https://ninkilim.com/articles/cosmology_radiation_driven_inflation/en.html
I propose a cosmological model in which the inflationary epoch is driven by radiation pressure rather than a scalar inflaton field. Beginning with linear expansion at the Planck epoch, the universe transitions to exponential inflation at \(t \approx 10^{22} \, t_P\) as spacetime stretches beyond causal horizons, redefining the speed of light (\(c\)) as a locally invariant parameter. Energy lost to photon redshift is hypothesized to be redistributed into radiation pressure, thereby fueling inflation and ensuring energy conservation in an expanding universe. Local Minkowski patches preserve the invariance of \(c\), addressing the horizon and flatness problems while reconciling special relativity with cosmological superluminal recession. Eight observational tests are outlined, with expected signatures in the CMB, gravitational waves, and large-scale structure. Current data align with \(\Lambda\)CDM but do not exclude this model, leaving a path open for validation with future high-precision experiments.
The standard \(\Lambda\)CDM cosmology describes a hot Big Bang at \(t = 0\), followed by a brief inflationary period from \(t \approx 10^{-36} \, \text{s}\) to \(10^{-34} \, \text{s}\). This epoch is driven by a scalar “inflaton” field, whose potential produces exponential expansion (\(a(t) \propto e^{Ht}\)) [1, 2]. This resolves the horizon and flatness problems and leaves imprints in the cosmic microwave background (CMB). Yet, despite its success, \(\Lambda\)CDM depends on speculative ingredients: an undetected inflaton particle, fine-tuned potential landscapes, and a tolerance for the apparent non-conservation of energy due to photon redshift.
I introduce a radiation-driven alternative. My model begins with linear expansion, transitions naturally into exponential inflation once photons dominate and horizons disconnect, and continues into the modern accelerating era. Three central principles distinguish this framework:
At the Planck epoch (\(t = 1 \, t_P = 5.39 \times 10^{-44} \, \text{s}\)), the universe expands linearly with scale factor \(a(t) \propto t\). Its proper size is \(R(t) = ct\), and the energy density is Planck-scale:
\[ \rho \approx 5 \times 10^{96} \, \text{kg} \, \text{m}^{-3}. \]
The Friedmann equation governs expansion:
\[ H^2 = \left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G \rho}{3} - \frac{k c^2}{a^2}, \]
with \(H = 1/t\) and negligible curvature. At this stage, photons are absent, so radiation pressure does not yet contribute.
By \(t \sim 10^{20} \, t_P \, (\sim 10^{-36} \, \text{s})\), particle formation produces photons in a quark-gluon plasma at \(T \approx 10^{28} \, \text{K}\). Radiation pressure emerges:
\[ P = \frac{1}{3}\rho c^2, \qquad \rho = \frac{a T^4}{c^2}, \]
with \(a = 7.566 \times 10^{-16} \, \text{J} \, \text{m}^{-3} \, \text{K}^{-4}\). This yields \(P \sim 10^{92} \, \text{Pa}\). While enormous, gravity still dominates, and expansion remains decelerating.
At \(t \approx 10^{22} \, t_P \, (\sim 10^{-34} \, \text{s})\), the universe’s radius exceeds its Schwarzschild-like horizon:
\[ r_s = \frac{2GM}{c^2}, \quad M = \rho \cdot \frac{4}{3} \pi R^3, \quad R = ct. \]
When the particle horizon \(d_p \approx ct\) surpasses \(r_s\), regions decouple causally.
Inside each horizon patch, observers measure \(c = 3 \times 10^8 \, \text{m/s}\), consistent with Einstein’s train and rocket thought experiments. Globally, however, recession velocities exceed \(c\), as in standard cosmology. I parameterize this as:
\[ c_{\text{eff}} = c_0 \left(\frac{a_0}{a}\right)^\beta, \qquad \beta > 0, \]
not implying a literal variation of \(c\), but rather encoding its locality. Thus, \(c\) remains invariant for any observer within their causal horizon, while globally superluminal expansion reflects disconnection, not a violation of relativity.
In \(\Lambda\)CDM, photon energy diminishes as wavelengths stretch:
\[ E = \frac{hc}{\lambda}, \quad \lambda \propto a, \quad E \propto a^{-1}. \]
The apparent loss of energy is attributed to expansion, with no global conservation law.
My model resolves this paradox: energy lost to redshift is absorbed at causal horizons and redistributed into radiation pressure, effectively doing work on the metric:
\[ \Delta E_{\text{redshift}} \;\rightarrow\; \Delta P_{\text{radiation}} \cdot V. \]
Einstein’s equivalence principle identifies gravity with acceleration. This provides a concrete way to see redshift not as destruction of energy, but as its conversion into kinetic work.
Thought experiment: Consider a blue laser fired upward from the surface of a planet. The photons climb out of the gravitational potential and arrive at a distant observer redshifted. To the observer, each photon appears to carry less energy. Yet the laser at the source experienced the full mass–energy of the emitted photons: it transferred momentum consistent with their unredshifted energy and radiation pressure.
Where has the “missing” energy gone? It has been invested into the gravitational field, performing the work necessary to lift the photons out of the potential well.
By analogy, in cosmology, photons emitted at early times lose energy through cosmological redshift. Locally, the emitting region experiences their full radiation pressure. But globally, the apparent deficit is not lost; it has been converted into work on the metric - specifically, into accelerated expansion.
\[ \Delta E_{\text{photon}} \;=\; W_{\text{expansion}} . \]
Building on this analogy, I propose that causal horizons act as mediators of redshift energy:
\[ P = \frac{1}{3}\rho c_{\text{eff}}^2 + \Delta P_{\text{redshift}}, \]
modifying the acceleration equation:
\[ \frac{\ddot{a}}{a} = -\frac{4\pi G}{3}\left(\rho + \frac{3P}{c^2}\right). \]
With \(\Delta P_{\text{redshift}} > 0\), the expansion accelerates without invoking an inflaton.
To formalize this mechanism requires:
At \(t \approx 2.6 \times 10^{71} \, t_P\) (13.8 Gyr), the CMB temperature is \(T = 2.7 \, \text{K}\), and radiation pressure has diminished to \(P \sim 10^{-31} \, \text{Pa}\). Yet the same horizon-mediated mechanism persists: redshift energy continues to fuel cosmic acceleration, contributing to the late-time dynamics typically attributed to dark energy (\(\Omega_\Lambda \approx 0.7\)).
I propose eight observational tests, each with distinct signatures that could differentiate this model from \(\Lambda\)CDM.
| Feature | \(\Lambda\)CDM | Radiation-Driven Model |
|---|---|---|
| Inflation driver | Scalar inflaton field | Radiation pressure + redshift energy |
| Energy conservation | Not globally defined | Thermodynamically enforced via horizons |
| Speed of light | Globally invariant | Locally invariant within horizons |
| Horizon/flatness problems | Solved by inflaton | Solved by radiation + horizons |
| Dark energy | Cosmological constant (\(\Lambda\)) | Continuation of redshift-radiation mechanism |
| CMB predictions | Standard spectrum | Small-scale enhancements, possible B-mode differences |
| Hubble tension | Unresolved | Natural intermediate \(H_0\) |
| Observational status | Supported but incomplete | Consistent with data, not yet falsified |
This framework reframes inflation as a thermodynamic process intrinsic to radiation, requiring no speculative inflaton. It provides a mechanism for energy conservation in expanding spacetime and reconciles relativity’s local postulates with cosmological horizons.
Challenges remain. The exact dynamics of redshift energy redistribution require further mathematical development, and numerical simulations of the modified Friedmann equations are essential. Observational discrimination will rely on future missions (CMB-S4, Euclid, LISA, SKA).
I present a cosmology in which radiation pressure, modulated by causal horizons and redshift energy, drives both inflation and present-day expansion. This model eliminates the need for a hypothetical inflaton, restores thermodynamic consistency, and reconciles Einstein’s local invariance of \(c\) with cosmological superluminality. Current data are compatible with \(\Lambda\)CDM, but the proposed observational tests provide a path to validation or falsification.
[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).