framework does not achieve
It does not resolve the Hubble tension.  The prediction
  () is firmly on the Planck side.  If SH0ES is
  correct, the framework is wrong.
It does not resolve the  tension fully.  The shift
  of - toward lensing surveys is helpful but
  insufficient.
The BAO-only best fit () is 
  from the prediction.  This is manageable (3.3% probability
  under the null) but warrants monitoring.
The DESI  signal, if confirmed at 
  by DESI Y5, would falsify the framework entirely.

Three honest vulnerabilities
 universality.
  The area-law coefficient has been measured only in the
  Srednicki discretization class.  Other lattice schemes
  show 73% spread at accessible sizes.  The prediction relies
  on Srednicki convergence being physical, not accidental.
Fermion  unverifiable.
  The heat kernel ratio  cannot
  be confirmed on the lattice due to the Fermi surface doubling
  problem.  Bosonic ratios (vector/scalar, graviton/scalar) are
  verified to .
 assumed.
  The vanishing of the bare cosmological constant is argued
  independently  but remains the
  single unproven assumption.
Conclusion
We have tested the entanglement entropy prediction 
against 28 cosmological observables spanning the CMB, BAO, structure
growth, lensing, supernovae, and direct Hubble measurements.  The
results are:
The prediction agrees with Planck at , with a
  joint CMB .
The prediction fits structure growth ()
  better than the Planck best fit ().
Across all 26 data points from five probe classes, the
  framework achieves lower total  (172.65 vs. 178.02)
  despite having one fewer free parameter.
Bayesian model comparison yields Bayes factors of -
  in the framework's favour ("very strong" on the Jeffreys
  scale).
The equation of state  is a theorem; current DESI
  tension fails all four criteria for genuine new physics.
Derived predictions-, eV (NH), -are all
  consistent with current data.

The framework is not yet confirmed.  The  BAO tension
and  DESI  tension are real, and DESI Y5 (2028)
will either vindicate or falsify the prediction.  What we have shown
is that a zero-parameter theory, built entirely from quantum field
theory and lattice entanglement entropy, currently fits the
cosmological data as well as the best one-parameter model
available-and is preferred by Bayesian model selection at every
dataset combination tested.
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