ninkilim.com/29
The world was more outraged about the fake story about 40 beheaded Israeli babies than about 700 Palestinian babies murdered by Israel. https://x.com/R34lB0rg/status/1893440507327431044/photo/1
Today is my birthday. I want to celebrate by publishing my cosmology paper on arXiv. I need an Endorsement for http://astro-ph.CO. #Followerpower #Science
https://farid.ps/articles/cosmology_radiation_driven_inflation/en https://x.com/R34lB0rg/status/1893368583767441652/photo/1
A police officer stops Heisenberg and asks, 'Do you know where you are and how fast you’ve been going?' Heisenberg replies, 'I can either tell you where I am or how fast I’ve been going, but not both at the same time!
A cop stops a physicist speeding. He asks, "Do you know how fast you’ve been going?" The physicist answers, "Well, officer, our galaxy is moving with a velocity of about 600 km/s relative to the Local Group, our solar system is moving with a velocity of roughly 828 km/s around the galaxy, the Earth is moving with a velocity of 30 km/s around the Sun, and we are moving around the Earth with a velocity of about 465 m/s.
The post proposes eight specific tests to confirm or falsify the model, each with expected observational signatures if correct. These tests address current limitations in precision and scale, as of February 21, 2025:
CMB Anisotropies:
Redshift-Dependent Radiation Density:
Gravitational Wave Background (GWB):
Hubble Tension and Late-Time Acceleration:
Horizon-Scale Structure and Galaxy Distribution:
Spectral Line Shifts Beyond Redshift:
Thermodynamic Signatures at Cosmic Horizons:
Primordial Nucleosynthesis (BBN) and Light Element Abundances:
Theoretical Challenges:
Observational Challenges:
Comparison to Lambda-CDM:
The model’s theoretical foundation (radiation pressure, local c, redshift energy) is innovative but speculative, requiring significant mathematical and physical development to address:
It builds on established concepts (Schwarzschild horizons, Friedmann equations, CMB observations) but extends them in untested ways, making it a high-risk, high-reward hypothesis.
The target post presents a bold, speculative cosmological model challenging Lambda-CDM by proposing radiation-pressure-driven inflation with local causal horizons and redshift energy redistribution. It offers a novel perspective on inflation’s origins, preserves c’s invariance locally, and outlines eight testable predictions. However, current observations align with Lambda-CDM, and the model’s feasibility hinges on future experiments with enhanced precision and scale.
As of February 21, 2025, the model is intriguing but unproven, requiring rigorous theoretical refinement and observational validation. Its development on X, aided by AI, exemplifies the evolving intersection of social media, technology, and science, offering a fascinating case study for both cosmology and digital scholarship.
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. Expected observational signatures are proposed to guide future research.
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 increase 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. For each test, we include expected observational signatures if the model is correct.
CMB Anisotropies
Redshift-Dependent Energy Density of Radiation
Gravitational Wave Background (GWB)
Hubble Tension and Late-Time Acceleration
Horizon-Scale Structure and Galaxy Distribution
Spectral Line Shifts Beyond Redshift
Thermodynamic Signatures at Cosmic Horizons
Primordial Nucleosynthesis and Light Element Abundances
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 and expected observations offer a pathway to confirm or falsify the model, advancing our understanding of the early universe and thermodynamic consistency in cosmology.
We gratefully acknowledge the contributions of Grok 3, an artificial intelligence developed by xAI, as a co-author in drafting, structuring, and refining this paper. Grok 3 mini assisted in elaborating the theoretical framework, proposing observational tests, checking them against the current state of the art, and assembling references, enabling the rapid transformation of conceptual ideas into a formal scientific manuscript. This collaboration exemplifies the potential of AI-human partnerships in advancing cosmological research, aligning with xAI’s mission to foster a deeper understanding of the universe.
[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).
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).
You may want to read this @lirarandall @ProfBrianCox https://x.com/R34lB0rg/status/1892695456884412642
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
Picture this: 13.8 billion years ago, the universe explodes into existence from a point smaller than an atom. Time starts ticking in tiny increments—Planck time, a mind-boggling \( 5.39 \times 10^{-44} \) seconds—and space begins to stretch. Scientists call this the Big Bang, but what if the story we’ve been told is missing a cosmic twist? What if the speed of light, that ultimate universal constant we call \( c \), isn’t quite as constant as it seems—and what if radiation, the glow of the cosmos, has been pushing the universe apart all along?
In the first fleeting moments, at \( t = 1 \) Planck time, the universe is a speck, tinier than anything we can imagine, buzzing with energy denser than a trillion suns packed into a pinhead. There’s no light as we know it—photons, those massless messengers, haven’t formed yet, so there’s no radiation pressure to speak of. Instead, the universe expands at the speed of light, a straight-line sprint where its size grows as \( c \) times time. Imagine spacetime unfurling like a scroll, but gravity—this monstrous pull from all that energy—tries to reel it back in. It’s a tug-of-war, and for now, expansion just barely wins.
Fast forward to \( t = 10^{20} \) Planck times (that’s still just \( 10^{-36} \) seconds). The universe has cooled enough for particles to pop into existence—quarks, electrons, and yes, photons. Suddenly, there’s light, and it’s bouncing off everything in a hot, chaotic soup. This is where radiation pressure kicks in, a force born from light pushing against matter. At first, it’s feeble—gravity’s grip is still titan-strong, and the inertia of all that energy resists the shove. But the universe keeps growing, and something wild is brewing.
Here’s the kicker: the speed of light isn’t a global rulebook—it’s local, tied to the fabric of spacetime around it. Think of it like this: if the Sun vanished in a puff of matter-antimatter annihilation, Earth would keep orbiting for 8 minutes, oblivious, because gravity’s signal travels at \( c \). In the early universe, everything’s so close that light and gravity connect it all. But by \( t = 10^{22} \) Planck times (\( 10^{-34} \) seconds), the universe is stretching fast—faster than light can keep up across its full span.
This is where the 4D Schwarzschild radius comes in—not just a black hole’s edge, but a spacetime boundary. It’s the limit of how far an event, like a photon’s flash or gravity’s tug, can reach at \( c \) before expansion tears it apart. When the universe’s size outstrips this 4D horizon—when particles on one side can’t “talk” to the other—\( c \) stops being a cosmic constant and becomes a local one. Each patch of spacetime gets its own speed limit, stretched by the expanding fabric between them.
With gravity’s reach lagging, radiation pressure—powered by those relentless photons—takes over. In standard cosmology, light’s push weakens as the universe grows, but here, with \( c \) turning local, it’s as if the pressure gets a boost. The stretching spacetime amplifies light’s shove, overcoming inertia and gravity’s fading grip. The result? Exponential inflation—a runaway expansion where the universe doubles in size every fraction of a second. From a speck to a grapefruit in a cosmic blink, all driven by the glow of radiation, not some mysterious “inflaton” field.
Zoom to now, February 20, 2025, or \( 2.6 \times 10^{71} \) Planck times since the start. The universe is 13.8 billion years old, and its edges are racing away faster than light, beyond our Hubble horizon. That faint microwave glow we detect—the cosmic microwave background, at a chilly 2.7 Kelvin—still exerts a whisper of radiation pressure. It’s tiny, but in this model, it’s a legacy of that early push, stretched across a cosmos where \( c \) is local to each bubble of spacetime. We see galaxies receding, and they see us the same way, each with our own \( c \), stitched into a vast, expanding tapestry.
This isn’t the textbook Big Bang. It ditches the inflaton for radiation pressure and reimagines \( c \) as a local player, tied to spacetime’s stretch and a 4D horizon. Does it hold up? The cosmic microwave background’s smoothness and the universe’s flatness suggest something like inflation happened, and this model aims to fit. But it’s a bold leap—varying \( c \) challenges Einstein’s bedrock, and radiation alone struggles to match the math of standard inflation. Still, it’s a thrilling “what if”: a universe where light doesn’t just illuminate—it expands, stretching space itself into the vastness we call home.
Next time you look at the stars, imagine them riding a wave of radiation, propelled by a speed of light that’s more neighborly than universal. The Big Bang might just have a glow all its own.