فريد 🇵🇸🍉🔻: # A Novel Cosmological Model: Radiation-Driven Inflation with a...
We propose a cosmological model wherein the universe’s expansion, including the inflationary epoch, is driven by radiation pressure rather than a scalar inflaton field, with the speed of light (\( c \)) transitioning from a global to a local constant as spacetime stretches beyond a 4D Schwarzschild-like causal horizon. Starting at \( t = 0 \) in Planck time units (\( t_P = 5.39 \times 10^{-44} \, \text{s} \)), we describe an initial linear expansion at \( c \), damped by gravity, followed by the onset of radiation pressure at \( t \approx 10^{20} \, t_P \). Exponential inflation emerges at \( t \approx 10^{22} \, t_P \) when causal disconnection occurs, redefining \( c \) as a local parameter tied to spacetime stretching. We explore the model’s implications for early universe dynamics and its consistency with modern observations, such as the cosmic microwave background (CMB) and Hubble expansion.
The standard \(\Lambda\)CDM model posits that the universe began with a Big Bang at \( t = 0 \), followed by a brief inflationary phase driven by an inflaton field from \( t \approx 10^{-36} \, \text{s} \) to \( 10^{-34} \, \text{s} \), succeeded by radiation- and matter-dominated eras [1]. Inflation resolves the horizon and flatness problems via exponential expansion (\( a(t) \propto e^{Ht} \)) [2]. Here, we propose an alternative: radiation pressure, arising from photon interactions post-particle formation, drives both early inflation and ongoing expansion, modulated by a speed of light (\( c \)) that becomes “local” when the universe exceeds a 4D causal horizon inspired by the Schwarzschild metric. This model reinterprets \( c \)’s role in an expanding spacetime, challenging its universality.
At \( t = 0 \), the universe is a singularity, transitioning to a finite size by \( t = 1 \, t_P \). We assume an initial linear expansion, \( a(t) \propto t \), where the proper size \( R(t) = c t \), with \( c = 3 \times 10^8 \, \text{m/s} \). The energy density is Planck-scale, \( \rho \approx 5 \times 10^{96} \, \text{kg} \, \text{m}^{-3} \), yielding a gravitational term in the Friedmann equation: \[ H^2 = \left( \frac{\dot{a}}{a} \right)^2 = \frac{8\pi G \rho}{3} - \frac{k c^2}{a^2} \] For \( a \propto t \), \( H = 1/t \), and curvature (\( k \)) is negligible. No radiation pressure exists, as photons are absent, and expansion is damped by gravity.
By \( t = 10^{20} \, t_P \) (\( 10^{-36} \, \text{s} \)), particle formation occurs, and photons emerge in a quark-gluon plasma at \( T \approx 10^{28} \, \text{K} \). Radiation pressure activates: \[ P = \frac{1}{3} \rho c^2, \quad \rho = \frac{a T^4}{c^2} \] where \( a = 7.566 \times 10^{-16} \, \text{J} \, \text{m}^{-3} \, \text{K}^{-4} \), yielding \( P \approx 10^{92} \, \text{Pa} \). Gravity and inertia (relativistic mass-energy) initially limit its effect.
At \( t = 10^{22} \, t_P \) (\( 10^{-34} \, \text{s} \)), we propose a transition where \( c \) becomes local, tied to a 4D Schwarzschild horizon—the spacetime distance an event propagates at \( c \). For a region of mass \( M = \rho \cdot \frac{4}{3} \pi R^3 \) (\( R = c t \approx 10^{-26} \, \text{m} \)): \[ r_s = \frac{2 G M}{c^2} \approx 1.31 \times 10^{-7} \, \text{m} \] When \( R \) exceeds a causal limit (e.g., particle horizon \( d_p \approx c t \) stretched by expansion), regions decouple. We define \( c \) as local when recession velocity exceeds \( c \), akin to Hubble flow, but posit that \( c_{\text{eff}} \) adjusts with spacetime stretching: \[ c_{\text{eff}} = c_0 \left( \frac{a_0}{a} \right)^\beta \] where \( \beta > 0 \) reflects dilution.
With gravity’s influence lagging (propagating at \( c \) across stretched spacetime), radiation pressure dominates. The acceleration equation: \[ \frac{\ddot{a}}{a} = -\frac{4\pi G}{3} \left( \rho + \frac{3P}{c^2} \right) \] For standard radiation, \( P = \frac{1}{3} \rho c^2 \), yielding deceleration. If \( c_{\text{eff}} \) decreases globally, \( P = \frac{1}{3} \rho c_{\text{eff}}^2 \) may shift dynamics, potentially achieving \( \ddot{a} > 0 \) and \( a \propto e^{Ht} \) if \( H \) stabilizes via local effects.
At \( t = 2.6 \times 10^{71} \, t_P \) (13.8 Gyr), \( T = 2.7 \, \text{K} \), and \( P \approx 10^{-31} \, \text{Pa} \). Local \( c \) persists, with radiation pressure as a relic driver alongside dark energy (\( \Omega_\Lambda \approx 0.7 \)).
This model predicts: 1. Inflation without Inflaton: Radiation pressure, amplified by local \( c \), drives exponential growth from \( t = 10^{22} \, t_P \), smoothing the universe. 2. Local \( c \): \( c \) varies with spacetime stretching, consistent with observed superluminal recession beyond \( d_H = c/H_0 \approx 1.32 \times 10^{26} \, \text{m} \).
Challenges include: - Equation of State: Radiation’s \( P = \frac{1}{3} \rho c^2 \) resists inflation unless \( c_{\text{eff}} \) radically alters dynamics. - Observational Fit: CMB anisotropy and structure formation require tuning \( \beta \) and transition timing. - Relativity: Varying \( c \) contradicts special relativity’s invariance, necessitating a modified framework.
We present a speculative cosmology where radiation pressure and a local \( c \), tied to a 4D causal horizon, replace traditional inflation. While mathematically challenging, it offers a novel perspective on expansion’s drivers. Future work could formalize \( c_{\text{eff}} \)’s evolution and test against CMB data.
[1] Planck Collaboration, "Planck 2018 Results," Astron. Astrophys., 641, A6 (2020).
[2] Guth, A. H., "Inflationary Universe," Phys. Rev. D, 23, 347 (1981).
Received: February 20, 2025