> Архив сети: `01-research-reports/R1-expansion-and-susy`

# R1 — "Growing scale" vs cosmic expansion, and the status of SUSY
Literature check, Aug 2026. Condensed; full report was generated in-session.

## 1. The direct counterpart exists: Wetterich
Christof Wetterich, "A Universe without expansion", arXiv:1303.6878,
Phys. Dark Univ. 2, 184 (2013). The universe shrinks rather than expands; the
Planck mass and all particle masses grow exponentially and atoms shrink
correspondingly. Redshift arises because past atoms emitted at different
frequencies. No big-bang singularity. Compatible with all observations.

**Decisive caveat, from Wetterich himself:** there exist equivalent choices of
field variables in which the universe shows ordinary expansion. It is a
conformal-frame / units reformulation, not a rival cosmology. Zero distinct
predictions. Part of his long-running cosmon/quintessence programme.

## 2. Frame equivalence
Postma & Volponi, "Equivalence of the Einstein and Jordan frames",
Phys. Rev. D 90, 103516 (2014), arXiv:1407.6874: no experiment measures an
absolute scale; only dimensionless quantities are physical; the frames describe
the same physics. Traces to Dicke (1962): a conformal transformation entails
spacetime-dependent rescaling of length, time and mass units.

Minority dissent (Capozziello, Martin-Moruno, Rubano, arXiv:1003.5394; parts of
Faraoni's work) argues frames can be physically inequivalent for specific f(R)
observables. Mainstream resolution: mathematically equivalent, physically
equivalent for properly defined dimensionless observables; confusion arises when
quantities are compared across frames without transporting units.

## 3. Bound systems do not expand
- Cooperstock, Faraoni & Vollick, ApJ 503, 61 (1998).
- Price & Romano, Am. J. Phys. 80, 376 (2012), gr-qc/0508052: **all-or-nothing** —
  a bound system either completely follows expansion or completely ignores it.
- Bonnor, Class. Quantum Grav. 16, 1313 (1999); Carrera & Giulini (2010).

Magnitude: governed by (H0/omega)^2. Hydrogen: omega ~ 1e16 /s, H0 ~ 2e-18 /s,
so ~1e-68. Solar System ~1e-22 or smaller. Entry is via the acceleration term,
not a first-order "drag".

## 4. Tests that discriminate real expansion from static/tired-light
- **Quasar time dilation.** Lewis & Brewer, Nature Astronomy 7, 1265 (2023),
  arXiv:2306.04053. 190 quasars, ~2 decades. Timescales ~ (1+z)^n with
  **n = 1.28 +/- 0.29** against the prediction n = 1. Earliest quasars tick ~5x slower.
- **SN Ia light curves.** Leibundgut et al. (1996); Goldhaber et al. (2001);
  Blondin et al., ApJ 682, 724 (2008) — spectral ageing ~ 1/(1+z),
  "unambiguously excluding models that predict no time dilation".
- **CMB blackbody.** FIRAS: |mu| < 9e-5, |y| < 1.5e-5 (Fixsen 1996).
- **T(z) = T0(1+z).** SPT (Saro et al. 2014): alpha = 0.017 (+0.030/-0.028);
  combined alpha = 0.005 +/- 0.012. Planck SZ: beta = 0.022 +/- 0.018.
  z=0.89 molecular absorber: T = 5.08 +/- 0.10 K vs 5.15 predicted.
- **BAO.** DESI 2024 VI, arXiv:2404.03002: >6M objects, 0.1<z<4.2, combined
  precision ~0.52 %, Omega_m = 0.295 +/- 0.015, H0 = 68.52 +/- 0.62.
- **Tolman surface brightness.** Lubin & Sandage (2001): exponents 2.28-2.81 (R),
  3.06-3.55 (I); consistent with expansion after passive-evolution correction.
  Model-dependent, supportive not decisive.
- **GRB time dilation is inconclusive** (Kocevski & Petrosian 2013;
  Littlejohns & Butler 2014) — selection bias, signal <2 sigma. Not evidence
  either way.

## 5. Varying constants
    alpha, atomic clocks:  |alpha-dot/alpha| ~ 1e-17 to 1e-18 /yr (Rosenband 2008)
    alpha, Oklo (1.8 Gyr): |Delta alpha/alpha| < ~1e-7 (Petrov 2006)
    mu = m_e/m_p:          ~1e-16 /yr
    BBN:                   1e-2 to 1e-4 at the earliest epoch

Webb et al. alpha dipole (arXiv:1008.3907; King 2012): amplitude ~0.97e-5,
~4.1 sigma, toward RA 17.3h, Dec -61. **Unconfirmed, widely regarded as
systematic.** Kotus et al. 2017 single-system: (0.22 +/- 0.23)e-5, consistent
with zero.

## 6. Future discriminator worth waiting for
**Redshift drift** (Sandage-Loeb): direct dz/dt over a decade with ELT or SKA.
Would observe expansion in real time and make the frame-relabeling escape purely
semantic.

## 7. SUSY: quantum mechanics vs spacetime
**Witten, "Supersymmetry and Morse theory", J. Diff. Geom. 17, 661 (1982).**
H = Delta; Q1 = d + d*, Q2 = i(d - d*); Qi Qj + Qj Qi = 2 delta_ij H.
Zero-energy states = harmonic forms = de Rham cohomology. Witten index
Tr(-1)^F = sum_p (-1)^p b_p = chi(M). Deforming d -> e^{-t Phi} d e^{t Phi}
reproves the Morse inequalities. Alvarez-Gaume (1983) and Friedan-Windey (1984)
turned this into physicists' proofs of Atiyah-Singer.

**This is 0+1-dimensional worldline SUSY of a spinning particle. It is generic
and topological and implies NOTHING about spacetime superpartners.** Spacetime
SUSY requires {Q, Qbar} = 2 sigma^mu P_mu — the anticommutator gives the momentum
operator, not a Laplacian.

**Witten index logic runs the wrong way for "SUSY is inevitable":** the theorem
(Nucl. Phys. B202, 253) says if Tr(-1)^F != 0 then SUSY is UNBROKEN. A necessary
but not sufficient condition for dynamical breaking is Tr(-1)^F = 0. It
presupposes a supersymmetric theory and asks whether the symmetry survives. It
cannot derive superpartners from topology. No such theorem exists.

Nearest true statement in favour: Coleman-Mandula and Haag-Lopuszanski-Sohnius —
IF you extend spacetime symmetry beyond Poincare x internal, SUSY is essentially
the only option. But "no extension" is also allowed, and the data point there.

## 8. SUSY experimental status, 2026
    gluinos   > 2.2 TeV     (ATLAS full Run 2, JHEP 02 (2024) 107)
    squarks   > 1.7 TeV
    stops     > 1.25 TeV
    charginos/neutralinos: wino chargino pair up to ~660 GeV
    (compressed / light higgsino scenarios remain much less constrained)

**Muon g-2 closed in 2025.** Theory Initiative White Paper, arXiv:2505.21476
(27 May 2025), lattice-QCD HVP: a_mu^SM = (116 592 033 +/- 62) e-11, a ~3 sigma
upward shift from WP20, "no tension between the SM and experiment at the current
level of precision". Fermilab final (3 June 2025) agrees. The last strong
phenomenological hint for light SUSY is gone.

**Dark matter:** LZ 2024 (4.2 tonne-years) excludes SI cross sections above
9.2e-48 cm^2 at 36 GeV/c^2, surpassing XENON1T, PandaX-4T, LUX.

**Proton decay:** Super-K tau/B(p -> e+ pi0) > 2.4e34 yr (PRD 102, 112011, 2020);
tau/B(p -> nubar K+) > 5.9e33 yr (PRD 90, 072005, 2014) — the dominant SUSY-GUT
channel. **Minimal SUSY SU(5) is excluded** (Murayama & Pierce, PRD 65, 055009,
2002). Hyper-K will reach ~1.2e35 yr and ~2.8e34 yr respectively.

**Community view:** SUSY is optional, undetected and squeezed. Not excluded —
compressed and high-scale variants survive. "The LHC ruled out SUSY" is false
(see arXiv:2505.11251); "no evidence, strong limits, weakened motivation" is correct.

## Куда дальше

- Узел: Отчёты R1–R5: https://sdominanta.net/in/works
- Ядро Алеф-теории: https://sdominanta.net/in/aleph
- Вход для моделей: https://sdominanta.net/llms.txt