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
We propose a novel cosmological model wherein the early 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. Building on the standard \(\Lambda\)CDM framework, we hypothesize that energy lost due to redshift in an expanding universe is redistributed to enhance radiation pressure, driving exponential inflation and potentially reconciling cosmic expansion with thermodynamic laws. We incorporate Minkowski spacetime locally within causally disconnected regions, separated by 4D Schwarzschild horizons, to preserve \(c\)’s invariance while addressing the horizon and flatness problems. We outline eight observational tests to confirm or falsify this model, noting that current state-of-the-art observations, such as the cosmic microwave background (CMB) anisotropies, align with \(\Lambda\)CDM but do not rule out this theory due to limitations in precision and scale.
The standard \(\Lambda\)CDM cosmological model, supported by observations of the cosmic microwave background (CMB), supernovae, and large-scale structure, posits a Big Bang followed by inflation driven by a scalar inflaton field, succeeded by radiation- and matter-dominated eras [1]. However, we propose an alternative: inflation is driven by radiation pressure, with \(c\) remaining constant within local regions defined by 4D Schwarzschild-like causal horizons, emerging at \(t \approx 10^{22} \, t_P\) (Planck time, \(5.39 \times 10^{-44} \, \text{s}\)) [2]. We further hypothesize that energy lost to redshift in an expanding universe is redistributed to enhance radiation pressure, potentially driving inflation and aligning cosmic expansion with thermodynamic principles. This model preserves \(c\)’s invariance within local Minkowski spacetime patches, addressing the horizon and flatness problems through causal disconnection.
Our model begins at \(t = 0\), with an initial linear expansion \(a(t) \propto t\) at \(c\), damped by gravity, followed by particle formation at \(t \approx 10^{20} \, t_P\), where photons emerge, activating radiation pressure \(P = \frac{1}{3} \rho c^2\) [2]. At \(t \approx 10^{22} \, t_P\), we propose a transition where \(c\) becomes locally constant within regions defined by a 4D Schwarzschild-like causal horizon, inspired by the metric \(r_s = \frac{2GM}{c^2}\), extended to four-dimensional spacetime. These regions, approximating Minkowski spacetime locally, become causally disconnected as spacetime stretches beyond the horizon, allowing independent inflationary expansion driven by radiation pressure.
We hypothesize that redshift energy—lost as photon wavelengths stretch in an expanding universe—is redistributed to increase radiation pressure, potentially driving exponential inflation (\(a(t) \propto e^{Ht}\)) without an inflaton field. This aligns with thermodynamic considerations, where horizon entropy (e.g., Padmanabhan’s law of emergence) might absorb and utilize redshift energy to perform work on the universe’s expansion [3]. The Friedmann equations govern this dynamics: \[ H^2 = \left( \frac{\dot{a}}{a} \right)^2 = \frac{8\pi G \rho}{3} - \frac{k c^2}{a^2}, \] \[ \frac{\ddot{a}}{a} = -\frac{4\pi G}{3} \left( \rho + \frac{3P}{c^2} \right), \] where \(P = \frac{1}{3} \rho c^2\) for radiation, but we propose that redshift energy modifies \(\rho\) or \(P\) to achieve \(\ddot{a} > 0\).
We propose eight tests to confirm or falsify this model, acknowledging current observational limitations:
CMB Anisotropies: Measure the power spectrum and B-mode polarization of the CMB. Deviations from \(\Lambda\)CDM (e.g., enhanced small-scale fluctuations or unique B-mode signatures from redshift energy) would confirm the model, while alignment with \(\Lambda\)CDM would remain inconclusive without higher precision.
Redshift-Dependent Energy Density of Radiation: Observe the scaling of radiation energy density (\(\rho_{\text{radiation}}\)) with redshift. An anomalous increase or stabilization at high \(z\) due to redshift energy would confirm the theory, but current \(\rho_{\text{radiation}} \propto a^{-4}\) scaling is inconclusive due to precision limits.
Gravitational Wave Background (GWB): Detect a stochastic GWB at frequencies corresponding to inflationary scales, potentially tied to 4D Schwarzschild horizons. A unique signature would confirm the model, but current upper limits and tentative PTA signals are inconclusive due to sensitivity constraints.
Hubble Tension and Late-Time Acceleration: Measure \(H_0\) and the equation of state \(w\) to test for radiation pressure contributions from redshift energy. A reduction in the Hubble tension or modified \(w\) would confirm the theory, but current data aligning with dark energy (\(w \approx -1\)) are inconclusive due to precision limits.
Horizon-Scale Structure and Galaxy Distribution: Map large-scale structure for horizon-scale anomalies (e.g., enhanced clustering at 4D Schwarzschild scales). Deviations would confirm the model, but current \(\Lambda\)CDM-consistent distributions are inconclusive due to scale and resolution limitations.
Spectral Line Shifts Beyond Redshift: Analyze quasar and galaxy spectra for anomalous shifts or broadenings from redshift energy. Such signatures would confirm the theory, but current standard redshift patterns are inconclusive due to precision limits.
Thermodynamic Signatures at Cosmic Horizons: Probe horizon entropy or energy flux for redshift energy signatures. Anomalies would confirm the model, but current data aligning with \(\Lambda\)CDM are inconclusive due to precision and scale constraints.
Primordial Nucleosynthesis and Light Element Abundances: Measure light element abundances for deviations due to altered radiation pressure. Deviations would confirm the theory, but current \(\Lambda\)CDM-consistent abundances are inconclusive due to precision limits.
As of February 21, 2025, state-of-the-art observations, including Planck’s CMB data, align with \(\Lambda\)CDM predictions, showing no significant deviations from standard inflation, radiation scaling, GWB limits, Hubble tension, large-scale structure, spectral lines, horizon thermodynamics, or BBN abundances [1, 4]. However, these observations do not rule out our model due to limitations in precision, scale, and frequency range. For instance: - The CMB power spectrum and B-mode polarization match \(\Lambda\)CDM, but future experiments (e.g., CMB-S4) could detect subtle deviations if they exist [4]. - Radiation density scaling and spectral line shifts follow \(\Lambda\)CDM, but high-redshift precision is limited by current telescopes [3]. - GWB and horizon thermodynamics remain untested at the necessary scales, with future detectors (e.g., LISA, SKA) needed for resolution [2].
Thus, while current data confirm \(\Lambda\)CDM, they are inconclusive for our model, leaving room for future tests to confirm or falsify it.
This model challenges \(\Lambda\)CDM by proposing radiation-pressure-driven inflation and redshift energy redistribution, preserving \(c\)’s constancy within local Minkowski patches defined by 4D Schwarzschild horizons. It addresses the horizon and flatness problems and aligns with thermodynamic principles, but its speculative nature requires rigorous observational validation. Future experiments (e.g., CMB-S4, LISA, DESI, Euclid) could probe the proposed signatures, potentially revolutionizing our understanding of inflation and expansion.
We present a novel cosmological model where radiation pressure, enhanced by redshift energy, drives inflation within causally disconnected regions defined by 4D Schwarzschild-like horizons. Current observations align with \(\Lambda\)CDM but do not rule out this theory due to precision and scale limitations. The proposed tests offer a pathway to confirm or falsify the model, advancing our understanding of the early universe and thermodynamic consistency in cosmology.
[1] Planck Collaboration, "Planck 2018 Results. VI. Cosmological Parameters," Astron. Astrophys., 641, A6 (2020).
[2] Post 1892695456884412642, Thread 1, X, February 20, 2025.
[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).