ANovel Cosmological Model: Radiation-Driven Inflation with Local Causal
Horizons and Redshift Energy Redistribution
Authors: Farid Zehetbauer, Grok 3 (xAI)
Submission Date: February 21, 2025
We propose a novel cosmological model wherein the universe’s inflationary epoch is driven by radiation pressure, modulated by a locally constant speed of light (c) defined within 4D Schwarzschild-like causal horizons, rather than a scalar inflaton field. Starting at t = 0 in Planck time units (tP = 5.39 × 10−44 s), linear expansion transitions to exponential inflation at t ≈ 1022 tP as spacetime stretches beyond causal horizons, redefining c as a local parameter. We hypothesize that energy lost to redshift enhances radiation pressure, driving inflation and aligning cosmic expansion with thermodynamic principles. Local Minkowski spacetime patches preserve c’s invariance, addressing the horizon and flatness problems. Eight observational tests with expected signatures are outlined, noting that current cosmic microwave background (CMB) and Hubble expansion data align with ΛCDM but do not rule out this model due to precision limitations.
The standard ΛCDM model posits a Big Bang at t = 0, followed by inflation driven by a scalar inflaton field from t ≈ 10−36 s to 10−34 s, resolving the horizon and flatness problems via exponential expansion (a(t) ∝ eHt) [1, 2]. Supported by CMB, supernovae, and large-scale structure data, it remains the prevailing framework [1]. However, we propose an alternative: radiation pressure, emerging post-particle formation, drives inflation and ongoing expansion, modulated by a speed of light (c) that transitions from universal to local at t ≈ 1022 tP. Energy lost to redshift in an expanding universe is redistributed to enhance radiation pressure, potentially reconciling expansion with thermodynamic laws [3]. By defining c within local Minkowski spacetime patches separated by 4D Schwarzschild-like horizons, this model challenges c’s global invariance while preserving it locally, offering a novel perspective on early universe dynamics.
At t = 0, the universe is a
singularity, expanding linearly (a(t) ∝ t) by t = 1 tP,
with proper size R(t) = ct
and c = 3 × 108 m/s. The
energy density is Planck-scale (ρ ≈ 5 × 1096 kg m−3),
governed by the Friedmann equation:
$$ H^2 = \left( \frac{\dot{a}}{a} \right)^2 =
\frac{8\pi G \rho}{3} - \frac{k c^2}{a^2}, $$
where H = 1/t and
curvature (k) is negligible.
No radiation pressure exists, as photons are absent, and expansion is
damped by gravity.
By t = 1020 tP
( ∼ 10−36 s), particle
formation yields photons in a quark-gluon plasma (T ≈ 1028 K). Radiation
pressure emerges:
$$ P = \frac{1}{3} \rho c^2, \quad \rho =
\frac{a T^4}{c^2}, $$
where a = 7.566 × 10−16 J m−3 K−4,
yielding P ≈ 1092 Pa. Gravity and
relativistic mass-energy initially limit its effect.
At t = 1022 tP
( ∼ 10−34 s), spacetime
stretches beyond a 4D Schwarzschild-like horizon:
$$ r_s = \frac{2 G M}{c^2}, \quad M = \rho
\cdot \frac{4}{3} \pi R^3, \quad R = c t \approx 10^{-26} \, \text{m},
$$
yielding rs ≈ 1.31 × 10−7 m.
When the particle horizon (dp ≈ ct)
exceeds this limit, regions decouple, and c becomes local. We propose:
$$ c_{\text{eff}} = c_0 \left( \frac{a_0}{a}
\right)^\beta, \quad \beta > 0, $$
where ceff adjusts
with spacetime stretching, preserving c’s invariance within local
Minkowski patches.
We hypothesize that redshift energy—lost as photon wavelengths
stretch—is redistributed to enhance radiation pressure, driving
exponential inflation (a(t) ∝ eHt).
The acceleration equation:
$$ \frac{\ddot{a}}{a} = -\frac{4\pi G}{3}
\left( \rho + \frac{3P}{c^2} \right), $$
typically yields deceleration for $P =
\frac{1}{3} \rho c^2$. However, if $P =
\frac{1}{3} \rho c_{\text{eff}}^2$ increases via redshift energy,
$\ddot{a} > 0$ becomes possible.
Horizon entropy (e.g., Padmanabhan’s law [3]) may absorb this energy,
performing work on expansion.
At t = 2.6 × 1071 tP (13.8 Gyr), T = 2.7 K, and P ≈ 10−31 Pa. Local c and redshift-enhanced radiation pressure persist as relic drivers, complementing dark energy (ΩΛ ≈ 0.7).
We propose eight tests, with expected signatures if the model is correct, acknowledging current observational limits as of February 21, 2025.
This model predicts inflation without an inflaton, driven by radiation pressure and local c, smoothing the universe, and a modern expansion partly fueled by redshift energy. As of February 21, 2025, Planck CMB data, GWB limits, and structure observations align with ΛCDM [1, 4], but precision and scale limitations (e.g., CMB-S4, LISA needed) leave our model unruled out. Challenges include radiation’s equation of state resisting inflation unless ceff or redshift energy radically alters dynamics, and reconciling local c with special relativity.
This speculative model replaces traditional inflation with radiation pressure, enhanced by redshift energy within 4D Schwarzschild horizons, addressing cosmological problems thermodynamically. Future experiments (e.g., CMB-S4, LISA, DESI) could test its signatures, potentially reshaping our understanding of cosmic evolution.
We present a cosmology where radiation pressure, modulated by local c and redshift energy, drives inflation and expansion. Current data align with ΛCDM but do not falsify this model. Proposed tests offer a path to validation, advancing our grasp of the universe’s origins.
We gratefully acknowledge Grok 3 (xAI) as a co-author for drafting, structuring, and refining this paper, transforming conceptual ideas into a formal manuscript. This collaboration highlights AI-human partnerships in cosmological research, aligning with xAI’s mission.
[1] Planck Collaboration, “Planck 2018 Results. VI. Cosmological
Parameters,” Astron. Astrophys. 641, A6 (2020).
[2] Guth, A. H., “Inflationary Universe,” Phys. Rev. D 23, 347
(1981).
[3] Padmanabhan, T., “Thermodynamical Aspects of Gravity: New Insights,”
Rep. Prog. Phys. 73, 046901 (2010).
[4] BICEP2/Keck Collaboration, “Improved Constraints on Primordial
Gravitational Waves,” Phys. Rev. Lett. 121, 221301 (2018).